Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Authors: Yaolong Yu
Fan Yao
Sinno Jialin Pan
Venue: ICML 2025 poster (2025)
Keywords: Recommendation system
content creator competition game
group strategy
price of anarchy
Primary area: theory->game_theory

Abstract: We employ a game-theoretic framework to study the impact of a specific strategic behavior among creators---group behavior---on recommendation platforms. In this setting, creators within a group collaborate to maximize their collective utility.
We show that group behavior has a limited effect on the game's equilibrium when the group size is small. However, when the group size is large, group behavior can significantly alter content distribution and user welfare.
Specifically, in a top-$K$ recommendation system with exposure-based rewards, we demonstrate that user welfare can suffer a significant loss due to group strategies, and user welfare does not necessarily increase with larger values of $K$ or more random matching, contrasting sharply with the individual creator case. Furthermore, we investigate user welfare guarantees through the lens of the Price of Anarchy (PoA). In the general case, we establish a negative result on the bound of PoA with exposure rewards, proving that it can be arbitrarily large. We then investigate a user engagement rewarding mechanism, which mitigates the issues caused by large group behavior, showing that $\text{PoA}\leq K+1$ in the general case and $\text{PoA}\leq 2$ in the binary case. Empirical results from simulations further support the effectiveness of the user engagement rewarding mechanism.

Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Yaolong Yu
Fan Yao? Sinno Jialin Pan
Abstract
2024). Driven by platforms' rewarding mechanisms, cre- ators generate income proportional to their output and often strive to maximize their earnings by optimizing their content, such as selecting formats or topics that yield higher profitability (Glotfelter, 2019; Hodgson, 2021). To maxi- mize user utility, leading platforms like Instagram, TikTok, and YouTube employ sophisticated algorithms to match users with the most relevant content. This process involves calculating relevance scores and applying top- ranking methods to prioritize and display content that aligns closely with user preferences.
We employ a game- thee-the framework to study the impact of specific strategic behavior among creators- group behavior- on recommendation platforms. In this setting, creators within a group collaborate to maximize their collective utility. We show that group behavior has a limited effect the game's equilibrium when the group size is small. However, when the group size is large, group behavior can significantly alter content dis- tribution and user welfare. Specifically, in top- K recommendation system with exposure-based rewards, we demonstrate that user welfare can suf- fer a significant loss due group strategies, and user welfare does not necessarily increase with larger values of K or more random matching, con- trasting sharply with the individual creator case. Furthermore, we investigate user welfare guar- antees through the lens of the Price of Anarchy (PoA). In the general case, we establish a nega- tive result on the bound PoA with exposure rewards, proving that it can be arbitrarily large. We then investigate user engagement rewarding mechanism, which mitigates the issues caused by large group behavior, showing that PoA < K + in the general case and PoA < 2 in the binary case. Empirical results from simulations further support the effectiveness of the user engagement rewarding mechanism.
However, recent studies have shown that user utility can- not be maximized solely by optimizing matching rules, as creators can act strategically, leading dynamic shifts in content distribution (Ben-Porat & Tennenholtz, 2018; Yao et al., 2024c;b; Jagadeesan et al., 2023; Hron et al., 2022). Previous works mainly study this problem under self-played content creators' strategic behavior, where every content creator only focuses on maximizing its utility. As online rec- ommendation platforms become extremely prevalent these days, despite individual creators, some creators form group to strategically act in this content creation competition, usu- ally united by a media company, such as MCN (Gardner & Lehnert, 2016; Gardner, 2015; Boyle & Boyle, 2018; 8; Liang & Ji, 2024). To this group of creators, the company needs to consider assigning and adjusting topics for each creator in this group to maximize the group's 's utility.
Within group creators, competition among members can be strategically reduced to enhance collective utility. Impor- tantly, the strategies that maximize group utility often differ significantly from those that maximize individual utilities when creators act in a self-interested manner. The implica- tions of group behavior extend beyond merely improving group utility: such strategic collaboration can alter the equi- librium of the content creation competition, resulting in a content distribution that diverges from the equilibrium ob- served when only individual creators present. This shift in content distribution can influence user satisfaction with recommended content and may potentially diminish overall user welfare. For instance, consider a scenario where the user base consists predominantly of sports fans, with only small fraction interested in niche topics. When creators collaborate to boost revenue, they may shift from sports
1. Introduction
With the increasing popularity of online media, content creation has emerged as a prominent profession in contem- porary society (Bobadilla et al., 2013; Hoose & Rosenbohm,
'Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China 'Department of Computer Science, University of Virginia, Char- lottesville, Virginia, USA. Correspondence to: Sinno Jialin Pan <sinnopan cubk.edu.hk>.
