Selective Response Strategies for GenAI
Authors: Boaz Taitler
Omer Ben-Porat
Venue: ICML 2025 poster (2025)
Keywords: game theory
generative ai
Primary area: theory->game_theory
TL;DR: We show that GenAI and society can both benefit from selective response of GenAI.

Abstract: The rise of Generative AI (GenAI) has significantly impacted human-based forums like Stack Overflow, which are essential for generating high-quality data. This creates a negative feedback loop, hindering the development of GenAI systems, which rely on such data to provide accurate responses. In this paper, we provide a possible remedy: A novel strategy we call selective response. Selective response implies that GenAI could strategically provide inaccurate (or conservative) responses to queries involving emerging topics and novel technologies, thereby driving users to use human-based forums. We show that selective response can potentially have a compounding effect on the data generation process, increasing both GenAI's revenue and user welfare in the long term. From an algorithmic perspective, we propose an approximately optimal approach to maximize GenAI's revenue under social welfare constraints. From a regulatory perspective, we derive sufficient and necessary conditions for selective response to improve welfare.

Selective Response Strategies for GenAI
Boaz Taitler!
Omer Ben-Porat
Abstract
2024). Another scenario involves questions concerning safety and ethics, with potentially life-threatening conse- quences (Shin, 2023; Mello Guha, 2023; Li et al., 2024). However, as we argue in this paper, it can be advantageous for both GenAl operators and users if the system avoids re- sponding indiscriminately to every prompt, especially when addressing emerging technologies and novel content.
The rise of Generative AI (GenAl) has signifi- cantly impacted human-based forums like Stack Overflow, which essential for generating high- quality data. This creates a negative feedback loop, hindering the development of GenAl sys- tems, which rely on such data to provide accurate responses. In this paper, we provide a possible remedy: A novel strategy we call selective re- sponse. Selective response implies that GenAl could strategically provide inaccurate (or conser- vative) responses queries involving emerging topics and novel technologies, thereby driving users to use human-based forums. We show that selective response can potentially have a com- pounding effect on the data generation process, increasing both GenAl's s revenue and user welfare in the long term. From algorithmic perspective, propose approximately optimal approach to maximize GenAl's revenue under social wel- fare constraints. From a regulatory perspective, we derive sufficient and necessary conditions for selective response to improve welfare.
To illustrate, consider GenAl's competitive relationship with a human-driven platform like Stack Overflow. Users may direct their questions to either GenAI or Stack Overflow, seeking solutions to their problems. Posting a code-related question on Stack Overflow generates clarification ques- tions in the comments, solutions offered by experts, feed- back from other users (upvotes) and the original poster (ac- ceptance flag), etc. Such valuable data could significantly enhance GenAL, improving its performance. In contrast, querying GenAI can lead to quicker user satisfaction and increased engagement with GenAI, potentially enhancing its revenue streams. On the downside, the lack of community interaction may result in less comprehensive solutions and reduce the opportunity for generating rich, labeled data that community-drive platforms like Stack Overflow thrive on (del Rio-Chanona et al., 2024; Burtch et al., 2024; Li & Kim, 2024). This absence of dynamic, user- seer-generated content and in-depth discussions can be detrimental to user welfare in the long term, as GenAI's ability to provide high-quality answers depends on such data.
1. Introduction
The maxim, "Better to remain silent and be thought a fool than to speak and to remove all doubt," offers a compelling perspective on the strategic value of withholding informa- tion. While often invoked in interpersonal contexts, it res- onates surprisingly well in the context of Generative AI (GenAl) systems like ChatGPT. These systems are designed to answer user queries immediately, yet one might wonder: Are there situations where the system should remain silent?
Motivated by the issue above, this paper pioneers the frame- work of selective response. Namely, strategically choosing when, if, and how to engage with user queries. particularly those involving emerging topics and novel technologies. We explicitly suggest that when new topic emerges, GenAI could strategically decide to provide lower-quality answers than what it can or even disclaim to have not enough data to respond. We represent such behavior abstractly by modeling GenAl as not responding or "remaining silent". Clearly, se- lective response has a short-term negative impact; however, as we show, an appropriate selective response would lead to an improved data generation process, benefiting the long term for both GenAl's revenue and user social welfare.
One such scenario arises when the system hallucinates. Hal- lucinations, defined as the generation of incorrect or fabri- cated information, are an intrinsic property of generative models that cannot be entirely avoided (Kalai & Vempala,
'Technion Israel Institute of Technology, Israel. Correspon- dence to: Boaz Taitler <boaztaitler @ campus. wwwp://w..tccciocc.......
Our contribution Our contribution is two-fold. The first is conceptual: Our paper is the first to explore selective re- sponse for GenAI. We present a stylized model of an ecosys-
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Selective Response Strategies for GenAI
tem that evolves sequentially, featuring two platforms: A generative Al-based platform called GenAl and a human- driven Q&A platform named Forum. GenAl generates rev- enue by engaging with users and can adopt a selective re- sponse strategy: Determining the proportion of users it re- sponds to in each round. Here, "not responding" represents a broad spectrum of possible behaviors- such as strategi- cally withholding data, providing lower-quality answers than GenAl can produce, or claiming insufficient data, ulti- mately driving users to seek answers on Forum.! We treat these behaviors collectively as "selective response," which abstracts them for conceptual clarity. In contrast, Forum operates as a non-strategic player.
one-round intervention affects the data generation process and its implications welfare. We leverage these insights to demonstrate how regulators that aim to enhance social
welfare can have successful one-round interventions, im- proving user welfare while ensuring a bounded impact on GenAI's revenue.
Altogether, our work challenges the conventional notion that GenAI should always provide answers. Despite its theoret- ical nature, the messages our paper conveys can translate into practical considerations for both GenAl companies and regulators and influence how forum-GenAl collaborations should form.
Users decide between GenAl and Forum based on the utility they derive from each platform. Those who choose Forum contribute to the creation of new data, which GenAI can later incorporate during retraining. Crucially, Al's quality in each round depends on the cumulative data generated since the beginning of the interaction. Our novel model allows us to explore the dynamics of content creation, welfare, and revenue from a game-theoretic lens.
1.1. Related Work
The literature on generative Al is growing at an immense pace. Most research focuses on mitigating hallucinations (Ji et al., 2023), performance (Frieder et al., 2024; Kocoń et al., ju2yyunnou junyou li et al., 2024; Chow et al., 2025), and expand- ing applications (Kasneci et al., 2023; Liu et al., 2024). Our work connects to the emerging body of research on foun- dation models and game theory (Raghavan, 2024; Laufer et al., 2024; Conitzer et al., 2024; Dean et al., 2024). This literature studies competition between generative Al models and human content creators (Yao et al., 2024; Esmaeili et al., 2024; Keinan & Ben-Porat, 2025), the impact of generative AI on content diversity (Raghavan, 2024), and works mo- tivated by social choice and mechanism design (Conitzer et al., 2024; Sun et al., 2024).
2023;
Our second contribution is technical: We begin by demon- strating that selective response marint-dominate the always-responding approach. Specifically, we establish the following result.
Theorem 1.1 (Informal statement of Observation 3.1). Com- pared to the case where GenAl always answers, selective response strategies can improve user welfare, GenAl's rev- enue, and even both.
The most closely related work to ours is that of Taitler & Ben-Porat (2025), which examines whether the existence of generative AI is beneficial to users. In their model, the gen- erative AI platform decides when to train, and they propose regulatory approach to ensure social welfare for users. In contrast, our model introduces a different approach, where the generative AI chooses a portion of queries to answer, demonstrating that responding selectively can benefit both the generative Al platform and its users.
We also quantify the extent to which selective response can improve revenue and welfare w.r.t. the always-responding approach.
Next, we analyze the long-term effects of selective response, revealing that it leads to higher proportions of users choos- ing GenAI and increased data generation (Theorem 4. Building on this result, we devise an approximately optimal solution to GenAl's 's revenue maximization problem.
Our notion of selective response is also inspired by the economic literature on information design (Bergemann & Morris, 2019; Bergemann al., 2015), which explores how the strategic disclosure and withholding of information can influence agents' behavior within system. Another related concept is signaling (Crawford & Sobel, 1982; Milgrom, 1981), ), referring to strategic communication used by agents to potentially improve outcomes (Babichenko et al., 2024; Lu et al., 2023). Similarly, cheap talk (Lo et al., 2023; Cran- dall et al.. 2018) can be used for fostering cooperation. In that sense, selective response can be observed an infor- mation design problem, where GenAl strategically manages information disclosure to influence user behavior and ulti- mately optimize its revenue. Also related is the strand of literature of algorithmic deferring (Hemmer et al., 2023;
Theorem 1.2 (Informal statement of Theorem 4.4). Let be a small positive constant and let A be a finite set of selective responses. There exists an algorithm guaranteeing an ad- ditive OEE²²) approximation of GenAl's optimal revenue, and its runtime is O ( (T"
We extend this result the case where GenAl is constrained to meet an exogenously given social welfare threshold.
Finally, we analyze the impact of selective response on social welfare. We provide valuable insights into how
In real-world scenarios, multiple GenAl systems vie for user traffic, making the analysis of such competition significantly more complex. We address this complexity in Section? 7.
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Selective Response Strategies for GenAI
Mozannar & Sontag, 2020), where the algorithm can defer questions and tasks other experts.
where 7 represents the discount factor applied to the rev- enue round f, reflecting the decreasing value of future revenue. The function r [0, 1] + Rz0 maps the propor- tion of users (x() in round to revenue, and is assumed to be both non-decreasing and I,,-I.ischitz.. For instance, a superlinear r captures the compounding market effects of GenAl, where revenue grows at an accelerating rate as the proportion of users increases (Katz & Shapiro, 1985; Bailey et al., 2022; McIntyre & Srinivasan, 2017). Indeed, this is the case if higher user base attracts disproportionately more offers for collaborations and investment opportunities (rich getting richer).
Finally, since our model includes an ecosystem with two platforms (GenAl and Forum), it relates to a growing body of work on competition between platforms (Rietveld & Schilling, 2021; Karle et al., 2020; Bergemann & Bonatti, 2024: Tullock, 1980; McIntyre & Srinivasan, 2017). Previ- ous works explore the effects of competition in marketplaces on users' social welfare (Jagadeesan et al., 2023; Feldman et al., 2013), as we do in this paper.
2. Model
Data Accumulation. The cumulative data available to GenAl evolves as users interact with Forum. At the start of round i, the cumulative data Dz(x) defined recursively as:
We consider a sequential setting over T discrete rounds, where in each round, users interact either with Generative AI (GenAl) or a complementary human-driven platform, Fo- rum. An instance of our problem is represented by the tuple (a, 7 r, B, w²), and we now elaborate on the components of the model.
Dz(x) D + (1 Pt-1(x)),
with the initial condition D P1(x) = 0. This initial condition represents the emergence of new topic, where GenAl has not acquired any relevant data from previous training sets.
GenAL. GenAl adopts a selective response strategy x (I1, (T)), where I₁ E [0, 1] represents the propor- tion of users who receive answers in round & among those who have already chosen GenAl. For example, 2, = means that GenAl answers all users who selected it in round whereas 2₁ means it answers none. The performance of GenAI depends on the cumulative amount of data it has collected and trained on at the start of each round I, de- noted (x). The quality of GenAl is represented by the accuracy function a(D, (x)), strictly increasing function a: [0, - [0, 1]. satisfying da(D) 0 for all D Rzo. ?
Forum.
Forum provides human-driven platform where users can post and answer questions. The utility users derive from Forum, w", is constant across rounds and satisfies w E 1].
Users decide between GenAl and Forum by com- paring the expected utility they derive from each platform. We model user decisions using a softmax function:
Users.
Buy (x)
We use superscripts and s to denote the utility users receive from GenAl and Forum, respectively. The (expected) utility users derive from GenAl in round t, denoted wf (x), reflects the average quality a (x)( that users obtain from GenAl. is given by
(x)
eau?(x (x) + eB
where 3 > O is a sensitivity parameter that captures users' responsiveness to utility differences.
Recall that xe represents the proportion of users in o (x) who receive an answer from GenAI. The remaining users, who do not receive an answer, can either post their question on Forum or leave them unanswered. We assume the former, meaning that Pt (x) = x, is the proportion of users who receive an answer from GenAI, while the rest contribute to data generation by posting their question on Forum.
w (x) = (xDr xz.
(L)
Crucially, GenAl can intentionally respond less accurately than its maximum capability. In each round i, the proportion of users who choose GenAl is denoted by (x).. This fraction is determined by the selective response strategy x and user decisions, which will be discussed shortly.
User Welfare. The instantaneous user welfare wy (x) ac- counts for the utilities derived from both platforms in round t. It is defined by
The (time-discounted) revenue of GenAl over T rounds, Uxx), is defined by
T U(x) = Σ (r))
we (x) = (x(x))a(DD(xx)) + (1 - -xx(x))uf
(2)
The cumulative user welfare, W is therefore the sum of the instantaneous welfare over all the rounds W(x)
"We use the term accuracy for simplicity, allowing us to address user satisfaction abstractly. Evaluating the performance of GenAl significantly more complex.
Σl wx(x).
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Selective Response Strategies for GenAI
Assumptions and Useful Notations As we explain later, the following assumption on the structure of the accuracy function is crucial for analyzing the dynamics of the data generation process.
0.8
Assumption 2.1. The accuracy function a(D) is La- Lipschitz with constant La S B.
Proportions
0.6
We further discuss this assumption in Section 7. Addi- tionally, we use the following notions throughout the pa- per. Given an arbitrary strategy x, any strategy x" that obtained by reducing the response level in round and maintaining the other entries of x is called a r-selective modification x That is, x" is any strategy that is identical to strategy x except for round T, in which it answers less than ZT. Formally, x² E [0, and o = Iz for every 1 + r. For brevity, if x is clear for the context, we use x" as any arbitrary r-selective modification. Another useful notation in x, where = (1, ........1) 1) full response or the rlways-responding strategy; we use these interchangeably. We use this strategy baseline to test other strategies.
0.4
0.2
Selective response
Full response x
0
2
4
8
10
Round t
Figure I: A visualization for Example 2.2. The blue (circle) curve shows the proportion of users pr (x) for the selective response strategy x at each round t. The red (square) curve depicts the corresponding proportion for the full response.
point of comparison, establishing
Example 2.2. Consider the instance T 10, a(D) 1 - e 0.3D 7 0.9, r(p) = p², B = 10, and w" = 0.5. Consider the following selective response strategy x = (1,...,1) 1) and x which is defined by.
3. The Benefits of Selective Response
This section motivates our work by showing that selective response may benefit both GenAl and its users. We first demonstrate a qualitative result: Selective response can improve revenue, welfare, or both. Then, in Subsection 3.1, we quantify the extent of these improvements.
0 154 Ft === {1
otherwise
Recall the definition of the full response strategy X. We use it a benchmark in evaluating the potential impact of adopting selective response strategy on GenAl and its users.
At 1 it holds that di (x) di (x) 0. Notice that a(O) = 0 and therefore px( = 1 14 = 0.0067. Similarly, for x is pı (x) 0. ite = 0. Thus, the gen- erated data is dx( x - 0.0067 = 0.9933 and dz(x)) =
There exist instances and selective re- sponse strategy x that satisfy each one of the following inequalities:
Observation 3.1.
With that, we have the ingredients to calculate the instanta- neous welfare time =
W1 (x) P1 (x D, (x)) + (1 - (x)))=* 23 0.0067 0 0.9933 0.5 x 0.4966,
1. U(x) U(x) and W(x) > W(X).
wi (x) = 0-0+1-10 = 0.5.
2. (xx) < (x) and W(x > WXX).
Figure demonstrates the proportions of the strategies x and x as a function of the round for / E [7]. Notice that the selective response x induces lower user proportions in the earlier rounds, but it eventually surpasses the full response strategy x.
3. U(x) > Ux) and W(x) < W(x).
The first inequality in Observation 3.1 indicates that there exists selective response strategy that Pareto dominates the always-responding strategy. The subsequent two inequal- ities imply that increasing either GenAl's revenue or the users' social welfare may come at the expense of the other.
Finally, the revenue is attained by calculating U(x) E' (p)))) ( Computing this for the two strategies, we see that Uxx is roughly 5% higher than Ux). Simi- larly, the welfare (x) is about 7.6% higher than W (x). As this example suggests, selective response can improve both revenue and welfare. Indeed, this is the focus of the next section.
3.1. Price of Always Responding
In this subsection, we quantify the negative impact of al- ways answering users' queries. We introduce two indices: RPAR, an abbreviation for Revenue's Price of Always

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Selective Response Strategies for GenAI
Response, and WPAR, which stand for Welfare's Price of Always Response. Formally, RPAR
The first approach cannot han- dle welfare constraints, while the second is restricted to undiscounted revenue.
between our approaches:
maxe UXx and U(x)
WPAR maxy W(x are the price of always answering with respect to revenue and social welfare, respectively. These
W(x)
4.1. Selective Response Implies Increased User Proportions
metrics capture the inefficiencies in revenue and welfare that arise when GenAl always responds to all user queries. Our next result demonstrates that the revenue inefficiency is unbounded.
Next, we analyze the impact of using r-selective modi- fication of any base strategy on the proportions and data generation. At first glance, using selective responses harms immediate revenue, as it encourages users to turn to Forum. However, as suggested by Observation 3.1, lower response levels can ultimately prove beneficial. But why is this the case?
Proposition 3.2. For every M E TRyn there exists an in- stance I with L, ((In(M) such that [PAR(1) M.
Proposition 3.2 relies on the revenue scaling function r(p), which can bias GenAl's incentives toward data generation rather than immediate revenue. For example, when r(p) takes the form of sigmoid function, the parameter L, con- trols the steepness of the curve. If the sigmoid is sufficiently steep, r(p) approximates step function, requiring GenAl to surpass certain user proportion threshold to generate revenue. This mirrors threshold-based incentives, where substantial rewards are only provided once a predefined threshold is met.
The answer lies in the dynamics of data generation. By employing more selective response, GenAl incentivizes users to engage with Forum, which results in the creation of more data. This additional data becomes crucial in future rounds, enabling GenAl to attract a more significant user proportion in subsequent interactions. While this reason- ing is intuitive, its application over time presents techni- cal challenge: As the proportion of users choosing GenAl increases, the marginal data generated per round may de- crease, potentially leading to less data than strategy where GenAl answers every query. However, the theorem below demonstrates the compounding effect of selective response, guaranteeing consistently higher user proportions in future rounds.
Our next proposition shows that there exist instances where selective responses can result in social welfare nearly twice as large that of the always-responding strategy.
Proposition 3.3. For every E > 0 there exists an instance I with WPAR (1) > 2 - s.
We end this section by analyzing Price-of-Anareee (Kout- soupias & Papadimitriou, 1999; Roughgarden, 2005), a stan- dard economic concept that measures the harm due to strate- gic behavior of GenAL. Formally, PoA max, W(x) minseR W [x]* where R is the set of revenue-man maximizin strategies. We show that can increase with the smoothness parameter of the reward function L,. Since this analysis depends on the revenue-optimal strategy of GenAI, which only examine in later sections, we defer this analysis to the Appendix B.1
Theorem 4.1. Fix any strategy x. For every > T it holds Dx(x") > D((x) and px(x") 2 pe p((x) where pi(x") = (x(x) and only if x; x. 0.
Proof sketch of Theorem 4.1. To prove this theorem, we first show that Dz(x") Dx(x) > for every t > т. To do so, we introduce some additional notations. First, we define Q(D,z) = x + Buz, which represents the resulting proportion when using a selective response æ with data D. Next, we define fDD D - Q(D, x) as the total data generated when choosing x with initial data D. Note that for every E [T], we have fxD, xx)) = D:+1 (x) and (x), xx,) = (x). Following, we prove that f(D,x) is monotonically increasing with respect to D.
(a((D)
4. The Impact of Selective Response on GenAI's Revenue
In this section, we analyze the sicenuemmaximiztiion prob- lem faced by GenAL. Subsection 4.1 examines the impact of using selective responses on both user proportions and generated data. We show that any r-selective modification of any strategy and any T generates more future data and attracts more users to GenAI from round 7 + 1 onward. Subsequently, we develop two approaches for maximizing GenAl's welfare. In Subsection 4.2, we develop approxi- mately optimal algorithm for maximizing GenAl's optimal revenue, In Subsection 4.3, we focus on undiscounted set- tings, i.e., 7 = 1, and consider a welfare-constrain revenue maximization: Maximizing revenue under a minimal so- cial welfare level constraint. We emphasize the trade-off
Proposition 4.2. For every x E [0, 1] and D E Rzo it holds that (f
0.
dD
Proposition 4.2, combined with Assumption 2.1, imply that for every > r, if (x Dx(x), then it follows that Dx"1(x") > (x). Iterating Proposition 4.2 leads to Dx > D,(x) for every t > r. Finally, since Q(D, x) is monotonically increasing with respect to D, we conclude that (x()) 2 px(x) for every t > т, thus completing the proof of Theorem 4.1.
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4.2. Revenue Maximization
Proof sketch of Theorem 4.4. To prove the theorem, there are two key elements we need to establish. First, for any two similar data quantities under any selective response strategy, the resulting revenues are similar as well. Imagine that D is the actual data quantity generated by some strategy up to some arbitrary round, and D is the discretized data quantity of the same strategy in our succinct representation. If GenAl plays E A in the next round, how different do we expect the data quantity to be in the next round? In other words, we need to bound the difference [[(D), . [(D" .z)], where ʃ follows the definition from the proof of Theorem 4.1. To that end, we prove the following lemma.
In this subsection, we develop an approximately optimal algorithm for maximizing GenAl's revenue. We begin by noting the challenges of the problem, emphasizing why identifying the optimal strategy is nontrivial.
Recall that Theorem 4.1 demonstrates that employing a selective response increases future proportions. This ar- gument can be applied iteratively by employing selective responses in different rounds, further enhancing the future proportions. This intuition hints that step function-based strategy could be optimal: GenAl should answer queries in early rounds and then answer all queries. In such case, the effective space of optimal strategy reduces to all T step function-bes -based strategies. Unfortunately, this intuition is misleading.
Lemma 4.5. For any DJ D2 E R20 and & E A, it holds that [f f x) s DD' D2
We further leverage this lemma in proving the second key element: The discrepancy of the induced proportions is bounded by the discrepancy in the data quantities, i.e., Q(D', ,1) - Q(D² < (D' D Equipped with Lemma 4.5 and the former inequality, we bound the dis- crepancy the dynamic programming process propagates
Observation 4.3. There exist instances where the optimal strategy x* $ 10.
Due to Observation 4.3, the search for optimal strategies spans the continuous domain [0. 1)"" This observation moti- vates us to adopt an approximation-basee approach to iden- tify near-optimal strategies efficiently. To that end, we de- vise the ASR algorithm, which stands for Approximately op- timal Selective Response. ASR follows a standard dynamic programming structure, but its approximation analysis is nontrivial, as we elaborate below. Therefore, we introduce it in Appendix C.2 and provide an informal description here, along with key insights from its analysis.
throughout its execution.
Observe that Theorem 4.4 guarantees approximation with respect to the best strategy that chooses actions from A only. Indeed, the right-hand-side of Inequality (3) includes maxxeAT (x'). In fact, by taking to be the 8-uniform discretization of the [o, 1] interval for small enough 8 > O, we can extend our approximation guarantees the best continuous strategy at the expense of a slightly larger ap- proximation factor.
Overview of the ASR algorithm Fix any finite set A, A C [0, 1]. Naively, if we wish to find arg maxxEAT Uxx), could exhaustively search along all AT strategies via inefficient dynamic programming. However, we show how to design a small-size state representation and execute dy- namic programming effectively. The challenge is ensuring that any strategy's 's revenue within the small state represen- tation approximates the actual revenue of that strategy. To achieve this, we discretize the amount of data D. Recall that in each round, the amount of generated data is at most 1, meaning that for any strategy x. the total data up round t is (x E [0, - 1). Consequently, we define states by the round l. and the discretized data value within [0, f - 1]. At the heart of our dynamic programming approach is the calculation of the expected revenue for each state and action y E A. based on the induced proportions, generated data, and the anticipated next state. The next theorem provides the guarantees of ASR.
Theorem 4.6. Let 6 E (0, 11 and let As 8, 1}. Let x be the solution of ASR with parameters > 0 and As. Then,
78 +
U(x) 2 max U(x)
L,, EL,
4 411-))
and the run time of ASR is O
T
4.3. Celtfare-oontraiinet Revenue Maximization
While the ASR algorithm developed in the previous subsection guarantees approximately optimal revenue, it might harm user welfare. Indeed, Observation 3.1 implies that selective response can improve revenue but decrease welfare. This motivates the need for a wellfaee-constrained revenue maximization framework, where the objective is to maximize GenAl's 's revenue while ensuring that the social welfare remains above a predefined threshold W. Formally,
Theorem 4.4. Fix any instance and let E >> O. The ASR algorithm outputs a strategy x such that
U'x)) > max Uxx) - T2,
(3)
x' AE
max Uxx) A
and its run time is O 171
(PI)
s.t. W(x) 2 W.
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Selective Response Strategies for GenAI
Noticeably, if the constant W is too large, that is, W maxx W (x), Problem (P1) has feasible solutions; hence, we assume W S maxx W (x). Our approach for this con- strained optimization problem is inspired by the PARS-MDD MDP problem (Ben-Porat et al., 2024). We reduce it to a graph search problem, where we iteratively discover the Pareto frontier of feasible revenue and welfare pairs, propagating optimal solutions of sub-probe nub-problems. Due to space constraints, defer its description to Appendix C.3 and present here its formal guarantees.
modification x"; the black (dotted) line is the threshold B; and the orange (dashed) line is the threshold C. Figure 2b also uses the round number as the horizontal axis and in- cludes both strategies x and x", but its vertical axis shows the instantaneous welfare wt:-
Before round 7, the strategies agree on the response levels; thus, the utilities are identical, and the blue and red curves intersect in both figures. Next, we focus on round т. Re- call that the r-selective modification has lower response level in round i.e., x,7 < Ir. Consequently, Figure 2a demonstrates that the utility GenAl induces is lower. Part I of the theorem implies that the r-selective modification ob- tains a higher instantaneous welfare, as shown in Figure 2b. To see why, notice that both w (x*). ), wof(x (x) are less than B < w"; thus, any user that directed to Forum under the modification obtains higher utility.
Theorem 4.7. Fix an instance such that 7 = 1. Let > 0 and let x" be the optimal solution for Problem (PI), There exists an algorithm with output x that guarantees
1. Uxx > U(x*) - =22 ==T2max(1,, max((1, Lr 2. (x) > W- - -20T +
For any round f, f. > the blue curve is above the red curve in Figure 2a. Namely, GenAl's quality under the r-selective modification x" is greater than that of the base strategy x. This is a direct corollary of Theorem 4.1: More data is created (Dx(x") > (x)) and more users choose GenAI (p+(x)) 2 (x)):): hence w (x*) > (x).
and its running time is O log( (1AI)
Unfortunately, the technique we employed in the previous subsection for extending the approximation from the opti- mal discrete strategy to the optimal continuous strategy is ineffective in the constrained variant; see Section 7.
Next, we focus on Part 2 of the theorem, which is demon- strated by the shaded gray area (featuring horizontal lines) in the two figures. In Figure 2a, the gray area represents rounds with t > T and w (x-) < B. Consequently, Part 2 of Theorem 4.1 implies that the instantaneous welfare of x is lower than that of x (shaded area in Figure 2b).
5. The Impact of Selective Response on Social Welfare
In this section, we flesh out the impact of implementing r-selective modifications on social welfare. Specifically, we focus on modifying an arbitrary initial strategy x by applying selective response in single round r.
We can reformulate the instantaneous welfare from Equa- tion (2) to include ar(-), namely,
we = or (x) + (1 (x))())))))= (4)
The next Theorem 5.1 provides a powerful tool in char- acterizing the change in the instantancous user welfare in r-selective modifications. We first present the theorem and then analyze its consequences.
On the one hand, GenAl's expected utility increases un- der the r-selective modification (w](x") > w (x)), while both utilities are under B and thus under w". On the other hand, the proportion of users switching to GenAl grows: or (xTx)= > (x). Therefore, the first product on the right- hand side of Equation (4) increases for the 7-selective mod- ification, while the second product decreases. Part 2 quan- tifies this tradeoff, implying that the instantaneous welfare is decreasing overall. This is illustrated in the gray area in Figure 2b, as the red curve is above the blue curve.
Theorem 5.1. Fix any instance and a strategy x. There exist thresholds B and C, B < C < w", such that for any T-selective modification x" holds that:
1. In round r, if w] (x) < B then w- (xx) > w- wx(x);
2. For every round > T, if wi (xr)= < B, then it holds that wx(x") wx(x);
Similarly, Part of the theorem, represented by the green shaded area (with vertical lines), corresponds to rounds in which the red curve in Figure 2a exceeds the threshold C, that is, w (x) > C. In these rounds, Part 3 asserts that the instantaneous welfare of x exceeds that of (green area in Figure 2b).
3. For every round t > T such that w (x) > C, it holds that wx(x") > (x).
We interpret the theorem using the illustrations in Figure 2. In Figure 2a, the horizontal axis is the round number and the vertical axis is the expected utility users obtain from GenAL, wf. There are four curves: The red (circle) is the base strategy x; the blue (triangle) represents r-selective
Finally, we discuss the thresholds B and C. For the latter, the thcorem holds trivially for C = w However, as we show in the proof of the theorem, we have tighter threshold
7