Proceedings of the 4dnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
to niche topies minimize internal competition. Conse- quently, the limited supply of sports-related content may fail to meet the demand of the majority sports fan population. Thus, it is crucial to analyze the impact of this emerging group behavior on content distribution and user welfare, as it holds significant implications for the design and regulation of recommendation systems. In this study, we analyze the problem within a well-defined game-theoretes framework- the Content Creation Competition (C9) introduced by Yao top-K K recommendation mechanism with exposure reward, which is widely used by online content platforms (Ben-Porat& & Tennenholtz, 2018; Hron et al., 2022; Jagadeesan et al., 2023; Meta, 2022; Savy, 2019; Eilat& & Rosenfeld, 2023). We begin by examining simplified scenario, termed the bandit C game, where users' features and creators' action sets are represented as orthogonal unit basis vectors in R". We define the group equilibria and establish constraints under which the group equilibrium remains consistent with the individual case. While these constraints ensure that group behavior does not alter the content distribution, they are neither generally applicable nor practical in most real-world settings. We then investigate the resulting user welfare loss when these constraints are relaxed.
of Anarchy (PoA) can be arbitrarily bad. This is mainly due the inefficiency of the zero-sum structure in motivat- ing creators to generate high-quality content when certain groups dominate the entire exposure of users. We then in- vestigate another rewarding mechanism - user engagement rewards, which are deemed more effective for maximizing welfare as they better align with user preferences (Acharya et al., 2024; Yao et al., 2023). Engagement rewards alleviate the worst-case issue in exposure rewards, motivating creator groups to produce high-quality content and enhance user welfare. We establish an upper bound on the PoA for the Ca game with user engagement-basee rewards and group behavior, showing that the PoA can be as large as K + 1. To complement this, we construct a worst-case instance and derive lower bound, demonstrating that the lower bound nearly matches the upper bound. Although this PoA re- sult is negative, the worst-case scenario can be effectively mitigated through intervention methods ( (Yao et al., 2024c). Additionally, we demonstrate positive results in specific cases such as when relevance scores and user attention scores are sinary-showing that the PoA of this game is no more than 2. We construct simulations to further validate the effectiveness of the user engagement rewarding mechanism.
et al. (2023; (024aac)-under
We show that, due to the zero-sum like structure of the exposure-based rewarding mechanism, creators within a group can reduce internal competition to improve group utility. This strategic behavior can potentially harm user welfare. The worst-case scenario occurs when all creators form single group, leading to a user welfare loss large as (n).
2. Related Work
The study of game-theoretic aspects in recommendation systems began with the seminal works of Ben-Porat & Ten- nenholtz (2018; 2017), which introduced a recommendation system based on the Shapley value. This approach guaran- tees the existence of unique PNE while satisfying several fairness criteria. Recently, numerous studies have delved into the dynamics of strategic content creators, a topic that has attracted significant attention in both theoretical and empirical research (Yao et al., 2023; 2024a;c; Zhu et al., 2023; Hu et al., 2023; Hron et al., 2022; Dean et al., 2024b;a; Mladenov et al.. 2020; Prasad et al., 2023). This growing body of work underscores the importance of understanding creators' strategic behaviors and platform design to achieve sustainable and equitable outcomes in the long term. A common assumption in these studies is that creators are self- leff-interested, with their strategic behavior analyzed under the mediation of a recommendation system. In contrast, our work diverges from this assumption by considering creators who form groups and strategically optimize their collective utility.
We also show that the parameters K and B in the exposure rewarding mechanism can significantly influence user wel- fare. First, we demonstrate that in the case where users pay constant attention to the recommended items, increasing competition- as by increasing K or 8-can improve user welfare. However, given the diminishing attention spans of users (Carr, 2020), we present contrasting results. As highlighted in prior work (Yao et al., 2023), key in- sight in top-K mechanisms is that user welfare tends to improve as K or 3 increases, as both parameters augment the expected number of creators exposed to users (Yao et al., 2024c). This intuitive, as users are more likely to find sat- isfactory content when presented with more choices. How- ever, we present counterintuitive finding in the context of group behavior and the diminishing attention spans of users: user welfare does not necessarily increase with larger values of K or B. Together, these findings provide insights for se- lecting K and 3 in different practical scenarios, particularly when considering group dynamics.
Hron et al. (2022) studied equilibria in exposure games, where creators are incentivized by exposure-based rewards. Concurrently. Jagadeesan et al. (2023) explored a related problem, focusing on supply-side competition in scenarios where creators operate within a high-dimensional strategy space. Their study focused on characterizing NE and iden- tifying conditions under which specialization in creators'
In more general scenarios, we first analyze the worst case for 8 game with exposure reward, showing that the Price
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
strategies may emerge. Yao al. (2023; 2024a) studied creator dynamics within the Ca framework. Building on this framework, we analyze creators' strategic group behav- ior and its implications for user welfare. Recent work (Yao et al., 2023) highlights the impact of content creators' com- petitive behavior on user welfare in top-K recommenda-
matching. We focus on modeling the strategic behavior of creators and thus abstract away the estimation of
Matching probability: Given any user x E X and when each creator commits to strategy 84, the plat- form retrieves the top-K ranked content in terms of the relevance scores {a(s,, J= Specifically, let {T((1) 2 ... 2 d(())==)) be permutation of {a( .)};= The matching probability of 8 to user a is calculated using a softmax distribution with tem- perature / >> 0, i.c., for 1 < ((i) < K.
tion systems, suggesting that the user welfare guarantee improves as either K increases or 3 increases. However, in our work, we demonstrate that user welfare no longer necessarily increases with larger values of K or temperature 3 when considering the group behavior of creators.