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Selective Response Strategies for GenAI
Round
Round t
(a)
(b)
Figure 2: Illustrating Theorem 5.1. The left figure illustrates GenAl's expected utility vs round index, and the right figure illustrates instantaneous welfare round index. The red (circle). blue (triangle) curves represent the base strategy x, and r-selective modification x². The orange (dashed) and black (dotted) lines represent the thresholds B and C, respectively. The gray and green shaded areas highlight different parts of the theorem. The gray area indicates rounds where the condition of Part 2 is met (Figure 2a), and the resulting lower instantaneous welfare is illustrated in Figure 2b. The green region denotes rounds where x leads to higher instantaneous welfare (Part 3).
of - w Wie +1 where W is the Lambert function. Ø As for B, Theorem 4.1 implies its existence, yet finding closed-form expression remains an open question.
Corollary 6.1. Let B and be the thresholds from Theo- rem 5.1. Assume that w (x) B and that GenAl commits, ie., mine [we (x) w (x) 0} C holds for all t.
Then, W(x") (
6. Regulating Selective Response for Improved Social Welfare with Minimal Intervention
Intuitively, Corollary 6. ensures that the welfare improve- ment due this intervention (the green shaded region in Figure 2) surpasses the welfare reduction (the gray region).
In this section, we adopt the perspective of a regulator aim- ing to benefit users through interventions. We show how use the results from the previous section ensure that the intervention will be beneficial from welfare perspec- tive. Additionally, we bound the revenue gap that such intervention may create. A crucial part of our approach is that the regulator can see previous actions, but not future actions, making closer to real-world scenarios. Specif- ically, for any arbitrary round т, we assume the regulator observes 21....Zy. but has no access GenAI's future strategy (xt (st)fT=11
6.2. Bounding GenAl's Revenue Gap
A complementary question is what extent forcing T- selective response harm GenAl's revenue. Our goal is to establish bound on the revenue gap between the base strategy and the modified strategy x", where the selective response occurs in round We stress that incomplete infor- mation about future actions makes this analysis challenging.
By definition, x and x are identical except for round T. Consequently, they generate the same amount of data in all rounds before т. Using 7-selective response reduces the proportion of answers in that round, which in turn increases the accumulated data available in round T + 1. Therefore, the revenue gap can be decomposed into two components: (1) The immediate effect of the proportion change in round т, r(p- (x")) -xx")))(r((x))))) and (2) the downstream effects on subsequent rounds due to the change in the data generation process. Using several technical lemmas that we prove in Appendix E, show that:
6.1. Sufficient Conditions for Increasing Social Welfare
We focus on 7-selective modifications that guarantee to increase welfare w.r.t. base strategy x. We further assume GenAl commits to 0 response level as long its quality is below C, where C is the threshold from Theorem 5.1. This commitment, formally given by min (x) (x) >> 0} > C, represents the minimum utility required from
GenAl for rounds T.
8

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Selective Response Strategies for GenAI
Corollary 6.2. It holds that
of strategic interaction for GenAL. Moreover, data transfer between the platforms form the basis for collaboration: GenAl could employ selective response to bolster Forum content creation, and Forum could, in turn, attribute that content to GenAl for subsequent use in retraining.
U(x') - -U(x)
>--1 - (x))) + Layr Pr((x)) - -x)(x)
1-7
The above bound is less informative approaches 1. In Theorem E.I, we obtain tighter bound by having some additional assumptions.
A Acknowledgments
We thank the anonymous reviewers for their helpful com- ments. This research was supported by the Israel Science Foundation (ISF; Grant No. 3079/24).
7. Discussion and Future Work
This paper pioneers the novel approach of selective response, showing that withholding responses can be powerful tool for GenAl systems. By opting not to answer every query as accurately as it can--aarticllatte when new or complex topics emerge- GenAl can encourage user participation on community-driven platforms and thereby generate more high-quality data for future training. This mechanism ulti- mately enhances GenAl's long-tern performance and rev- enue. Therefore, selective response is related to active learn- ing, nudging users to generate more data. This mirrors the exploration-explootttion tradeoff from the multi-armed ban- dit literature: GenAl forgoes immediate gains and risks user dissatisfaction the pursuit of better long-term revenue. From a welfare perspective, our results indicate that selec- tive response can benefit users, leading to better solutions and increased overall satisfaction. Since this work is the first to address selective response strategies for GenAL, nu- merous promising directions remain for future research; we highlight some of them below.
Impact Statement
Our work aims to benefit both GenAl and its users by intro- ducing a new action: allowing GenAl to choose whether answer to adjust the quality of its answer. As shown in this work, a wise use of selective response can be beneficial for both GenAI and its users. From an ethical perspec- tive, using a selective response can be seen as responsible decision, as it allows GenAl to redirect users instead of providing lua-quality answers. Furthermore, GenAl is transparent about its need for data, it can notify users about its lack of confidence and explain that it may be able to assist them better in the future by choosing not to answer in the present.
References
Babichenko, Y., Talgam-Cohen I., Xu, H., and Zabarnyi, K. Algorithmic cheap talk. In Proceedings of the 25th ACM Conference on Economics and Computation, EC '24, pp. 5-6. Association for Computing Machinery, 2024.
First, from a technical standpoint, all of the results in this pa- per rely on Assumption 2.1, involving the Lipshitz condition of the accuracy function and the sensitivity parameter 3. Fu- ture work could seek to relax this assumption. Furthermore, our constrained optimization approach in Subsection 4.3 could be extended to approximate the optimal (continuous) strategy instead of the optimal discrete strategy.
Bailey, M., Johnston, D., Kuchler, T., Stroebel, J., and Wong, Peer effects in product adoption. American Economic Journal: Applied Economics, 14(3):488-522 2022.
Ben-Porat, O., Mansour, Y., Moshkovitz, M., and Taitler, B. Principal-agent reward shaping in mdps. In Proceed- ings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 9502-9510, 2024.
Second, our stylized model adopts the simplifying though unrealisti--asummptiis that only single GenAl platform exists. Admittedly, this makes it easier to focus the idea of selective responses, and indeed, this assumption is pivotal in keeping our analysis tractable. Future research could explore scenarios with multiple GenAl platforms and numan-centered forums. In such settings, one platform's 's selective response might redirect users to competing GenAl platforms, leading to the tragedy of the commons (Hardin, 1968): Although all GenAl platforms benefit from fresh data generation, none may choose to respond selectively if it means losing users to competitors.
Bergemann, D. and Bonatti, A. Data, competition, and digital platforms. American Economic Review, 114(8): 2553-2595, 2024.
Bergemann, D. and Morris, S. Information design: A unified perspective. Journal of Economic Literature, 57(1):44- 95, 2019.
Third, we assumed Forum behaves non von-strategically. In reality, human-centered platforms often monetize their data by selling it to GenAl platforms, adding further layer
Bergemann, D., Brooks, B., and Morris, S. The limits of price discrimination. American Economic Review, 105 (3).921-957) 2015.

---

Selective Response Strategies for GenAI
Burtch, G., Lee, D., and Chen, Z. The consequences of gen- erative ai for online knowledge communities. Scientific Reports, 14(1):10413, 2024.
Hardin, G.
The tragedy of the commons: the population problem has technical solution; it requires a fundamen- tal extension in morality, science, 12233899)1244312255 1968.
Chow, Y. Tennenholtz, G., Gur, I., Zhuang, V., Dai, B., Kumar, A., Agarwal, R., Thiagarajan. S., Boutilier, C., and Faust, A. Inference-aware fine-tuning for best-of-n sampling in large language models. In The Thirteenth International Conference on Learning Representations, 2025.
Hemmer, P., Thede, L.,, Vössing, M., Jakubik, J., and Kühl, N. Learning to defer with limited expert predictions. In Proceedings of the AAAI Conference on Artificial Intelli- gence, volume 37, pp. 6002-6011, 2023.
Jagadeesan, M., Jordan, M. I., and Haghtalab, N. Competi- tion, alignment, and equilibria in digital marketplaces. In Proceedings of the AAAI Conference on Artificial Intelli- gence, volume 37, pp. 5689-568860 -699,,,6622226 2023.
Conitzer, V., Freedman, R., Heitzig, J., Holliday, W. H., Jacobs, B. M., Lambert, N., Mossé, M., Pacuit, E., Russell, S., Schoelkopf, H., Tewolde, E., and Zwicker, W. S. Social choice for AI aligmment: Dealing with di- verse human feedback. CoRR, abs/2404. 10271, 2024. URL https: 10271.
Ji, Z., Lee, N., Frieske, R., Yu, T., Su, D., Xu, Y., Ishii, E., Bang, Y. J., Madotto, A., and Fung, Survey of halluci- nation in natural language generation. ACM Computing Surveys, 55(12):1-38 2023.
doi: 10448550/ARXIV.2404.. ///ooi.or///// 40000..855550/50
Crandall, J. W., Oudah, M., Tennom, Ishowo-Oloko, F., Abdallah, S., Bonnefon, J.-F., Cebrian, M., Shariff, A., Goodrich, M. A., and Rahwan, I. Cooperating with ma- chines. Nature communications, 9()):333, 2018.
junyou li, Zhang, Q., Yu, Y., FU, Q. and Ye, D. More agents is all you need. Transactions on Machine Learning Research, 2024. ISSN 2835-8856. URL https: /p enreview wtteeviwwweeteeeeeeeee Seett//orumlG-=ggzUeee
Crawford, V. P. and J. Strategic information transmis- sion. Econometrica: Journal of the Econometric Society, pp. 1431-1451, 1982.
Kalai, A. T. and Vempala, S. Calibrated language models must hallucinate. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, pp. 160-171, 2024.
Dean, S., Dong, E., Jagadeesan, M., and Leqi. L. Account- ing for ai and users shaping one another: The role of mathematical models. arXiv preprint arXiv:2404.12366,
Karle, H., Peitz, M., and Reisinger, M. Segmentation ver- sus agglomeration: Competition between platforms with competitive sellers. Journal of Political Economy, 128 (6):2329-2374, 2020.
2024.
del Rio-Chanona, R. M., Laurentsyeva, N., and Wachs, Large language models reduce public knowledge sharing on online q&a platforms. PNAS nexus, 3()):paae400, 2024.
Kasneci, E., Seßler, K., Küchemann, S., Bannert, M., Dementieva, D., Fischer, F., Gasser, U., Groh, G., Günnemann, S., Hüllermeier, E., et al. Chatgpt for good? on opportunities and challenges of large language models for education. Learning and individual differences, 103: 102274, 2023.
Esmaeili, S. A., Bhawalkar, K., Feng, Z., Wang, D., and Xu, H. How strategize human content creation in the era of genai? arXiv preprint arXiv:2406.05188 2024.
Katz, M. L. and Shapiro, C. Network externalities, competi- tion, and compatibility. The American economic review, 75(3):4244440 1985.
Feldman, M., Meir, R., and Tennenholtz, M. Competition in the presence of social networks: how many service providers maximize welfare? In International Conference Web and Internet Economics, pp. 174-187. Springer, 2013.
Keinan, G. and Ben-Porat, O. Strategic content creation in the age of genai: To share or not to share? arXiv preprint arXiv:2505. 16358, 2025.
Kocoñ, J., Cichecki, Kaszyca, O., Kochanek, M., Szydlo, D., Baran, J., Bielaniewicz. J., Gruza, M., Janz, A., Kan- clerz, K., al. Chatgpt: Jack of all trades, master of none. Information Fusion, pp. 101861 2023.
Frieder, S., Pinchetti, L., Griffiths, R.-R., Salvatori, T., Lukasiewicz, T., Petersen, P., and Berner, J. Mathematical capabilities of chatgpt. Advances in Neural Information Processing Systems, 36, 2024.
Koutsoupias, E. and Papadimitriou, C. Worst-case equilibria. Annual symposium on theoretical aspects of computer science, pp. 404 413. Springer, 1999.
Garey, M. R. and Johnson, D. S. Computers and intractabil- ity, volume 174. freeman San Francisco, 1979.
10

---

Selective Response Strategies for GenAI
Laufer, B., Kleinberg. J., and Heidari, H. Fine-tuning games: Bargaining and adaptation for general-purpose models. In Proceedings of the ACM on Web Conference 2024, pp. 66-76, 2024.
engine', June 2023. URL URLntttss//foortue.ccm
2023 20221/06//3//aaeerr=------111111 pt --lllllinnniions ionooossssinnooor/ooo/oooo
Sun, H., Chen, Y., Wang, S., Chen, W., and Deng. X. Mech- anism design for LLM fine-tuning with multiple reward models. In Pluralistic Alignment Workshop at NeurlPS 2024, 2024.
Li, K., Patel, O., Viégas, F., Pfister, H., and Wattenberg, M. Inference-ting -ieeneee--meeeeeeeeee intervention: Eliciting truthful answers from language model. Advances in Neural Information Processing Systems, 36, 2024.
Taitler, and Ben-Porat, O. Braess's paradox of generative In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 14139-14147, 2025.
X. and Kim, K. Impacts of generative user contribu- tions: evidence from coding &a platform. Marketing Letters, pp. 1-15, 2024.
Tullock, G. Efficient rent seeking. Buchanan, J. M.,
Liu, J., Xia, C. S., Wang, Y., and Zhang, L. Is your code generated by chatgpt really correct? nigorous evaluation of large language models for code generation. Advances in Neural Information Processing Systems, 36, 2024.
Tollison, D., and Tullock, G. (eds.), Toward a Theory of the Rent-Seeking Society, pp. 97-112. Texas A and M University Press, College Station, 1980.
Yao, F., Li, C.,, Nekipelov, D., Wang, H., and Xu, H. Human vs. generative content creation competition: symbio- sis or conflict? In Proceedings of the 41st International Conference on Machine Learning, ICML'24, JMLR.org 2024.
Lo, Y. L., de Witt, C. S., Sokota, S., Foerster, J. N., and Whiteson, S. Cheap talk discovery and utilization in multi-agent reinforcement learning. In The Eleventh Inter- national Conference on Learning Representations, 2023.
Lu, C., Willi, T., Letcher, A., and Foerster, J. N. Adversar- ial cheap talk. In International Conference on Machine Learning, pp. 22917-22941. PMLR, 2023.
McIntyre, D. P. and Srinivasan, A. Networks, platforms, and strategy: Emerging views and next steps. Strategic management journal, (8(1)):41-1666 2017.
Mello, M. M. and Guha, N. Chatgpt and physicians' mal- practice risk. JAMA Health Forum, 4(5):221933,, May 2023. doi: 10. 10.000//gonaaaahaooom.2222223230
URL fttppss/ http:///www...ooo/oooo//aaaaa//a
Milgrom, P. R. Good news and bad news: Representation theorems and applications. The Bell Journal of Eco- nomics, pp. 380-391, 1981.
Mozannar, H. and Sontag, D. Consistent estimators for learning to defer to expert. In International conference on machine learning, pp. 7076-7087. PMLR, 2020.
Raghavan, M. Competition and diversity in generative ai. arXiv preprint arXiv:2412.08610, 2024.
Rietveld, J. and Schilling, M. A. Platform competition: A systematic and interdisciplinary review of the literature. Journal of Management, 47(6):1528 -5661153,,, 2021.
Roughgarden, T. Selfish routing and the price of anarchy. MIT press, 2005.
Shin, R. Humiliated lawyers fined $5,000 for submitting chatgpt hallucinations in court: ii heard about this new site, which falsely assumed was, like, super search

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Selective Response Strategies for GenAI
A. Definitions and Notations
first define the following function:
((,x))=D4 (1 DD) @Bwe
Da(D)
Denote aD) (Ba(t)x+ Foau therefore I(D,2) x) can be expressed as S(D, = d (1- (D(D)x)).
Next, we define 1. as the discretization operator with respect to & E R. Formally, for any x: E IR, the discretization operator given by [+] -.].
B. Proofs Omitted from Section 3
Proof of Observation 3.1. We prove each clause separately.
Pareto dominance
This shown in Example 2.2, for which it holds that
(x) < 2.356.
Uxx) > 2.483.
(xx) < 5.73.
W(x) > 6.2.
2. Decreases revenue and increases welfare Let T and consider the instance a(D) = 1 e -0.4D ,7 1, 3. w 0.7 and r(p) p.
We calculate the revenue and the social welfare induced by x by calculating the proportions for every / E (T]. Therefore, the induced revenue is (xx) ) > 1.6 and the social welfare W(x) < 3.3.
Next, we denote (0, ........ 0), the strategy for which GenAl never answers. By definition we have that U(x)
Uxx and (xx) Tw" 3.5 (xx).
Increases revenue and decreases welfare Let T and consider the instance a(D) = 1 0.4D , 1, B 3, w 0.1 and r(p) is the step function defined as
{1
1 p2 9(4 Otherwise
r(p)=
We denote x the strategy that satisfies
[ t=T
Otherwise
Notice that (x()) > 0 and therefore for every e [5) it holds that D((x) 4. Thus, U(x) 0.
The revenue induced by x is equal the revenue induced round T. This is true since 2; 0 for every t T and therefore (x( = 0. At round T, the total generated data is DT(x) T - = 4. Thus, Uxx) -r(r(x)) (4,1) > 0.89
Calculating the welfare induced by x can be done by calculating (x)),, resulting in ( 1.17.
Similarly, we can calculate the welfare induced by strategy x. Repeating the same calculation leads to W(x) < 1.122; thus, we can conclude that U(x) (x) and W(x) > W(x). This completes the proof of Observation 3.1.
12

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Selective Response Strategies for GenAI
B.1. Proofs Omitted from Subsection 3.1
Proof of Proposition 3.2. Consider the instance a(D) defined as r(p) -()))=1 such that & 9(7-1,1)=0f "-
1, 1, w + and r(p) is the sigmoid function In(27M)
1+D
T
7
Notice that for every / E T holds that (x) = a((r(x)) = 14D,(8)
> T = w². Therefore, we get that px(X) > 0.5 and
D.
we now bound the revenue induced by X.
T U(x) Σ r(px(x)) Tr(g(- T T-1
2 1)).
Next, we define the scheme that answers only at the last round x = =00,, 0, 1). Notice that the revenue induced by x* Uxx)) = (T - 1, 1)) = 0.5. Therefore,
1 (()((T-1)-v( =
RPAR maxx (xx)
0.5
U(x)
Tr(a(
P-1
1))
2T
2
(((((T11)-g( (1)1)
1 clu(2TM-11)
M.
2T
2T
Notice that holds that
dr
L, max max rlp) (1)(1-((p)) s
PE 0. dp pE
For T = 10, we get that L, R 15.26 (M) This completes the proof of Proposition 3.2.
Proof of Proposition 3.3. Let T E R> and consider the instance a(D)
D 73.
7
1. 1, w"
and r(p) p.
Notice that the utility of the users from GenAl is bounded by
D 73
T
1
1
w (x) = a(D,)
21
w
73
7
T
Furthermore, we can bound the proportions by
(x(x)= 1 + (w(
@:0
Therefore, the users' social welfare satisfies that
wxxx)= = (x)p (x) + (1 Pe (x())) n
< 7 (x() (x) + - (x) w0
1
< T2 1 + Bw +(
1 Bwo ww
1
+ (11
T 14
1 1
Next, denote ă = (0, ..., the strategy for which GenAl does not answer any query. Therefore, by definition holds that w. (x) = =
13

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Selective Response Strategies for GenAI
We now bound the price of anarchy:
WPAR maxx (x)
(x)
(
(
Tw"
T
w
(x)
T T
+
(1
1te7
1
+
T
4
lte7
14e
Notice that 2-6 0.5. Next, denote ((T)
8
+
Observe that f(t) continuous in T and satisfies the
l4e7
lte7
following properties:
1. h(1) = 1,
2. +o0 h(T) + 0.5.
Therefore, by the intermediate value theorem, there exists To such that h(To) = 1 Furthermore,
2-c'
dh B
1
3 T
1
T +
1
dT T LteT
T1t
1te7
1 et
1 +
7
3
1
B
1
8
0;
T Tlt
1
1+
$
T
14
1
E
T
hence, for every T To holds that
1
WPAR 2
2
1 =
h(T)
h(Tp)
2-
This completes the proof of Proposition 3.3.
Theorem B.1. For every M E R2 there exists an instance with PoA(I) > M.
Proof of Theorem B.1. Let T E Ry and Consider the instance a(D) T. = 1, 8= 3, w
We let r(p) be the
T.
step function
(1 (T
r(p)
0
Otherwise
The purpose of choosing r(p) as step function is to show that GenAl's revenue maximiiiii strategy (0, 1). Notice that we can also represent this function sigmoid r(p) -= 1.)--p for & co.
Notice that in each turn, the maximal amount of data that can be generated is which occurs for 2; 0. Therefore, for T 1 rounds, the maximum amount of data that can be generated is T - 1, which is induced by the strategy that uses x; = 0 for every / < T - 1. Answering any query before round T results in r(p:) = 0 for every E [T]. Therefore, GenAl's optimal strategy is:
0 t T
Otherwise
We now evaluate the welfare for the schemes and x. We start with x*:
T-1
W(x*)
Σ wx(x") wr(x") (T 1xw1(x") + wr(xx) S (T (T- 1)w" +1 Tw +1
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Selective Response Strategies for GenAI
We move evaluate the social welfare induced by First, notice that for every T > it holds that
(x(x) 2 pi = q(0,1)= = 1 e a(0)) a(0)
2 > 0.04.
1 lte7
1 e
Similarly, we develop an upper bound on the proportions:
1
(x) + ef(w (D..()))
1 1 e 87 < 0.96.
1 0 ( 3pp
Using the bound on the proportions, we can get a lower bound on total amount data at each round
1-1
D.(x) = Σ (1 -1- (x))
0.04(L 1).
P=1
This allows us to evaluate the minimal welfare induced by strategy x:
T ((x)
T Σ
T
Σ
Pe
(x) (x) + (1- 111-p0 (x))))
(x 0.04
Σ
w
(x)
t=1
1=1
1=1
T Σ (D)( 0.04
T
0.04(t - 1)
0.042
0.04
(T 1).
T
2
We are now ready to plug everything we calculated so far into the definition of the PoA.
maxx W(x)
maxx W(x)
Pod
minxemax ((x)
W(x)
W(x*)
(x))
0.013
(T
1)
0.042
2
(T 1))
W(x*)
2
4
Therefore, for every T>
1M
holds that
0.04
0.042 4M
Pod >
+1 - 1) = M.
4
0.042
This completes the proof of Theorem B.I.
C. Proofs Omitted from Section 4
C.1. Proofs Omitted from Subsection 4.1
Proof of Proposition 4.2. We take the derivative of (D,
xD(
=1 dg( x)
dD
dD
= B (1 qDD,2)) dD
dD
Notice that qdd, x) E [0, 1] for every E Rx0 and x E [0, 1]. Furthermore, the expression q(1 q) has one maximum point g = 0.5, therefore
15

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Selective Response Strategies for GenAI
(D,
11 Bx²q (1 9(D, dD(D) dD
dD
3x do (D)
da (D)
2 1
2
dD > 0.
4 dD
This completes the proof of Proposition 4.2.
Proof' of Theorem 4.1. We first show that y < 2y then 1x-1(x") > Dx+1(x). By definition of x" and x it holds that
Di(x*) = (x) for every < r. Next, notice that if < 2, then
Bx(d D);;
P+ (x 2 (oldd D)a; + @0w
Bald, (x') 1)y
(x))r,
Iy cBa(d=(x))a== + eBw pr (x)x;;
(x' D)u @B
therefore, holds that
Dr+1(x))= = + -P+(x-))
>D,(x) + 11-ppri (1-Pr(xx) = (x)1(x))
Next, we use the following proposition to show that 1x-1 > Dx+1(x)-
Proposition C.1. Let E [T] and x, x be two selective response strategies such that æt 3t for every 2 T. If Di(x) > (x(x) and da(D) holds only if x =
dD Then for every t 2 it holds that Di(x), > D.(R), and pr(x) 2 Px(x) where inequality
Thus, by Proposition C.I holds that px(")) 2 pe (x)).. This completes the proof of Theorem 4.1.
Proof of Proposition C.1. We prove our claim by proving a slightly stronger version using induction over the rounds. In addition to the original claim, also prove that (x) (x( for every / We start with the base Notice that P- (x) o (x), (x), x,) and p- (x) (D) (-).
We now use the following lemma:
Lemma C.2. For every x [0, 1] and D R2o. holds that (D,, x)) satisfies dg(D,x)
2 0.
Since (x) > D, (x) then from Lemma C.2 it holds that p, (x) 2 Pr (x). Next, we show that Dx+1(x) > (X).
Notice that (x+ = (*) + (1 pr (x)) = f (x), R.), similarly (x+1 = fx),(x), x+)) By Proposition 4.2 holds that [D, xx,) is monotonic increasing in Therefore, D, > D, (X) leads to [(D, > (x), RT)) and thus (x) > (x).
Assume the claim holds for t 1 т, and prove it holds for Since it holds for t - 1, then D,(x) (x). Therefore, by Lemma C.2 it holds that (xx) >> (X). Lastly, by Proposition 4.2 it holds that
Dz+ (x) ( (8), 5.) Dz+1 (8).
This completes the proof of Proposition C.I.
Proof of Lemma C.2. We take the derivative of q(D,x))
dg(D, x)
(2, (1 ((D,::)) da(D)
dD
dD
As we assume in the model, completes the proof of Lemma C.2.
do(D) dD
2 0. Furthermore, q(D,x) E [0, for every I E [0, 1], and therefore
dg(D.x) dD
2
This
16

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Selective Response Strategies for GenAI
Algorithm 1 Approximately optimal Selective Response (ASR)
Input: A,
Output:
1: (tt,d) < 0, (t,
for every E [T 1] and e (0,6,...,7])
2: for T... do
3: for d E {O.E....,L 1) do
4: U(w) <- 0 for every E A
5:
for y A do
6:
p gKク Le
7:
d' d
p)
8:
va(y) - r(p) + (,,++
9:
end for (it, max, va(v)
10:
11:
T(t, d) 4- arg max, Va (y)
end for
13:
end for
14: extract from starting f 1, 0
15:
Return
C.2. Proofs Omitted from Subection 4.2
Proof of Observation 4.3. Consider the instance a(D) = e + 7 rpp) p. 41 and w 0.66.
Let T 3 and observe the revenue for the following schemes:
1. x 11,
2. x' (0,1,1).
3. x² (0,0, 1).
4. x 1).
5. (0.04, 0.97,
Notice that we do not consider schemes where 2g = 0 since for any such scheme, the scheme which is identical at round
t = 1, f and plays æ3 induces higher revenue; therefore, the revenue difference between x and the other schemes
as follows:
U(x) - U(x)= > 9.71 10-6
U(x) - (xx*) > 9.71 1
U(x) Uxx²) 7.9 10-6
U(x) - (x33) 7.89 10-6
This completes the proof of Observation 4.3.
Proof of Theorem 4.4. We denote A, (t 1)s and (x) the accumulated revenue from round until following scheme x, formally Ux(x)= = ( We use the following lemma to show the relationship between Vtt, [dl.)
and (x(x)).
Lemma C.3. Fix round t [TT For every E E0,,,...,TT. TT such that Id - Dz(x*)) S De it holds that
T
V(t,d)> Ux(x*) L, Σa
17

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Selective Response Strategies for GenAI
Notice that D by definition, and thus (1(**) Uxx*). Therefore, Lemma C.3 suggests that
T
V(1,0) > Ux() - L Ant
We use the following lemma to evaluate the differences between (x) and V)1
Lemma C.4. Let (de) be the sequence defined by = O and de+1 [de (1 reg(d,, xi))le- Then, for every t (T) holds that de (x).).
Therefore, by Lemma C.2 holds that
V(1,0) = Σ x( S Σ (x):)(D((x))x:))) = (((i((x)) = (x).
Thus, we can write:
Uxx) 2 V(1.0) U(x') L, Σ An
To complete the proof of Theorem 4.4, we prove the following lemma.
Lemma C.5. It holds that D A,7 < eT2.
This completes the proof of Theorem 4.4.
Proof of Lemma C.3. We prove this lemma using backward induction, starting with the base case from round T. For that, we start by bounding the difference in proportions using the following lemma.
Lemma C.6. Let d' d R2 and
[0. 1]. If df < dl then 0 S v(o(d? v) - g(d", b)) < d2 d!.
In round T' it holds that ld Dr(x*) Ar. Therefore, for every y A holds that y (g((, v) ((Dr(x'), < ld - Dr(x*)| AT.
Let d' = [d+ (1 yq(d, v) Consequently,
(VTT -r
max(r(o((dd:))++4VV
Ur(x*)
yEA
max maxr(yg(d,u)) -Ur(())))))((()) VEA maxr(yg(d, 9)) (a (x") x,x)
VEA
r(max wo(d, v) r (D (x"), x7:))
DEA
max y) 1Tg(Dr (x") x
WEA
AT
We finished with the base case and move on to the induction step. Assume the lemma is true for t + 1 and we show it holds for round
18