To maximize long-term user welfare, Hu et al. (2023) de- veloped a learning algorithm for the platform to encourage the production of high-quality content, Zhu et al. (2023) proposed an online learning approach that optimizes the recommendation policy and payment contracts for creators, and Yao et al. (2024c) provided intervention mechanisms for the platform to steer the equilibrium content distribution towards a desirable user welfare outcome. Specifically, Yao et al. (2024c) demonstrates that the platform can signal the importance of specific user æ by increasing K or B3 which enhances æ's 's visibility among creators. This increases the chance that creators who were previously unaware of æ recognize the potential benefits of catering to æ. We also analyze the roles of these two parameters in our setting, showing that larger values of K or B introduce additional competition to the C3 game, leading to distinct content dis- tribution and user welfare, which provides insights that the platform can improve user welfare by appropriately tuning K and B under different user attention scores on content.
(, x) _ Prob(s s((s] x expl8-'apo al) (I)
A small 8 makes the matching strategy more determin- istic, and 3 + Do corresponds to random matching.
4. User utilityy and user Welfare definitions: We define user xts 's utility from consuming list of ranked content as follows:
(8, = 1on (2) S
1=1
where 1 2 r1 2
2 nn 2 0. The sequence
{ri [0, 1]] represents the user's attention scores over the k-th ranked content, where content with a higher relevance score receives more attention. The user welfare W (s) is defined as the expected user util- ity:
W(s) Ex- (x),,,))
(2)
5. Creator utility: rewasurereward: reward:
3. Preliminary
( (aex( (
(3)
In this section, we formalize the game-theoretic framework the Content Creator Competition (C*) game-with the plat- form's rewarding mechanisms. This strategic game setup builds upon the framework introduced by Yao et al. (2023; 2024a). Each instance of the 3 game, denoted by G, is de- scribed by a tuple ((S, y I X, a, (ra)i (Co) B, K), as illustrated below:
This exposure rewarding mechanism is widely used in both theoretical and empirical fields (Ben-Porat et al., 2019; Hron et al., 2022; Jagadeesan et al., 2023; Meta, 2022; Savy, 2019).
6. Separation of creators into groups for multi-group setting: There are L groups of creators, cach C2 S [n]. [Cel = nn 2 1 for E [L]. 2/ = [n]. n
1. Basic setups: user distribution X' with finite sup- port {z, E 1 1-
Ø. Group utility for group E is denoted as
where x = æj with probabil- ity (p, Tn and a set of content creators denoted by [n] = [I. n). Each creator can take an action 8,, referred to as a pure strategy in game-theoretic lit- erature, from an action set S C IRd. Here, s; is the embedding of content creator will produce. Without loss of generality, ||æ||| S 1, || S 1.
Qe(s) = Σ Cu,(s, where s, = (st)iecc. (4)
IEC₁
4. Bandit C Games
An intriguing property for C games is that enhancing one creator's 's relevance score for a user can potentially decrease
2. Relevance function: the relevance function a(s, x) Rd x - R20 measures the relevance score between a user x ~ X' and content s. Without loss of general- ity, we normalize a to [0, 1), where suggests perfect
Another interpretation of this probability is that the user selects one item from the provided K items according to the Random Utility Model (Yao al., 2023), where depends the noise level.
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
the utilities of other creators about that user. Conversely, de- creasing creator's s relevance score may increase the utilities of other creators about that user. This dynamic underscores a fundamental limitation of self-interested utility maximiza- tion, which does not necessarily result in optimal group utility. Increases in the relevance score of one creator can detrimentally affect the utilities of others within the group.
equilibrium if for every E [n], 8/ E E.,,
uz(s") ) 2 un us s",)-
(5)
In other words, vanilla equilibrium is an individual PNE in bandit C games.
In bandit Ca games, a vanilla equilibrium can be represented as {qj m J==1. where q," denotes the number of creators se- lecting éj in specific equilibrium eq. With little abuse of notation,
Consider a simple scenario, where there are three creators labeled as 1, 2, and 3. Each of them produces videos about basketball under stable civllibruum-mmeniin them has an individual incentive to switch topics. How- ever, if creator 3 were to change her focus to another topic, e.g., music, this shift could potentially increase the rewards received by creators 1 and 2. Importantly, the additional rewards gained by creators 1 and might surpass the loss in rewards experienced by creator 3. Consequently, although creator 3's utility decreases, the overall utility of the group increases. This illustrates how individual actions within a collaborative environment can impact collective outcomes, sometimes positively, even if they are detrimental to the individual initiating the change.
use s s' to denote the profile of two equilibria 8 and s' shapes the same, i.e. they are equal up to a permutation of strategies.
none of
When there is only one group, i.e., [C1] = ne and |C2| [Cal = ..... = [Cr] 1, we denote this group of creators C as set S [n]. where |C| = ne. The group utility for is denoted Qs(s). For fixed group strategy 8c in a C3 game G, we denote the set of PNE for the remaining players as PNE(G, 8.). We can prove that PNE and PNE(G, 82) always exist in bandit C3 games.
Lemma 4.3. Any bandit C game has a vanilla equilibrium and a PNE se) for any fixed group strategy sc.
Building on this intuition, we analyze content distribution, equilibria, and user welfare in a representative class of C3 games, namely the Bandit C Game. The Bandit C Game models a scenario where the user population comprises multiple interest groups, each with orthogonal preference representations. Each content creator has the option to cater to one and only one user group. While this game simple and stylized, it simulates the fundamental scenario where every creator must select a topic to create content.
Ideally, this group of creators can optimize their group util- ity while considering the dynamics of other individual cre- ators. Based on Lemma 4.3, we know that a Nash equilib- rium for individual creators outside the group always exists when the group strategy fixed. This allows us to define Stackelberg-typ -typ equilibrium for this game. Its formal definition is as follows.
Definition 4.4 (Single group Stackelberg equilibrium). We denote $ as the solution for the following bilevel optimiza- tion:
Definition 4.1 (Bandit C Game). The Bandit O game is specified by the following RS environments:
max Qa(So: 8-c), S.L. 8-c E PPNE(G, 8c).
8,
The user population is a distribution on {e,ly where x = Bj with probability {p and E [ei.... em Rm is the set of unit basis vectors in Rm
And s'. s!) Here, 8-c is selected from PNE(G, se) according to a specific tie- beebbrekinng rule, such as a creator choosing the user with the smaller index when the utilities for selecting different users are equal. We name st as Type-I equilibrium, which denotes the single group Stackelberg equilibrium.
Without additional specification, all creators share the same action set S; = E. The relevance is measured by the inner product, i.c.. as: x) x.
We also consider the single-group PNE of this game by treating the group as single entity. A single-group PNE is a strategic profile where no entity, including both the group and individual creators, can improve its utility via unilateral deviation. single-group group PNE does not necessarily exist in bandit C game.
We first analyze the scenario in which a single group of creators coexists with individual creators.
4.1. Single-group
The pure Nash equilibrium (PNE) (Nash Jr, 1950) is the most widely recognized concept for characterizing the out- come of a game. At a PNE, no player can increase their utility by unilaterally deviating from their current strategy, given the strategies of the other players.
Definition 4.5 (Single-group group Nash equilibrium). Suppose Ill is Single-group Nash Equilibrium. Then, for any s and any & C, s" satisfies the following conditions:
(o(=")) 2 Qo(8', Sl s'),,, and u;( 2 u,(5/, s
Definition 4.2 ( (Vanilla equilibrium). We say 8 a vanilla
We refer to the joint strategy profile sll as a Type II.
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
4.2. Type vanilla equilibrium
4.3. Type I, II of vanilla equilibrium
Example 1. m = 2, 5, Pl = 0.7,p2 = 0.3, C (1,2}. s" s' (1,23) 01, e2). sll
TvN (Trend v.s. Niche) (Yao et al., 2024a) TvN game first introduced by Yao et al. (2024a), where p1
2n x+1 and
{811223) = c1. (4.5) e2).
p. 2n The TvN game captures the essence of real-world user populations and the dilemmas faced by creators. Creators often find themselves at a crossroads: they must decide whether to pursue popular trends to reach a broader audience, which leads to intense competition, or focus on niche topies with smaller audience and reduced competition.
P2
Example 2. m = 3. n = =04,04 = 0.1.
C= (1,2.. s" = [8(112] = -1,83 = e2). s = {81 =
C1 C3, 83 02). s (s = C1. $2 C2, 83 e1).
We use two example games to illustrate whether Type I is a vanilla equilibrium. When considering the dynamic strategic moves of out-of-group creators, some improve- ments to group strategies may ultimately fail to increase the group's utility. In Example 1, we first consider equilibrium I, where the group has the incentive to change the strategy. If they adjust 82 ei 5/ E2. then creator 4 has the incentive to change its strategy from $1 E2 + 8 C1, and this change will decrease the group utility. After these updates, the group utility decreases. Therefore, the orig- inal strategy profile remains as equilibrium I. This is be- cause individual creators who select eg. facing a change 82 G1 + $/2 C22 are influenced to shift strategies due to increased rewards for and reduced rewards for e2. Thus, considering the strategic moves of individual creators, the group will not change its strategy. In contrast, in Ex- ample 2, under the vanilla equilibrium profile, the group changes their strategy from 82 = e - 8/2 = eg. After this change, the individual creator has no incentive to change its strategy, and the group utility increases, indicating that equilibrium I differs from the vanilla equilibrium. Based on these observations, we develop constraints to ensure that Type I and Type II align with the vanilla equilibrium.