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Selective Response Strategies for GenAI
according the assumptions in the lemma, it holds that |d -D((*)) As therefore according to Lemma C.6, for every y E A it holds that
< L, Ld Dx(x')| L, Ir(ya(d. v)) r(gg(D((x")) L, x
We use the next lemma to bound the difference in data at step I.
Lemma C.7. it holds that [x(Dr(x*), - [f(d, v)Jel < A
Lemma C.7 suggests that the condition for the induction step holds, and therefore according to our induction step:
V(t 1, (x) - L, Σ Ant1((+1)
1m1+1
therefore,
va(0;) = =
> += T
> >=00(D(())))))) + Uc+i(x()) - Ly Σ A
t=++
= =x]g(D,(x') ), + -U1+1((x)) - L,A. -7hr Σ A
T
= U,((x) - L, Σ A
Finally, it holds that
T
dt, max va(v) 2 u,( L, > A. yЕΛ
This completes the proof of Lemma C.3.
Proof of Lemma C.6. Since de > d then according to Proposition 4.2 it holds that
S(d2, .) f(d",)) > 0;
hence,
f(d.v) f(d) d2 (1 ya v)) d' - (1 -(1-yq(d' .))
d8 -d v) d² yq(d! .y) 0.
Rearranging the above inequality, we get that
vlg(d - - g(d (idtta) a)) < de dd
Furthermore, from Lemma C.2 it holds that q(dl a) 2 gld a)) and therefore we summarize
0 5 v(g(d, a) gldt a)) d² d²
This completes the proof of Lemma C.6.
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Selective Response Strategies for GenAI
Proof of Lemma C.7. We prove that for any D E R2o holds that holds that IS(D.)) L((d.))Jel < <A41. First, we use the following lemma.
Lemma C.8. Let d', de [0 then it holds that
[f(d 9) - f(dd. w) < dd d'1
Therefore, using Lemma C.8 we get
IS(D,)) - LT(d, s [(d, +
< +
A
(t 1)E +e
te Aut1.
This completes the proof of Lemma C.7.
Proof of Lemma C.8. Assume without loss of generality that d' d2, Therefore, according Proposition 4.2, for every y A it holds that f(d', v) f(d,,v) y). Furthermore, from Lemma C.2 it holds that q(d', y) q(d?, a). Thus, we can write:
[fd v) f(d 2)
f(d 3) f(d y)
d + (1 yg(d? y)) - dl - (1 yg(d", .))
d' d' vg(d? y) + ya(d' y)
S df d' vo(d' 8) + vald' 9)
d d'
S dl d! |.
This completes the proof of Lemma C.8.
Proof of Lemma C.4. By definition and by Proposition 4.2 it holds that:
de+1 [d + (1 - (di(dd, xr)))ee (de,, S f(de, xx) & f(D:(x)) = Dx)1
This completes the proof of Lemma C.4.
Proof of Lemma C.5. Since 1 it holds that ET, Anti1 < ETT series and therefore
A. Notice that we now have sum of an arithmetic
T
T
T-1
T(T-1)
Σ
A
8
=
Σ
i= 2
< 2
1=0
This completes the proof of Lemma C.5.
Proof of Theorem 4.6. Denote x* = maxx U (x') and we define the following T different strategies {x(1)] T+1 such that
|
t21
x(1),
r
Otherwise
20

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Selective Response Strategies for GenAI
Notice that by definition x(7 +1 = x". Furthermore, observe that the strategies x(i) and x(i + 1) for every [7] differ only in round i. The following lemma bound the difference between strategy x(i) and strategy x(i + 1).
Lemma C.9. For every i E [T] it holds that
1)I s (28+1) Lrd. マーク 1-7
1-1
[U(x(i)
Observe that
T
(x)())) - Uxx(T 1))1 S
Σ
U(((i) Ux(i 1)M1
Therefore, by lemma C.9 we get that
T - 1-1
Σ (2
L, 73 1 L,
(x(())) Uxx(T + 1))1 V
Lastly, notice that U(x*)= 2 max U(x) 2 (((()). Therefore, we can write:
U(x*)-((x)
U(x*) max U(x') + max U(x') U(x)
x'EA]
x'En]
Uxx)) max U(x)
+ X'EA
max Uxx) U(x)
x'EAT
((x*) ) ((x(1)) U(((L)
max U(x') X'EA?
max U(x' U(x)
x'EA3
Ux*( - +(x(1))++
+ X'EA3
max
U(x) - U(x)
78+1 4(1 - -- Lid + EL,TZ
This completes the proof of Theorem 4.6.
Proof of Lemma C.9. By definition, æ(i); arii 1), for every t < and therefore D,(x(() Dx(x(i + 1)).
Next, we use the following lemma:
Lemma C.10. For every D D2 E [0, and x. x' E [0, 1] it holds that
Ig(D, Φ) qDD ) (D) x) (1 q(D, (('a))
Notice that in our case, for every (x(i); rii + 1)xl < 8. Therefore,
1))1
a(t + 1):)) (M
< - -ADD)(()))))))
38.
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Selective Response Strategies for GenAI
Where the last inequality follows from [1 --"l S for every |x|| < 1. Next, notice that for every D Rzo and J, [0, such that x'| it holds that
(z x) x' ='q(Dxx') = Ixq(D,x) l=q(D,x)-(t' (1)
Ixq(D,x) - zq(D,2') - (z' - (),
(xq(Dxx) x) - rq(D,2)) 21) + læ' x (D) x') (mq(D,x) xg(D,2)) + |x' x
7
B +1 8. 4
Therefore, by Corollary 6.2 it holds that
(U(x(i)) Uxx(i + 1))1 s (r - (x(( + 1))) + L, (m:(x(()) - pi(((i + 11)]
1-7
(mx(((i)
px(((i 1))1
S : Lu (x((x(()) px(x(1 1))1 4,7
1-7
--- L, (x((((1)) -x((x(t + 1))1 1-7
$ 7" 1-1 1 (2++1) L,
This completes the proof of Lemma C.9.
Proof of Lemma C.10. This lemma special case of Lemma E.7 and is hence omitted.
C.3. Proofs Omitted from Subsection 4.3
Proof of Theorem 4.7. The proof is constructed parts. First, we simplify and write our problem explicitly. Then, we define an approximation to our problem and build an MDP describe it. The third step is show that our approximation problem can be viewed as instance of the problem in (Ben-Porat al., 2024) and thus has optimal solution. In the last step, we calculate the gap between the optimal solution of the approximated problem and the optimal solution of our original problem.
Step 1.
We start by rewriting Problem Pl. Notice that the welfare at each round can be written as
w. (x) = pa (x))((())))) + (1 - (--pe())))' = (x() (a(Di w²) + w".
Therefore, the social welfare can be expressed as W(x) Tw" + Et=1p(()) (a(Di(x)) w²). By denoting W W Tw" rewrite problem
max
(pi(x))
Σ Pe (x) (x(D,(x)) w²) 2 W
Step 2. We now build graph to represent an approximation of our problem. Notice that the maximum amount of data that can be generated in each round is 1 and therefore (x(x) < T for every t E [T] and scheme x. Therefore, given E > 0, we discretize all the available data values by increments of T' 2 We know describe the components of our graph. Our graph is a deterministic MDP with an underlying layered graph as follows: let = (SI.... Sr+1} the set of all states where S. = {09, se,.... ... s denote the state in the f'th layer where sy represents the state where GenAl is round t
22

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Selective Response Strategies for GenAI
82
$3
00.5
1/ =
R =
W = 0
82
$3
Figure 3: Example of a constructed graph with a discretization factor of & = 0.5.
with d data. The set of actions is A, and there are 2 reward functions defined for each state-action pair. First is defined by R(s v) = [rve(d, 1) while the second is W(s y) = Lug(d, y) (a(d) w=)]e- Next, we let T(s, 8') denote the transition function, which denotes the probability of reaching state by playing y in state s. The transition function in our MDP deterministic and defined by
(1 t =t= and d' [dd gg(d.y)le
T(s v.
Otherwise
In terms of graphs, the states are analogous to vertices, and Us, specifies an edge from state to state s', An illustration of this graph for 0.5 is presented in Figure 3.
By the construction of the layered graph, the horizon be the mapping between each state and the action GenAl should take in that state. For a deterministic MDP, a policy equivalent to path т, which in case is sequence of T edges starting from state of and leading state in ST+1- Notice that each edge represents state and action from that state, and therefore, path can also be defined sequence of state-action pairs.
1, and GenAl starts at state sf. We define policy x S
The problem we aim to solve using the graph is the following problem:
max Σ R(s.y/ y)
(P3)
(a.8)ET
s.t Σ W(s, 2 W
(&.y)ET
Step 3. Recall that a selective response strategy is vector that specifies the portion of queries GenAl should answers. We
denote xx that follows scheme x, that is x assigns the same action to all states at round as Z₁, formally π (*(() = Iy for every / E [T] and d E (T.)
We now introduce some notations that we use this step. First, we denote Ux(x) and (x( the accumulative revenue and welfare from round until T, following scheme x. Formally
U.(x) = ((x:)(xx)))))). mx)) (x),
W.(x) (x. (x))
w²) + W (x).
We now define the analog of U, and W, in our MDP. Let V s) denote the sum of rewards with respect to reward function R. following policy æ and starting state s in our MDP. Similarly, denote V (Iz, 8) the sum of rewards with respect to reward function W. Formally
(T sf)) R(s x(s)) + VO (T.
VW VW(T, sg)) W(s (s)) + VW (T,, oif ))
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Selective Response Strategies for GenAI
We ready compare the values of the revenue and social welfare following given selective response strategy those from the MDP. Let x be arbitrary selective response strategy and M max 1, J- We use the following lemma.
Lemma C.11. Fix round E [T], the every d E {O,E,... .T such that (-D((xx) (t 1)s it holds that
| * Ut(x) & eM Ei= 4
( - wx(x) & E(La + 11
Notice that Σ i < T and therefore we can simplify the summations in Lemma C.III
Given the optimal selective response strategy x", Lemma C.11 suggests that
(xx" st) 2 Ux(x*) =MT?
(nx 2)) Wi(x*) (La 1)
We finished Step and now move on to develop the machinery to find the selective response strategy that gives us the guarantees of our theorem.
Step 4. We define the Weight-Constraine Shortest Path (WCSSP) (Garey & Johnson, 1979). Given weighted graph G = (V, E') with weights {we JeEE, costs {ce hEEE and maximum weight W E R, the problem is to find the path with the
least cost while keeping the total weights below W. Let T denote a path, and therefore, the WCSSP problem is defined as
min Σ Ce
(P4)
CET
W. W.
Problem P3 can be seen as an instance of Problem (P4) for by setting:
c(s,))= R(s,v), v),
w(s,y) y) (W y),
W- -W1
To account for the approximation error in the welfare due to calculating it using the MDP, we choose W (W1 - (T. 1)).
Problem (P4) is a known NP-Hard problem with a reduction to the PARS-MDP problem (Ben-Porat et al., 2024) with deterministic transition function. The PARSE-MDP problem defined over an MDP with two reward functions RA, R S A R20 and budget B R22- The goal is to construct new reward function R. S A Rzo such that the total rewards over the whole MDP is less than B, and the induced policy that maximizes R + R also maximizes R under the constraint. Formally, the PARS-MDD is defined as follows:
max V(T, R²))
Σ R (s, B
(P5)
eES.VEA
R (s, 2 0 for every S.y A(s)
क E A RB)
24

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Selective Response Strategies for GenAI
where (T, RP) is the total of rewards from Re following policy æ. Therefore, make the following definitions represent Problem (P3) as instance of Problem (P5): First, denote 7 the path that maximizes RA, i.e 7 arg m E RA (s, v). Notice that 7 can be computed using standard methods which run in polynomial time with respect to the problem's parameters. Thus, we refer to A as a known parameter and define the parameters of PARS-MDP follows:
Rs(s,)) R(sss))) y),
(s, W(s, v),
B= E..EET (s (WI cTa 1)).
Notice that W, R are in increments of by the construction of our MDP. Therefore, can use Theorem (5) from (Ben-Porat et al., 2024) to show that the optimal path of Problem (P3) can be found in polynomial time with respect to the problem's parameters.
Theorem C.12. There known algorithm to compute the path which induces
SnEE Rº (s, max, Enger (C
Enyes R (s, 2 EsyerA (*, B.
in time O
0 log( (A!T))
Using the terms from our MDP, the solution from the algorithm in Theorem C.12 guarantees
ΣnNEr R(8,y) = max, Exyer R(s,y).
En W(s,y) W ( + 1).
Let be the path corresponding to x*. Notice that T" guarantees
Σ
W(s,y) (T
+ 11 W ET +).
The path 7* is possible solution of the PARS-MDP and therefore, by Theorem C.12, the path F guarantees
EeNEr R(s,8) 2 E. e.yEr R(s v) 2 U(x') eMT.
Enper W(s.y) 2 W - (L. 1).
Step 5. Let x be the selective response strategy corresponding to path F and we compare the revenue and welfare when playing &.
We begin with the following lemma.
Lemma C.13. Fix scheme Let (de)t= be the sequence defined by de 0 and de+1 (d), then for every E [T] holds that de < (x))).
Let (d.) be the sequence defined by d, 0 and d+t1 (dg, then by Lemma C.2 we get that
T
(G
#c))l 5
rygg(d,, i1))
(() b.))
(p)) (x)).
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Ar+1(Lo 1). Selective Response Strategies for GenAI
Therefore, it holds that
U(x)
U(x*) -MMT.
We move to evaluate the welfare. Notice that the welfare is not monotonic in ps. Instead of using our previous technique, we use Lemma C. 1 and get that
( 2 r (x, - ET + 1) 2 W - (T +1) ET 1)
W 2=1 2 (Le +1)
This completes the proof of Theorem 4.7.
Proof of Lemma C.111 We begin by showing that there cannot be a large gap between the data accumulated in the original problem and the data according to our MDP following the same scheme. Let A, (L - 1)e and [= y) [f(d, y)Je [d (d++1 yg( d. y)Js the data in the next round given that in the current round, GenAl started with d data and played y. We the following lemma show that the accumulated data in the MDP cannot be too far from the accumulated in original problem.
Lemma C.14. Let d E (0, and fix round t e [T]. If d [f)) < A then (f D++1(x)] < Ae41.
We now use backward induction to prove our lemma, starting at round T. Let ( T) such that ld - (x(()x) < Ar and we use the following lemma:
Lemma C.15. Let E ( T} and fix round E (T). 1f ( (x)x < A, then it holds that
MA
Therefore, by Lemma C.15 we get that
(T Ux)(x) = =[((rrg(d,x)) (()))(D(()) s M AA+1
Similarly for V and Wr. We the following lemma.
Lemma C.16. Let d', d E R2o and any y [0, 1] then it holds that
vaqld', y) (a(d') w²) yq(d .v) (a(dP) w²') ldd d (La 1).
Therefore, holds that:
VW "y(",, (Tx Wr[x)]
[[TTqd, xT) (a(d) x (a(Dr(x)) w0'll < |orald, aT) (a(d) - w²) - (a(D((x) w²'l +
ld - (x) (L +1) +E
AL + +1 +
We are done with the base case and can continue towards the induction step. Assume the lemma holds for round t + 1, and we prove it for round
26