Next, we use this TvN game to illustrate the difference in user welfare between the group case and the individual case.
Theorem 4.7. In TvN game with exposure rewards, we have s' = =s" If r1 = T2 ... = TK = L, the following results hold:
1. Individual case (ne = 1):
n 1
W(s", ,K)
K,
2n
and the optimal welfare is
+
W max max ((,, s,K
2
2. Full group case (n. = =n);
W(s" K) =
3. Partial group case (1 ne < nz: If - 0. then
of S max {1, [[[++ (nn) }
Theorem 4.6. Under a specific tie tie-breaking rule, ifa bandit C game admits a vanilla equilibrium s", a Type I equilib- rium 8 a Type II equilibrium 8ll, and n. S minje[mm 1j, then s = ss'l s".
and the welfare loss is
ql'
W Wmax- W('!)) = 2
If B + oc, then qf = and Wmnx ))
A specific tie-breaking rule can be creator will choose the user with the smaller index when the utilities for selecting different users are equal. This theorem demonstrates that, when the group size is small, group behavior does not affect the equilibrium of the bandit C game. This is primarily be- cause, when a group creator attempts to strategically change its topic to enhance group utility, other individual creators will fill the resulting gap. as demonstrated in Example 1.
We present the results for the case where users have constant attention over the recommended content, i.e., r2 = F = 1. This attention is truncated by the parameter K and it assumes users allocate a fixed amount of attention uniformly across the top-K items they are shown. This setting is relevant in practice, particularly in user interfaces where content displayed in fixed-sized, unordered blocks (e.g., "For You" page with K equally weighted items). These findings can be readily extended to the general case of (r:)%_, through straightforward adaptation.
When the group size is small and there no niche topics (a small p group behavior does not influence the equilib- rium profile. However, in many practical cases, such as in TvN games in the following analysis, the group strategies have a significant influence on content distribution and user welfare.
To emphasize the potential negative impact of group strate- gic behavior on user welfare, we consider the TvN game as an example for worst-case analysis (Yao et al., 2024a).
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In this game, individual creators are restricted from selecting e1, reflecting real-world scenarios where such limitations arise. Potential reasons for this include: (1) They lack Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
The user proportion p in the TvN game, although stylized, reflects user distributions in real-world online content plat- forms, which are often highly skewed and unbalanced. And our choice of this p is also primarily for clarity and simpli- fication of presentation. We extend our results to a more general unbalanced case in the Appendix A.4, where the largest user proportion in the TvN game can vary, and this will provide a more smooth transit from the extreme case to the even case.
Theorem 4.9. In a TvN game with exposure reward, Y1 -n -0, 3 is sufficiently large, S, = E {e for i & S = E for i E C, and the group size nh. > then
122 = -r 1, r-+1
n+1
K n-k
K
w(s" "1 K) =
2n
2n
n+
+
n-
T+IsK nec ne.
Theorem 4.9 considers another setting with diminishing
attention, modeled as =... ....-% r, = 1, T++1
In this setting, the formation of groups can significantly impact user welfare. The content creation game with expo- sure rewards exhibits a nearly zero-sum structure. When all creators form a single group, they have no incentive to compete internally, and the optimal group strategy becomes {s: - This strategy leads drastic decline in user welfare compared to the optimal welfare scenario. This result indicates that the worst-case scenario for user welfare occurs when a group of creators dominates the entire expo- sure to certain users or topics, which means these users are only exposed to content created by this group.
In = 0, which captures the case where users only pay attention to the top r items. These two cype-cconsie
(Theorem 4.7) and
common user
behaviors corresponding to slow-decay and rapid drop-off attention curves, respectively.
expertise in c1, making the cost of creating content related to e prohibitively high. (2) Due to their local updates, they only explore limited region of the strategy space. The group will assign at most K creators e₁ to capture all the exposure associated with e1. This result also provides insight into the scenario where single group specializes in a specific topic and monopolizes the associated exposure. In such cases, the group can reduce its collective effort on the topic while still capturing the entirety of the exposure.
The scenario where all creators form a group has practical relevance in real-world cases. For instance, in online media platforms, certain modules restrict user access to content creators within a specific geographic proximity (e.g., the "People Nearby" feature). In such cases, it is reasonable to assume that all creators within a small region may form a group, especially when the creator population is limited. Furthermore, joining a group is dominant strategy, as the group utility non-decreasing compared to the individual case-at the very least, it remains unchanged if creators maintain their previous actions.
For the first part of Theorem 4.9, when K S т, increas- ing K under constant attention scores leads to improved user welfare. For the second part of Theorem 4.9, when T + 1 S K I Ne. the results reveal a counterintuitive phenomenon: in a top-K recommendation system, user wel- fare does not necessarily increase with larger values of K. This contrasts with established findings that user welfare typically improves as K increases (Yao et al., 2023) and provides insight that platforms should avoid selecting ex- cessively large K in recommendation systems where users have diminishing attention spans. Additionally, we pro- vide a game instance under the low attention spans of users, demonstrating that a higher 3 does not always lead to better user welfare. The proof follows a similar approach to the proof of Theorem 4.7, item 3.
Remark 4.8. In a TvN game with exposure rewards, adjust- ments to the parameters K and cannot influence individ- ual creators' decisions to select e and chase the trend (Yao et al., 2024a). However, when considering creators' group behavior, the platform can adjust K and | to improve user welfare. Increasing | results in a more uniform distribution of user ætss matches across the top- K candidates, while in- creasing K expands the set of creators that user æ is exposed to (Yao et al.. 2024c), so both of them introduce additional competition into the game. As shown in Theorem 4.7 item 3, under constant attention scores, additional competition leads to improved user welfare outcomes. For general {r:) ) the user welfare is given by
Corollary 4.10. In TvN game with exposure rewards, if r1 = 1 and = I'n = 0, and when 1 < na < n,
33 - ws ,8 (08)"8=o00) n 91.0
n 11 1 min K.))) (sx)=
w(s",3=0)
91 2m
rs +
2n
2n
where Ho S max {1, [ (n + 1)(n- (((n-n))) m
By tuning K and B, the platform can regulate the number of creators within the group who select e1. thereby enhancing user welfare. More generally, the platform can strategically set values for K and 3 to achieve a limited improvement on user welfare by steering the equilibrium of the game.
4.4. Multi-groups in bandit C games
For bandit 3 games with multiple groups, the results are similar to those the angle-group case. We briefly present
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
these results here, as they share similar intuition and in- sights.
As the previous section indicates, when the group is big. especially when all creators form as group or multiple groups dominate multiple topics respectively, we show that group strategies can inevitably lead to a big fraction loss of the optimal welfare. Now we show that in the worst case, PoA in a C game with exposure reward can be arbitrarily bad.
Definition 4.11 (Multi-group PNE). For any l E [L], 8f is multi-group PNE if for any 8'y.
Qe( s-x S Qe(s").
Theorem 4.12. In bandit C game with 3 + O, sup- pose vanilla equilibrium is {g] 1 If maxtelL] S min FJ. then for any multi-group PNE 8 in this game, we have for any j E [m].
Theorem 5.3. For any C instance 9 with exposure re- wards,
PoA(G) 00. Co.
{ (1+ max Pr 1 r7s P. 3%8
This phenomenon occurs when a group dominates the total exposure to a user, even though they reduce their effort and produce low-quality content (s; = =1, & is an arbitrarily small value), they still dominate the exposure to this user. Both Theorem 4.7 and 5.3 indicate that the most severe issue with exposure-based rewards occurs when a group of creators monopolizes the total exposure to users or when only a group of creators specializes in specific topics. As highlighted in Yao et al. (2023), rewarding creators based on user engagement is likely to improve the user welfare of recommendations. In this work, the engagement reward for creator i is defined as follows:
of - 93 S 2.9 of S min
The proof is in Appendix A.7. Similar to Theorem 4.6, Theorem 4.12 demonstrates that the multi-group PNE (if it exists) is unlikely to differ significantly from the vanilla equilibrium when the group size is small. We also intro- duce a Restricted Preli- vs. Niche (MTvN) game in Appendix A.6, a variant of the TvN game adapted to the multi-group setting. This game exhibits results similar to those in the mugle-group TvN game.
5. General Case and PoA
Engagment reward: u,(s) = E (a.
In this section, we analyze user welfare under any possible creator group partition and group coarse correlated equilib- rium (GCCE) in the C3 game through the lens of the Price of Anarchy (PoA) (Koutsoupias & Papadimitriou, 1999). The PoA quantifies the inefficiency in user welfare resulting from creators' strategic group behaviors and self leff-interested actions.
Notably, when user engagement is used as the reward mech- anism, the welfare of creators aligns with user welfare. Con- sequently, when all creators act as group, the optimal group strategy also maximizes user welfare, which means PoA = in this case. This engagement reward mitigates the user welfare loss caused by large or professional groups, leading to optimal user welfare outcomes in the TvN and MTvN games discussed in previous sections. However, we provide a negative result on the PoA bound under the user engagement reward mechanism with constant user attention and construct lower-bound instance to demonstrate the tightness of this bound.
Definition 5.1 (GCCE). is a group CCE, for every group L E [L] and every group strategy 8/z.
[+()] 2 Es-a (irs,, sc]]
(6)
Definition 5.2 (PoA under GCCE). Define the price of
anarchy of a C instance G as
Theorem 5.4 (PoA under engagement reward). For any C3 instance G with engagement rewards, B 2 1, K I n, and user welfare defined as in Eq. (2), if rk 1, then
max, ((s)
PoA(G)= min Ea [s)]
where GCCE(G) is the set of GCCEs of & for all possible creator group partitions.
PoA S 51+K. K.