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Selective Response Strategies for GenAI
We start with the revenue at round L. Let d (0, T and denote d' (dd, Then, for every such that
ld - (x)x < A it holds that
(T - U,(x)] = [r(rag (x))e V (44) ((x)g(D)(()) - U++1(x)
- [[r(zi 2.)) ( a.))) + (C sitt) - Ux+1(x)
We use Lemma C.15 to bound the first expression. Furthermore, notice that according Lemma C.14 it holds that vo 14+1) satisfies the conditions of our induction step. Therefore,
T+1 Σ 1=1+
(a Ux(x) S MA +
MA, = M Σ A++1 &M Σ i.
i=f
We perform a similar calculation for the welfare:
| (T*,,s²) s8) Wx(x]]
= -I(xgg(d,xx) (a(d) w²)l + VW =x.)))))))(((()))))))))))) --)- --++1((x)
< [kig(d, (a(d) w')le - zig (x), 21) (d(D((x))
w (=<tts5f+1)) W(+1(x)
T+1
< ATa +1) (Te + 1)
Σ A
T A (Tig + 1)8
T
= (Ti + +1)
i=t
This completes the proof of Lemma C.III
Proof of Lemma C.14. This is special case of Lemma C.7 and is hence omitted.
Proof of Lemma C.15. By Lemma C.6, it holds that
x)))) - r(=, x;)) s (r(ng(d; (D)) xx),) +
< Lr |,, x.) (ig(Dr()), +
Ly ld Dr(x)] +6
L A te
x AT+I max Lp, 1}.
This completes the proof of Lemma C.15.
Proof of Lemma C.16. We prove this by starting with the definition.
lgq(d,, v) (a(d") w²) vo 8) (a(d²) w*)l
ly (g(dd y) q(c v) q(d 8) (a(d)) w²) vg(de v) (a(d)) w¹)l
< leqld, v) (a(d') w²) - yq(d 3) (a(d3) - w¹)l
+ lu (g(d', .y) - q(d,, w)) (a(d') - =
lo v) (a(d") w" -a wx)l + ly (a(d) y) -
-(d (((2v))) (a(d") w²)
lug(d?, v) .))
(a(d") a(d))) ly (g(d) w) g(o2, w)) (a(d') 10)--w- w²)l
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Selective Response Strategies for GenAI
We Lemma C.6 and therefore
wa(d', v) (a(d)) - w²) - yq(d. y) (a(d)) - w¹)l
I uu((d, v) (a(d") a(d")) + |d' dl aa(d)) w²1
uq(d, v) la(d") - -a(d)) = dd' -d | w01
S yq(a, La d' d |d d² | {a(dd)) w"
Notice that y, g)) a(d'), w² < 1 and thus we get that
lpbed u) (a(d') - w²) - (q((2,)) (a(d²) w²)
S La dd - dl + +Id -d (La + 1) ld - df
This completes the proof of Lemma C.16.
Proof Lemma C.13. This is special case of Lemma C.4 and is hence omitted.
D. Proofs Omitted from Section
Proof of Theorem 5.1. We use the following lemma.
We define h(y, x)) = x poou y + (1
Pxy
Bov eRoy -en wx and observe that wx(x) = h(a(D,(x)), z1). We analyze cach
property separately.
1. If (x) 2 C. From Proposition C.I, for every t> it holds that (x(x)) de(x) and therefore w/ (x7) w/ (x) C.
Notice that
dh(y, x)
2²3
1 (www + e f(w (y w²) + x
dy
1
((w
2 x²3
ef(w" 1 8(w xz) (ry - w²) + + c3(we-sy))
1
2 2²3
El (ww- [w zg) rry w²) + x²²
+ (0("-=zz)
=
B + ((w"r-yy) + e f('= (xy w²)
+ ef(w"-
Therefore, for every x > 0, if 3
1tel( -aol 1 -tw -uyj (ry - -2²) + Itella*- 0 then it holds that dl((v.2) dy
>
0
Next, we define the auxiliary function x(v,x)= = e eoute y/ + (1 (1-2 x esu teuue
w² and notice that
dg(y, dy
x @B(w"~ + e- kww (y w²) + x
1 + eww
Therefore, for every x it holds that
dg(y, x²)
= sign (s (
sign
(ww + e B(w= - vi (y w²) +
dy
+ ((w
and by definition of g .z) get that for every x, y such that y Tz and delv.w) Now, we use the following lemma:
0 then
dbly' .2) 0.
dy
dy
28

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Selective Response Strategies for GenAI
Lemma D.1. For every it holds that
dg(y.z) m) dy
sign
sign(y - C).
Thus, according to Lemma D.1 it holds that if w((x)) we(x"" (x") >> (x).
(x) > C' then h(a(D)(x")), > h(a(Di(x)) x4) and equivalently
2. For the next two properties, we show that there exists yo IR such that for every x >> 0 it holds that dh((o..))
dy < O.
First, we rewrite dh(y..))
dy
dh(y, x)
1
x²6 3-
+ e -(w( -ay) (y w²) ef(wu-aay
dy
+
p0(w 22y)
1
1
1 + r/
(u w²)
1 1
6-((w--zg)
1
1 x
I1w" -zy
+ 6-((w--xp)
1
1 + 8
+ e B(w" -zy) Ty
1+ 8:w"" -yy
Notice that x "1+) and therefore if Muu-y ty then dh(g.a) dy
0.
1te
Next, observe that
lim 1 3
1 e Blw my) Ty = lim 1 1 Bry -os
Let h(yx)) = 1 B 1pe--(u--nn ry. Since dh(y.z) is continuous in y, and hyy x) is continuous and represents a lower dy
bound of (yzz,, it holds that there exists such that if yz 2g then dh(yaz) Next, the following observation:
dy < 0.
Observation D.2. For every and y < 20 it holds that dh(y.z)
O.
dg
We denote C" = 20 Using Observation D.2, if a(Dr(x")) < C" (which means that wx(xx) < zp) then (x")) < h(a((D(x)))
2.
3. The result h(a(D, )), xnf) (x(D.(x)), follows immediately from the previous arguement.
This completes the proof of Theorem 5.1.
Proof of Lemma D.1. Fix x E [0, 1] and we denote g(v) xg(y)y + (1 =g(y))"". The derivative g(y) is
ev e tou Therefore, g(v) can be written as g(v)
dg(v) dÿ(y) y xQ(v) dī(v)
dy w² dō(y)
dy (y w²) xr(1)).
(5)
dy dy
Notice that q(y) is sigmoid function and therefore dūlu)
Bī(y) (1 ((v)). Plugging this result in Equation 5 results in
dg(v) xg(21) (1 ((v)) Bly - w²) + xQ(y).
dy
29

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Selective Response Strategies for GenAI
Next, notice that ((y)
We denote = Bly w²) and get
Itep(e
dg(y)
1
1
dy
1+e==+te
1te=
1
(1+=22+]
lte
1
2+lte
1te
1t
e+tl
1+e=++e" (Itt +e-1)
Therefore, to find the yo that results in dy y= = 0 is equivalent to finding the solution of
(= + 1)+1 (++1) + +e- = 0.
Denote -- 1) and we have the inverse of the Lambert function
Ee = ee"
and therefore ī = -V(e")) )), which leads to 20 WWe 1) - 1 and yo W(e *) w === C.
Next, denote h(2) (z + 1)e-(x+1) + e and notice that the sign of dg is determined by the sign of h(2), that is dy
sign( sign(h(z)).
The derivative of (=) is given by
dh(2) =c + ((-11= -1 e (x+1) -ze -(++1)
dz
Therefore h(2) an increasing function for = < 0 and a decreasing function for > 0. Recall that h(20) 0 and 20 -1 < thus l(z)) < for every < ōn- Furthermore, lu(z) is an increasing function in z E [zo. 0), therefore it holds that h(2) > 0 for every (20, 0). Lastly, notice that for every 2 0 it holds that 1 > 0 and e-(++1 O. and such summarize that h(2) 0 for every 2g.
This completes the proof of Lemma D.I.
Proof of Observation D.2. Let y for any y1 y* < 8 get that
20, First, observe that if dk(y',a) dy
then must hold that y* < w". Furthermore,
0 >>> 1 + x + Blw myr) (y" w²)
+ x3
+ F(w x (y1 w²)
+ x,
+ e 3(w0-181) (v1 w²)
E. Proofs Omitted from Section 6
E. Proofs Omitted from Subsection 6.2
Proof of Corollary 6.2. First, notice that for every S T it holds that D,(x) DxTx)). Next, from Lemma C.8 it holds that for every / > т, the data satisfies
[D+(x) D.(xT) < [x)+1(x) (x 1x)(x) -p- (x(('))
30

---

Selective Response Strategies for GenAI
Therefore, we can bound the revenue:
- S (((x)))>>(((( - + Ty
Σ
(m((("))pp()))
-pp))-preh px(x)).
1=T+1
By Lemma C.6 we get that
T
- (x)) + Lr - ( (x-oxxx)(" -
Σ
(D,(xx)
- (x()))
1=++1
T
5 (r(e((x)) (x))) L (x) Pr px-(x))
Σ
?
(=++1
5 - r(pr (x))) + L,,"" P- D+(xx) - -P (x)
1 1-9
This completes the proof of Corollary 6.2.
Theorem E.1. Let min t> T4 > 0} and k
B Aminpe m.
de( 401+e
1f BL S 1, then
- -(())-
Nー (x(x r(p, T,n> Px²")((x") Pr (x)
1 7(1 kx 2)
Proof of Theorem E.1. By definition, we get that
T
T
U(x') Uxx)= =
x" (px((x)) - - ~x-xx((((x))
-
t=1
1=1
1-1 (r(p((x)) (x((xx)))
Σ
1-1
- -r(x(())))r(((x)))
= - - -((x))))))((()))))
Σ 7- - -((xxx
1=
(rl, (x)) + L,
Σ (p((x) -x)(
t=7+1
Next, we use the following lemma to get an upper bound on px(x)) p((x).
Lemma E.2. For every >> T it holds that
1-1
g²
0 S (x(") Pr(x) & (x) Pr (x=)|
II
1
x
3Lo
4
1m++1
Therefore, according to Lemma E.2, it holds that
T
1-1
x² xx
- S -- -T (r(p)(x3) ( + Ly
Σ (x) -
-x-(x")
II
1
BL
t=
imr+1
T
t-1
Σ
II
1
x
LL
t=
#=
31

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Selective Response Strategies for GenAI
We now simplify the second term using the following lemma.
Lemma E.3. It holds that
T
q²
T
q²
t---1
Σ
1
L
S
Σ 1=7+1
x-1
1
x
L
4
(=++1
i=++1
Therefore, we get that
f
U(x)) U(x) 5- (r(x(x()))))) r(p-(x)))) (xx(x)x p+(x Ly
Σ
71=1
1
2 LL
A-1
= =-- (r(,, - (x, (p, p+ L,7
1
x
L
4
Notice that T-T gp-1 (1 1- I2
t-1
is a sum of a geometric series, and therefore it holds that
T T-
q²
--
(7 (1
o 1 BLg
T-r
f-1
x
La
4
7 1 T 22
-1
Thus, we conclude that
S S-- (r(p+(x3)) (((-((x)))-((x(x))) + 1+((x) p+(xx) Lay? (7 (1- 2² 3
P-t
7 (1 2-2 B2
-1
This completes the proof of Theorem E.
Proof of Lemma E.2. We start from the left inequality. From Theorem 4.1 it holds that (x(x)) 2 pr(x) for every > We move on the right inequality. For that, we use Lemma C.6 and get that
px(x') (x) < Dx(x") (x)..
Next, couple it with the following lemma.
Lemma E.4. For every > T it holds that
q²
0 Dx(x)) Dx(x) s (x) (x())
II
1
x
BL
4
i=71
Therefore, we conclude that
px(x²) - Px(x) <x)(x)) -D(())
q²
$ (l(((x) p+(x))
II
1
3
3m
4
(=++1
This completes the proof of Lemma E.2.
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Selective Response Strategies for GenAI
Proof of Lemma E.7. We expand according to the definition:
Ba(D")a" ym²
)a(D))
la(D", " 2((22,00)))
eBa(D-)at + 6 eBa(Di)a² + e
eaa(DD)at
(cBa(D))a² + +ell") eBa(DD)u² (BBa(D))at + eBw"
(eAa(D!)at + eBww (eBa(DA)a² eBrun)
@a((Dt)a' @Ba(Di)2²
Buu
(eBa(D')x' e (e + (umg
1 - ( (_e((""((""=-aaaa()) ((
Bu" ga((D)x
(cfa(D1)z ) + (000)) (
a(D', ,-') (1 x(D2xx²))
q(D xx)) ) (1 (D² x²2) (f
This completes the proof of Lemma E.7.
Proof of Lemma E.4. We prove by induction, starting with the base case at t + 1. By definition,
(x)+1(x)= - D++1(x")) =>> - (x( Dr(x") + p=(x))]-
Since (x)x) (xT) we get that
Dr+1(x) - Dx+1(x")|= (xx - Pr (x')l.
Therefore, we can conclude the base case. Next, assume that the inequality holds for + and we prove for +
We use the following lemma:
Lemma E.S. For every >> t + holds that
-² LL (Dc(x) De(x")) 1-
[x+1 D s
4
We plug the inequality from assumption into the inequality of lemma E.5, Therefore, get that
q²
[De+1(x) D1+1(x*)) 5
1
La
ID((x) Dx(x²)
2 LL
(Di(x') Dc(x))
q²
g² x
LL
1x+(x) pr px7))
LL
q²
[x(xx) - (x()")
1
x
4
1=++1
This completes the proof of Lemma E.4.
33

---

Selective Response Strategies for GenAI
Proof of Lemma E.5. By definition,
[D--(xx) (x)) (x)( Dx(x") pe((x)))))))) - pr(x)]
Since x, then from Theorem 4.1 it holds that (x Dx(x) and px(x*) > Pa(x) for every t > Next, we get an upper bound using the following lemma, which suggests lower bound for the proportions.
Lemma E.6. For every > it holds that
L { 1.3L (D( -x(xx))
44"
Using Lemma E.6, we get that
[D)+1(x) - D=+1(x")] = -D((x)xxx)>>))))) - Dx(x) + px(() - -Pr(x)
DD((')) D,(x) L-
29 (Di(x') - -)(x))
4
(Di(x²) -x)())
(1-
(1
4 2i 3L
-º
-º x 3La
[D((x) Dx(x'))
This completes the proof of Lemma E.5.
Proof of Lemma E.6. From Theorem 4.1, for every t > 7 it holds that D((x²) > Dí(x). Therefore, we get that a(D:(x")) )) > (x).. Furthermore, from Proposition C.2 it holds that ((D, (x))..)) 2 (xD,(x), 2t). Thus, we use the following lemma to write ((Pr(x)), x) - (x), differently:
Lemma E.7. For every D D'DD² E [0,T] and x x² E [o, 1] it holds that
xx)) yD x²) (D)) x (1-1(1',,
,(D),,2))
-
Therefore,
(6)
= +x(D)(x'),)) (1 q(D) -
Notice that ((D,x), (D),x) 2 q for every E [0, and [0, 1]. Furthermore, it holds that Ja(D2) - aa('))
Lag 2
D=| Therefore,
L - - { (x()) - -L
- -D+(x))).
Notice that Le (D(())))D((x)
-D((")) < 0 and therefore [1 - (I-
Plugging
everything into Equation (6) results in the following inequality:
2 - (X))) )
Next, we show that rBLL (D((x) - D2(x 1. For that, we use the following lemma.
Lemma F.8. For every > T holds that (D(()) D+(x 1.
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Selective Response Strategies for GenAI
Therefore, get that
2.L1aa [Dx(x) - -D((T)) S aBL S BLa S BLg 1.
Thus, we can use the inequality |1 ed1 2 |ol for |a| S 1 and conclude that
L
(D,(x'), - (x),(x),,) 2 23 (D:(x) D:(x')
q²
4 23 (Dr(x") - Dr(x)).
This completes the proof of Lemma E.6.
Proof of Lemma E.8. By definition, we get that
[D((x) Dx(x")1 ) (D)-1(x) + (1 - (x- (x-1 (1 p(-1(x")))
(D) Pt-1(x) D (x=) + px-1
-x-1(x²)) - (x) + Pr (x) Pt- (x"). 1
Observe that the proportions satisfies that (x) - (x=) S 0. Therefore,
DD(x)) Dx(x=)l S (D=- Dx-1(x))
Thus, by induction it follows that
- -x(x) S [D++1 (x) - D++1 (x*) [D+ (1 pr (x)) -Dr(x") - -(1 (1- (x-x(()))
1x- px(x 11
This completes the proof of Lemma E.8.
Proof of Lemma E.3. Let t' > T be the maximum t' E [T] such that zv 0. Therefore,
1
x
2
BLg
t-1
T
d²
1
2LL
+
-
1
_ x
LL
|=#+1
#=
L 2
T
1
LL
1
2 B L
|=:+1
i=11
35

---

Selective Response Strategies for GenAI
We now focus on the second term:
q²
T
q²
1
2 LLg
Σ
1 -
2
La
4
1=
(=7+1
1=t++1
(=++1 fist"
q²
Σ
1
t=t'11
i=7+1 igft!
T
q
1-7-2
=
Σ
t-1
1
LL
1
q²
Σ 7
1
2 3L
4
x²
1-9-1
1
1
LLa
-²
1-9-1
f-1
1
33L
4
Therefore, we conclude that
q2 4
9² x
T
_² x
t-r-1
II 1=++1
1
27 LL
1
LLa
x-1
1
LLa
4
1=++1
(=
+=++
At this point, we iteratively apply it while going backward using backward induction. each step, we take the latest round t' such that x/= = 0 and apply the equation above to the first term. Ultimately, we get that
b---1
L2 r
Σ 1=T+1
1
x
LL
S
Σ tm7+1
1-1
1
=²
LLa
This completes the proof of Lemma E.3.
F. Simulations
In this section we provide empirical demonstration of the effect of selective responses.
Experimental Model We set our model with the following parameters: T 50, w a 1 1 and r(p) nd for a E R. We show our results for varying values of 8, y and Ideally, we would compute the optimal selective response strategy for each set of model parameters, but doing requires using fine discretization of the range [0, for each selection of x4. To ease our computation for large values of T, we choose the optimal selective response strategy in the set of cutoff strategies. We denote by X. the set of cutoff strategies, namely, the set of all strategies in which GenAl remains does not answer until a specific round and fully responds thereafter. Formally, for every strategy x E Xx, there exists 7 E T such that x, = 0 for all f < T and 2; = 1 for all t 2 т. For each set of model parameters, we calculate the optimal cutoff strategy to maximize GenAl's 's revenue and plot the differences in GenAl revenue and the users social welfare relative the revenue and welfare induced by the full response strategy.
Experiment Setup We report the induced revenues and welfare from 60 instances. We used a standard PC with intel Core 17-9700k CPU and 16GB RAM for running the simulations. The entire execution took roughly hour.
36

---

Selective Response Strategies for GenAI
1
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
1.5
2
2.5
3.5
1.5
2.5
3
3.5
(a) Revenue difference
Welfare difference
15
15
8
10
8
10
0
1.5
3.5
2.5
3.5
(c) Revenue difference
(d) Welfare difference
Figure 4: Revenue and welfare difference between the GenAl's optimal cutoff selective response and the full response strategy function of the revenue scaling power and temperature B.
F.1. Results
Figure 4 illustrates how GenAl's revenue (users' social welfare) changes with respect to the discount paramter 7, the proportions scaling power a and the sensitivity parameter 3. Light colors indicate high differences in the revenue and social welfare, while darker colors indicate lower differences. Figure 4a and Figure 4c shows the difference between the optimal cutoff strategy and the full response strategy in log scale. Formally maxxex. U(x) U(x). Figure 4b and Figure 4d illustrate the difference in the users' social welfare between GenAl's optimal cutoff strategy and the full-response strategy. Formally we compute W (x) (x) such that maxxex. (xx).
In our first experiment, we set | = and computed the revenue and social welfare for various combinations of a and As shown in Figure 4a, revenue increases with both a and y. Observe that decreasing the discount factor and increasing the power a can have opposing effects on revenue. A lower y makes GenAl more myopic, favoring strategies that maximize immediate gains from current proportions. Consequently, tends to adopt strategies close to full response, resulting in minor revenue differences. In contrast, higher a amplifies the influence of high proportions on revenue. This drives GenAl the cost of short-term revenue, leading more long-term approach.
to prioritize increasing the proportions,
Figure 4b presents the social welfare as a function of a and Although users' welfare does not explicitly depend on GenAI's discount factor we observe six distinct regions with uniform color. This dependence arises through GenAl's strategy. which is sensitive to 7. Within each region, GenAl adopts the same selective response strategy across all combinations of a and y. As discussed in Section 5, using a selective response when GenAl is inaccurate improves social welfare. This typically occurs for small values of f, when GenAl prioritizes future proportions, which is the same underlying reason
37

---

Selective Response Strategies for GenAI
behind the observed increase in revenue as and y grow.
Figures 4c and 4d show the differences in revenue and welfare functions of the temperature 3 and the power parameter When 3 = O, users are indifferent between platforms, regardless of the utilities they receive. In this case, the accuracy of GenAI, and therefore the data it accumulates, has no impact on user decisions. As result, choosing a selective response can only reduce both GenAl's revenue and social welfare.
As 3 increases, users become more sensitive to utility differences, and value the data GenAl accumulates becomes more apparent. This leads to two opposing effects. First, selective response allows GenAl influence the amount of data generated in each round, which in turn affects how many users choose GenAL. Second, when becomes very large, the effectiveness of selective response decreases. In this case, user behavior resembles a best response dynamic: as long as GenAl's s utility is lower than that of Forum, users prefer Forum and generate data there, regardless of GenAl's strategy. Once GenAl's utility exceeds that of Forum, the optimal strategy is to always choose the full response, since users will consistently choose GenAI.
Notably, the welfare in Figure 4d exhibits the same pattern as the revenue, but in a more nuanced fashion. This because welfare influenced by both GenAl's response strategy and 3. From Theorem 5.1, it follows that the threshold C' increases with 8, and therefore using selective response when the utility from GenAI is below C may lead to a decrease in welfare. This results in a cyclic pattern in welfare when is held constant.
38