Based on the definition, PoA(g)= 2 1, and larger values indicate worse user welfare. The definition of PoA under GCCE (Blum et al., 2008) provides the strongest possible welfare guarantee. Specifically, any upper bound on the Price of Anarchy (PoA) under GCCE automatically applies to the PoA under more refined equilibrium concepts, such as group CE, group PNE, or mixed group NE (if they exist), as these equílibria are all special cases of GCCE.
The proof of Theorem 5.4 is provided in Appendix B.2. One important observation regarding the bound is that the benchmark max, W(s, K) varies with K. As K increases, the benchmark max, W(s, K) may also increase. Although the PoA of the C3 game is no longer infinite, it still suffers from a significant loss in user welfare. We next conduct a worst-case analysis to identify the scenarios that lead to this unsatisfactory PoA result.
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Theorem 5.5 (Lower Bound). Given any K S n, 3 2 1, and ri =... = -rK- 1, there exists C game
m = 10 users from the unit sphere Sd-1, The distribution of the 10 users is p 200
1 x [100, 50, 20, 10, 10, 5, 2,1,1 1,1,1]] 1].
instance with engagement rewards such that
We then slightly polarize the user distribution to simulate a real-world scenario (Dean & Morgenstern, 2022; Lin et al., 2024), where the largest user group is positioned at one pole and has some distance from the other users. This setup presents a more challenging case for user welfare optimization, as in some scenarios, creators must traverse a long path from one pole to the other to improve user welfare.
PoA(G) 2 1 (K- - -1)e 3.
The proof of Theorem 5.5 is provided in Appendix B.3, which explicitly constructs a game instance that achieves the stated PoA lower bound. In this instance, the vanilla equilibrium occurs when all creators in the game select user with a very small proportion. This leads to high utility for that user, which in turn results in high creator utility. Consequently, no creator has an incentive to deviate from their strategy. This leads to a suboptimal outcome for user welfare, but this worst-case scenario can be alleviated by the approach proposed in Yao et al. (2024c), which helps creators escape from the current suboptimal state through a user importance reweighting method.
The relevance score function is set to a x)) 2/(8" x + 1) E [0, 1]. We use 2 kinds of user attention scores: constant attention scores where r; = 1 for i E [5] and log cutoff atten- tion scores {r:}a= = logg 2 loga 31.... log, 6 .,................ 0}. We set (3, K) = (0.1,5) by default. This synthetic dataset characterizes a class of clustered user preference distribu- tions, such as majority versus minority user groups.
On the creators' side, there are n = 30 creators in total, including one group of creators. We vary the group size The E {10, 15, 20, 25, 30). The group of creators' strategies is initialized near user ø1, while the remaining creators' strategies are initialized near the other users. This setup models a scenario where the group of creators specializes in a specific topic. Individual creators use the LBR algo- rithm (Yao et al., 2024c;a) to update their strategies, while the group performs multiple steps of gradient descent on the objective Qo(se, s-e) with respect to the group strategy Se = ($1, 82, " ).,)-
These results collectively provide insights for online content platforms to mitigate user welfare loss caused by group strategies: use user engagement-based rewarding mech- anisms and implement intervention methods such as the user importance reweighting method proposed in Yao al. (2024c). The importance reweighting method enables the platform to steer creator incentives toward under-served users by modifying the reward structure. Specifically, the platform defines the creator's utility as
(s) ExEx [w(x)](xx 8) (s,.
We analyze the average user welfare under vary- ing reward types, group sizes, and attention score distribu- tions, with a fixed time horizon of T = 100. The results are presented in Figure 1. Our experiments reveal that user welfare under engagement- based rewards consistently sur- passes that under exposure-based rewards. Notably, user welfare experiences significant decline when the group size increases to n. 25 or 30 under exposure rewards, whereas it remains stably high under engagement rewards. This observation is further supported by a visualization ex- ample in Appendix C.2 (n. = 10), which illustrates that creators in the exposure reward setting do not overlap with the largest user segment 11, as they already dominate the exposure of æ1. In contrast, creators under engagement rewards exhibit overlap with 21, leading to enhanced user welfare compared to the exposure reward scenario. Our experiments also demonstrate that the PoA for engagement rewards remains close to 1. This result is supported by the theoretical bounds max, W W(s) < in the constant attention case and max, ((s) < Σ. log, (+1 case, highlighting the effectiveness of engagement rewards.
Results
where w(x:) represents the importance weight of user æ. When the platform detects that user is being under-served under the current content distribution, it increases w(xr) for that user. This effectively amplifies the reward for creators who target such users, encouraging them to shift their con- tent that direction. Over time, this reshapes the content distribution and improves overall user welfare.
We also show that in some cases, such as when B + 0 and relevance scores and user attention scores are binary (i.c., E (0, 1). F1 = 72 =... 'r- = 1, and rr+1 In = 0), we obtain positive result on the PoA.