Reviews:
[{"review_id": "XLkkAdHcMi", "reviewer": "Reviewer_E2o5", "summary": "The paper introduces a novel strategy called \"selective response\" for Generative AI (GenAI) systems, particularly in the context of human-based forums like Stack Overflow. The main idea is that GenAI could strategically provide inaccurate or conservative responses to queries involving emerging topics and novel technologies, thereby driving users to use human-based forums. This approach aims to create a compounding effect on the data generation process, ultimately increasing both GenAI's revenue and user welfare in the long term. The paper presents a game-theoretic model to explore the dynamics of content creation, welfare, and revenue. Key contributions include:\n\n- Conceptual Contribution: The paper is the first to explore selective response for GenAI, proposing a model where GenAI strategically chooses when, if, and how to engage with user queries.\n\n- Technical Contribution: The authors demonstrate that selective response can Pareto-dominate the always-responding approach, improving user welfare and GenAI's revenue. They also provide an approximately optimal algorithm for maximizing GenAI's revenue under social welfare constraints.\n\n- Regulatory Perspective: The paper derives sufficient and necessary conditions for selective response to improve welfare improvements, offering insights for regulators.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer's thoughtful and positive evaluation of our work.\n\nRegarding \"*The paper does a good job of citing relevant literature, but it could benefit from discussing more recent work on the interaction between AI systems and human content creation platforms*\". Given your advice, we have discovered [1-3] below, which we intend to address in the paper. If you have additional pointers to relevant work, we would appreciate it.\nAddressing the reviewer's specific questions and concerns, \n\n1. Regarding \"*How do you envision the practical implementation of selective response in real-world GenAI systems?*\" Platforms like Stack Overflow, providing both GenAI services [4] and user-driven forums, could implement selective response mechanisms. In the broader GenAI market, companies may need to establish contractual agreements governing the use of selective responses. For example, platforms could selectively respond to queries about emerging topics by withholding answers when the LLM of all major companies' confidence falls below a predefined threshold. Given your question, we shall elaborate on this aspect in the paper.\n\n\n2. Regarding \"*Have you considered the ethical implications of selectively withholding information from users? How might this impact user trust and satisfaction?*\" Choosing not to answer may be beneficial when GenAI is uncertain about the correctness of its response (or if the response is not sufficiently accurate). In such cases, users may appreciate transparency if they are informed in advance that the expected answer quality is low. We do acknowledge that aggressive selective response could lead to an undesired behavior if this transparency is perceived as unreliability. Indeed, our work suggests opportunities and freedom to apply selective response strategies to real-world systems. We shall address this in our discussion.\n\n\n3. The reviewer asks, \"*Could you elaborate on how the model might be extended to account for multiple competing GenAI platforms?*\" Multiple GenAI platforms could induce a Prisoner's Dilemma-like interaction. If one platform chooses to withhold responses, it benefits all other platforms while preserving the same data generation dynamics as always responding. Conversely, if all platforms choose to withhold, they would collectively be better off. In this scenario, the payoffs (expected revenue) depend on the decisions of all platforms as well as user preferences. As in the classic Prisoner's Dilemma, collective cooperation (i.e., not answering) could be enforced through contracts or incentivized by other means. This is a fascinating research direction, and we intend to expand on it in our discussion, thanks for bringing this up.\n\nReferences:\n\n[1] R Maria del Rio-Chanona, Nadzeya Laurentsyeva, Johannes Wachs, Large language models reduce public knowledge sharing on online Q&A platforms.\n\n[2] Gordon Burtch, Dokyun Lee, Zhichen Chen, The consequences of generative AI for online knowledge communities.\n\n[3] Xinyu Li, Keongtae Kim, Impacts of generative AI on user contributions: evidence from a coding Q&A platform.\n\n[4] https://stackoverflow.blog/2023/07/27/announcing-overflowai/", "claims_and_evidence": "The claims made in the paper are generally supported by clear and convincing evidence. The authors provide a detailed game-theoretic model and derive theoretical results that support their claims. For example, Theorem 1.1 and Theorem 1.2 are supported by rigorous proofs and examples. The paper also includes a discussion on the long-term effects of selective response, supported by Theorem 4.1 and Theorem 4.4. However, some claims, particularly those related to the practical implementation of selective response, could benefit from more empirical validation.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are appropriate for the problem at hand. The game-theoretic model is well-suited to analyze the strategic interactions between GenAI and human-based forums. The authors use a sequential setting over discrete rounds, which allows them to explore the dynamics of content creation, welfare, and revenue. The evaluation criteria, such as the accuracy function and the utility functions, are well-defined and align with the objectives of the study.", "theoretical_claims": "The theoretical claims in the paper are supported by detailed proofs. For example, Theorem 4.1 is supported by a proof sketch that demonstrates the compounding effect of selective response. Theorem 4.4 is supported by an approximately optimal algorithm (ASR) and its analysis. The proofs are generally clear and convincing, though some technical details are deferred to the appendix, which is common in theoretical papers.", "experimental_designs_or_analyses": "The paper is primarily theoretical, and as such, it does not include experimental designs or analyses. However, the theoretical analyses are sound and well-justified. The authors provide examples and simulations to illustrate their findings, which help to validate the theoretical results.", "relation_to_broader_scientific_literature": "The paper is well-situated within the broader scientific literature on generative AI and game theory. It connects to emerging research on foundation models, competition between generative AI and human content creators, and the impact of generative AI on content diversity. The authors also draw on economic literature on information design and signaling, which adds depth to their analysis. The paper builds on prior work by introducing a novel approach (selective response) and demonstrating its potential benefits.", "essential_references_not_discussed": "The paper does a good job of citing relevant literature, but it could benefit from discussing more recent work on the interaction between AI systems and human content creation platforms. For example, recent studies on the impact of AI on user behavior and data generation in online forums could provide additional context for the proposed selective response strategy.", "other_strengths_and_weaknesses": "Strengths:\n\n- The paper introduces a novel and creative approach (selective response) that has the potential to significantly impact the development of GenAI systems.\n\n- The theoretical analysis is rigorous and well-supported by proofs and examples.\n\n- The paper provides valuable insights for both GenAI companies and regulators, making it relevant to both academic and industry audiences.\n\nWeaknesses:\n\n- The paper is primarily theoretical, and the practical implementation of selective response is not explored in depth. Empirical validation would strengthen the paper's claims.\n\n- The model assumes a single GenAI platform, which may not fully capture the complexities of real-world scenarios with multiple competing platforms.", "other_comments_or_suggestions": "The paper is well-written and clearly presents its contributions. However, it could benefit from a more detailed discussion of the limitations and potential challenges of implementing selective response in practice. Additionally, the authors could consider exploring the ethical implications of selectively withholding information from users.", "questions_for_authors": "- Question 1: How do you envision the practical implementation of selective response in real-world GenAI systems? What are the potential challenges and how might they be addressed?\n\nResponse Impact: A detailed discussion on practical implementation would provide more confidence in the feasibility of the proposed strategy.\n\n- Question 2: Have you considered the ethical implications of selectively withholding information from users? How might this impact user trust and satisfaction?\n\nResponse Impact: Addressing ethical concerns would strengthen the paper's relevance and appeal to a broader audience.\n\n- Question 3: Could you elaborate on how the model might be extended to account for multiple competing GenAI platforms?\n\nResponse Impact: Extending the model to multiple platforms would make the analysis more robust and applicable to real-world scenarios.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "F9kodebyVq", "reviewer": "Reviewer_TMmF", "summary": "In this paper, the authors introduce a selective response model where a \"GenAI system\" behaves strategically -- e.g, giving lower quality response, does not respond, etc. They provide a game theoretic based proof that shows that selective response can be beneficial in practice, when the other option is to utilize a human-based forum.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer's positive and helpful feedback, we hope to leverage it to improve our paper.\n\nIndeed, our work  \"*is also related to algorithmic deferral.*\" We thank the reviewer for making this connection, which we weren't aware of. We shall address the two papers in our related work.\n\nThe reviewer mentions that \"*the scope of such selective response strategies in the real world could be considered more closely,*\" asking whether \"*actively withholding knowledge possible.*\"\n\nWe believe that selective responses are indeed feasible. To exemplify, recommender systems often face exploration-exploitation tradeoffs, where taking a risky action today (uncertain whether the user will like it or not) trades present rewards with future gains. In this example, the system \"selectively\" chooses the non-myopic option (sub-optimal in the present) to gain information to improve its utility in the future. In our paper, GenAI prefers inaccurate answers and (slightly) unsatisfied present users with more accurate answers and satisfied future users. \n\nDoes this make sense? We came up with this argument while discussing your review. If you find it convincing, we can elaborate on it and include it in the paper.\n\nAnswering your specific questions, \n\n1. Regarding extending on \"*how models would scale to multiple GenAI agents.*\" Multiple GenAI platforms could induce a Prisoner's Dilemma-like interaction. If one platform chooses to withhold responses, it benefits all other platforms while preserving the same data generation dynamics as always responding. Conversely, if all platforms choose to withhold, they would collectively be better off. In this scenario, the payoffs (expected revenue) depend on the decisions of all platforms as well as user preferences. As in the classic Prisoner's Dilemma, collective cooperation (i.e., not answering) could be enforced through contracts or incentivized by other means. This is a fascinating research direction, and we intend to expand on it in our discussion. Thanks for bringing this up.\n\n\n2. Regarding \"*do we expect value in any action except choosing not to produce an output vs producing an output?*\" Just to be sure: Does the reviewer mean answering with varying quality? That is, could it provide lower-quality answers than GenAI could produce deliberately? If that is the case, from a theoretical perspective and for our purposes, there is no substantial difference between providing low-quality answers to all users or providing the highest-quality answers to a subset of users. All the theoretical results extend to lower-quality answers as well. Selective response serves as the mechanism for controlling whether GenAI invests its full efforts with the hope of driving users to generate more data.", "claims_and_evidence": "Claims are well-supported by evidence", "methods_and_evaluation_criteria": "The work is primarily theoretical", "theoretical_claims": "Mathematical proofs were not thoroughly checked", "experimental_designs_or_analyses": "- The game theoretical model makes sense, though it debatable how ethical some choices (e.g., providing partial knowledge etc.) is meaningful. Under this case, the two actions that GenAI can take seem limited (either generate or defer).\n- The utility of such an approach in a real-world setting (via simulation) would have improved the paper, and clarified the findings", "relation_to_broader_scientific_literature": "- The work relates to optimal policies that GenAI should adopt, assume a multi-competition market\n- The work is also related to algorithmic deferral [1], which the authors have not considered explicitly in the related work section \n\nReferences:\n[1] Hemmer, Patrick, et al. \"Learning to defer with limited expert predictions.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 37. No. 5. 2023.", "essential_references_not_discussed": "- The authors could connect their work to the selective prediction / deferral literature  (though their model is different from standard prediction-based tasks studied in prior works) -- for example, [1,2]\n\n[1] Hemmer, Patrick, et al. \"Learning to defer with limited expert predictions.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 37. No. 5. 2023.\n[2] Mozannar, Hussein, and David Sontag. \"Consistent estimators for learning to defer to an expert.\" International conference on machine learning. PMLR, 2020.", "other_strengths_and_weaknesses": "- Work addresses a meaningful gap in literature, and clearly elucidates limitations (e.g. assumption of single algorithmic competitor, non-strategic forum behavior, etc.)\n- However, the scope of such selective response strategies in the real world could be considered more closely -- for example, is actively withholding knowledge possible?", "other_comments_or_suggestions": "- Can authors expand on how models would scale to multiple GenAI agents?", "questions_for_authors": "- Can authors expand on how models would scale to multiple GenAI agents?\n- Do some of the selective actions -- for example, actively withholding knowledge -- seem feasible in the real world?  That is, do we expect value in any action except choosing not to produce an output vs producing an output?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "UeqeeyhNqv", "reviewer": "Reviewer_KDdP", "summary": "This paper contributes a framework for optimizing model generation for data generation  (e.g., encouraging engagement on a forum) and long-term revenue rather than for quality and completeness of response. The authors adopt a two party model where a generative model and a forum share a user set. Over a series of time steps, users decide between GenAI and Forum by comparing the expected utility they derive from each platform. Notably, the GenAI utility is defined by a cumulative data function while the Forum utility is constant. They then show the always-responding condition is Pareto-dominated by selective response, contrasting social welfare and GenAI’s revenue.\n\nThe authors' model closely relates to economics papers like Bergemann & Bonatti (2024) and McIntyre & Srinivasan (2017), which consider how platforms & data accumulation, shape user experiences and firm outcomes. To this end, the contributions are specifically a framing of how selectively *not* responding may benefit the overall ecosystem.", "questions": "", "limitations": "", "rating": 5, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the useful feedback and for finding our work novel.\n\nWe find the works you mentioned, namely Bergemann & Bonatti (2024), McIntyre & Srinivasan (2017), and Shumailov et al. (2023), highly relevant and will incorporate them into our literature review. Thank you for pointing us to them.\n\nRegarding the \"*assumptions that introduce some weaknesses to the work*\", we fully agree with the reviewer's observation. Our goal was to present a simplified and clean model to highlight the conceptual benefits of using selective responses. While our assumptions impose certain limitations on our results, we have carefully ensured that each assumption is well-motivated. Additionally, we believe that some assumptions could be relaxed while preserving the conceptual contribution, though this will come at the cost of less clean results. We thank the reviewer for bringing this up, as we believe that addressing this point would be a great addition to our paper. \n\nThe reviewer mentioned that \"*The softmax definition of user choice is symmetric and memoryless… It doesn't account for any of the following effects: (1) User stickiness (2) Frustration penalty if GenAI gives poor/no answers (3) Platform trust*\". The reviewer is correct in pointing this out as an aspect we do not address. Capturing all possible factors in a single model is challenging and often makes theoretical analysis impossible. Therefore, these aspects are fascinating research directions that offer opportunities for new stylized theoretical frameworks as well as comprehensive empirical work.", "claims_and_evidence": "1. This work is a purely theoretical paper with no experimental data, simulations, or case studies to validate the claim that selective response increases data quality or user welfare. The work falls closer to traditional economics than representative learning, but it is topically of great interest to the ICML community.\n\n2. The paper does what it claims, with a number of assumptions that introduce limitations or constraints on its usefulness. For example, the assumption that Forum utility can be treated as a constant is surprising through perhaps reasonable simplification. Forum utility can also be a function of cumulative content or user engagement, which may add complexity to the analysis but benefits the GenAI system (GenAI gets more training data for new content, at a compounding rate)--and can be done without extending into two-player strategic games. The concept of “not responding” is homogenized, but in practice there are substantive differences between refusal, incorrect information, and redirection (sending users to the Forum), each of which would have different effects on user experience, and similarly offer different penalties. These simplifications are largely fine, however, given this is an idealized model. \n\n3. The softmax definition of user choice is symmetric and memoryless (though includes a sensitivity parameter that captures users’ responsiveness to utility differences). It doesn’t account for any of the following effects:\n(1) User stickiness (repeated use of the same platform)\n(2) Frustration penalty if GenAI gives poor/no answers\n(3) Platform trust (e.g., if GenAI’s quality fluctuates, do users downgrade expectations?)\nall of which are important context for the argument that GenAI platforms benefit from refusal / incomplete responses. To be more concrete,  single-round decisions are a significant simplification.", "methods_and_evaluation_criteria": "There is no substantive evaluation as this is a theoretical paper.", "theoretical_claims": "I read carefully through 4.1. Selective Response Implies Increased User Proportions and Appendix D.1. They are correct, though the proof is parameter-sensitive and assumes exact retraining each round, no delays or stochasticity. Again, as this is intended as simplified model of the setting this is reasonable. I do, however, believe the paper would benefit from further exposition on the limitations of the work.", "experimental_designs_or_analyses": "There are none.", "relation_to_broader_scientific_literature": "This paper offers a novel framing for how GenAI providers might choose to give partial / incomplete / no information in response to key queries, thus incubating discourse and data production on alternative platforms (ensuring additional data is available in the future). The framing is nice, though substantively limited, and as a first step offers several directions for future work to build upon.", "essential_references_not_discussed": "The related works are largely covered within the paper. The authors may be interested in extended discussion contrasting generated data with human-produced data, such as Shumailov et al. (2023), “The Curse of Recursion: Training on Generated Data Makes Models Forget\" as further motivation for emphasizing human data production.", "other_strengths_and_weaknesses": "The setting is novel and of interest to the community. The paper is generally well-written. There are a number of assumptions that introduce some weaknesses to the work. More substantively, given the ICML setting, there are no simulations or other forms of evaluation to show the model holds in practice.", "other_comments_or_suggestions": "The regulator's capabilities are barely sketched. It would be nice to include further discussion on this point by the authors.\n\n*** I have updated my score to reflect the authors continued rebuttal engagement and addition of simulation.", "questions_for_authors": "See above!", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "lxSdFbOESq", "reviewer": "Reviewer_S9Pd", "summary": "This paper introduces the concept of \"selective response\" for GenAI systems. \n\nBased on this notion, the contribution of the paper is two-fold. \n\nFirst, on the conceptual side, it  presents a stylized model with two platforms (a GenAI system and a human-driven forum) where users choose between them sequentially. In this model, by sometimes not responding optimally, GenAI systems drive users to human forums like Stack Overflow, generating valuable training data that later improves the GenAI system. \n\nOn the technical side, the paper shows that under this model,  selective response can improve both GenAI revenue, user welfare, or even both, compared to always-responding. Finally, the work provides an approximately optimal algorithm for maximizing GenAI revenue under social welfare constraints.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the thoughtful evaluation and for finding our work novel.\n\nAddressing the reviewer's questions:\n\n1. Regarding \"*how users might react if they become aware of selective response strategies from GenAI?*\" \nWhile we model users as non-strategic and indifferent to the actions of GenAI, we totally agree that this might be a concern. There are many ways to reconcile it:\n\n    - This behavior is akin to multi-armed bandit settings, in which to maximize the total reward, we sometimes have to explore (trading short-term reward for future rewards). Users that participate in exploration rounds effectively receive a lower utility from the system. We cannot argue that users will comply with this behavior for the GenAI case, but such multi-armed bandit mechanisms are prevalent in real-world settings.\n\n    - If selective response is used in a way that is opaque to users, users would not be able to tell. Thus, we can assume they are indifferent to it. Alternatively, if GenAI is transparent about its need for more data on a matter, a message that could be conveyed by saying it has low confidence, users might respond allostratically. \n\n    - Future work could explicitly model user dissatisfaction of deliberate selective response, potentially optimizing revenue, welfare, or other metrics under more complex user behavior.\n\n    This comment is spot-on, and, upon acceptance, we intend to use the extra space to extend this discussion. Thanks for raising it.\n\n\n2. Regarding \"*do we assume that, when posting contents, the GenAI always reveal their identity, if that matters at all under this model?*\"  We do not make any assumptions regarding GenAI revealing user identities. Moreover, GenAI's actions are independent of user identities. \n\nThe reviewer also mentions that studying \"*the full dynamics of multiple GenAI platforms… could make the work stronger.*\" Moving from one GenAI to several requires a more game-theoretic approach; we see this as a promising future work. Our intuition is that we would get a Prisoner's Dilemma-like interaction. If one platform chooses to withhold responses, it benefits all other platforms while preserving the same data generation dynamics as always responding. Conversely, if all platforms choose to withhold, they would collectively be better off. In this scenario, the payoffs (expected revenue) depend on the decisions of all platforms as well as user preferences. As in the classic Prisoner's Dilemma, collective cooperation (i.e., not answering) could be enforced through contracts or incentivized by other means.", "claims_and_evidence": "The main results of the work are theoretical.  In particular, the paper shows that\n\n* Selective response can Pareto-dominate always-responding strategies (Observation 3.1)\n* The revenue inefficiency of always responding can be unbounded (Proposition 3.2)\n* Selective response can nearly double social welfare in some instances (Proposition 3.3)\n* For any strategy, a selective modification generates more future data (Theorem 4.1)\n\nThe claims are primarily theoretical, with formal proofs. I have checked the main proof of Theorem 1.1 and 1.2, and the proofs are sound. \n\nAt a conceptual level, the insight from this paper challenges the conventional notion that\nGenAI should always provide answers. I find that this idea is well supported by the theoretical claims.\n\n(It's not a weakness of the work at all, but note that the paper is not experimental and provides no empirical benchmark to evaluate their results.)", "methods_and_evaluation_criteria": "The paper uses a game theoretical model to study the dynamics between GenAI and human responses on question-answer platforms.  I think the lens of game theory is appropriate for analyzing strategic interactions between platforms and users. \n\nUnder this model, the paper provides a theoretical guarantee on selective response and inspired by that, an approximately optimal algorithm for social welfare.\n\nWhile the theoretical results, in my view, are strong and significant, they are somewhat simplified relative to the real-world GenAI dynamics. For example, as the author(s) admitted, the paper only considers the case where a single GenAI platform exists. Incooporating the full dynamics of multiple GenAI platforms and/or modelling multiple heterogeneous user distributions could make the work stronger.", "theoretical_claims": "I reviewed several of the key theoretical claims, mostly surroudning theorem 1.1 and 1.2. The proofs appear sound.", "experimental_designs_or_analyses": "The paper is primarily theoretical and does not include empirical experiments. While this is acceptable for a foundational theoretical paper, even simple simulations would have strengthened the work. Specifically, I wonder if the dynamics can be simulated by multiple self-training rounds on synthetic data with simpler models.", "relation_to_broader_scientific_literature": "I am not familiar with the literature on game theory", "essential_references_not_discussed": "I am not familiar with the literature on game theory", "other_strengths_and_weaknesses": "Overall, I find the paper very well written and clearly structured. \n\nThe conceptual message was delivered and supported by the theoretical claims. Importantly, I think the regulatory perspective provides actionable insights for policymakers (section 6), where they give conditions under which policy interventions improve welfare.\n\nTo my knowledge, the main theoretical framework of the paper is novel (though, again, I am not an expert in game-theory or the study of AI and society).\n\nAs the author(s) acknowledged, the paper does make a few simplifying assumptions, although, in my view, this is a good work as the first step in studying this dynamics between GenAI and human responses. Finally, I believe the paper could be strengthened if the author(s) could validate their results with a bit of experimental simulation.\n\nGiven the strength of the theoretical results and novelty of the main framework, I lean towards accept.", "other_comments_or_suggestions": "na", "questions_for_authors": "Have you considered how users might react if they become aware of selective response strategies from GenAI? Also, do we assume that, when posting contents, the GenAI always reveal their identity, if that matters at all under this model?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This manuscript received favourable reviews from all 4 reviewers. The reviews and discussions highlighted both strengths and weaknesses but the general tendency is in favour.

Among the strengths, it was commented that the paper introduces a novel and creative approach (selective response) that has the potential to significantly impact the development of GenAI systems, with rigorous analyses and well-supported by proofs and examples, that the work addresses a meaningful gap in literature, and clearly elucidates limitations (e.g. assumption of single algorithmic competitor, non-strategic forum behavior, etc.), the setting is novel and of interest to the community, and the paper is generally well-written. 

Among the weaknesses, it was commented that the assumptions could weaken the work, given the ICML setting, there are no simulations or other forms of evaluation to show the model holds in practice, whereas the paper is primarily theoretical, and the practical implementation of selective response is not explored in depth. Empirical validation would strengthen the paper's claims. Also that the scope of such selective response strategies in the real world could be considered more closely.

The rebuttals alleviated some concerns and the reviewers reiterated their positive evaluation of this paper.
Decision: Accept (poster)