Proposition 5.6 (PoA under binary a). For any C instance G with engagement rewards, 3 + 0, and user welfare de- fined as in Eq. (2), if the relevance scores and user attention scores are binary (i.e., o, r. E {0, 1}}, then
PoA(g) <
1 < 2.95 in the general
6. Simulations
Synthetic Environment For the synthetic environment, we first construct the user population as follows: we fix an embedding dimension d and independently sample
We conduct additional simulations with varying values of K and 3 to validate two key theoretical results presented in Section 4. The outcomes are reported in Appendix C.3 and
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Beyond Self-Interest; How Group Strategies Reshape Content Creation in Recommendation Platforms?
Average Welfare Constant
Average
Log
1.-
2.50
2.00
Average User Welfare
Average User Welfare
2.80
2.75
4.
28/
127
Reward Type
Reward Type
Exposure
240
Exposure
Group Size
Group Size
(a) Constant attention scores
(b) Log cutoff attention scores
Figure I: User welfare under different reward types, group sizes, and attention scores.
Appendix C.4. We further evaluate the robustness of our findings under more general user distribution p following Zipf-like pattern, detailed in Appendix C.5. Additionally, we consider an alternative creator initialization, where all creators are initialized around users 2 to 10. The results of this setting are provided in Appendix C.6.
Impact Statement
This paper presents work whose goal is to advance the field of game theory for recommendation systems. There are many potential societal consequences our work, none of which feel must be specifically highlighted here.
References
7. Conclusion
Acharya, K., Vangala, V., Wang, J., and Ziani, Producers equilibria and dynamics in engagement-driven recom- mender systems. arXiv preprint 1rXiv:2401.166411 2024.
Our work sheds light the critical implications of group strategies among content creators in online recommendation platforms. Using a game-theoree theoretic framework, we demon- strate how group strategies reshape content distribution and user welfare. While small groups exhibit limited effects, large groups can significantly alter content distribution, lead- ing to substantial user welfare losses. We analyze the role of key parameters K and 3 in exposure rewards and in- vestigate user engagement-base based rewarding mechanism, demonstrating their potential to mitigate the adverse effects of strategic group behavior. These findings offer valuable in- sights for designing recommendation systems that enhance user welfare while addressing challenges posed by strategic group behavior.
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Appendix
A. Proofs for Section 4
A.1. Proof for Lemma 4.3
Proof. We prove the existence of a single-group pure Nash equilibrium (PNE) by constructing it using a self-greedy algorithm. Suppose creators select strategies sequentially, and let:
of denote the number of creators selecting e; at time t. The final number of creators selecting e; is of where T = n.
(g(g:) represent the utility for selecting e; defined as:
Py 8
15 S K,
v:(y:)
gexple
Pi
2 K +
Note that vg(g:) is non-increasing in 9:- When more than K creators have identical relevance scores for user ties are broken by uniformly and randomly selecting K creators, ensuring (4(4:) P: for qi K + 1.
q
The equilibrium condition requires:
0s v2(g u5(0, +1) for all j.
We construct the equilibrium using a self-greedy algorithm, where creators sequentially select strategies to maximize their utility. The algorithm proceeds as follows:
Algorithm Self-Greedy Algorithm for Constructing a PNE
Require: Number of creators n, initial counts of 0 for all i.
1: for = 1 to n do
2: argmax;ggm (1 + 1)
3: end for
Let E denote the time when the last creator selects e;, i.c., E argmin, of q.. The algorithm ensures:
vs va( u: 2 (3 + 1) for all j * i.
Since (g;) is non-increasing in qj. we have (0) +1 N v (o + 1) because 9j s Saf Thus, {q Tm constitutes pure Nash equilibrium.
To extend this result to group of creators with fixed strategies 8., revise the initial conditions {q and repeat the procedure. This yields a PNE for the out-of-group creators, denoted as PNE(s.).
A.2. Proof for Theorem 4.6
Proof. We assume Type is {g If ( {g * {9, 1m there must exists j [m]] q > q7, then there exists k * j. Qo %h and we have
Un (gk + 1) > 2n (gh) 2 (4) + 1) 2 vy(g)).
Since n. S minj Qj. then there exists i s ej. If (4 > U3 (9 + 1), then creator will have incentive to change its action from e; to ex. so {0i}7= is not an Type I. If vz = 04 + 1). by the assumption that {4) 1 is formed by some specific tie- tie-breaking rules, meaning that creators prefer selecting action from to ex. so {q, ) is not an Type 1. By contradiction, Type I is a vanilla equilibrium. Analogously, Type 11 is also a vanilla equilibrium.
to ej, then creator i will change its
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Lemma A.I. In the TvN game, for any equilibrium 8", st, 8 the the following conditions the q values hold:
Q1 2 1, 98 {0, for # 1.
Additionally, the strategy of any individual creator is e1, and we have s' = 8l!
Proof. In the TvN game, the probabilities of exposure are given by: The reward for selecting strategy e; is determined as follows:
+ 1 P1
1
Pi
for i + 1.
2n
2n
0,
if = 0,
8y (g:))
p. exp(3-t) g (6668811++( ()((K=))) Pt
if S S K, 2 k+
Now, suppose @1 = O. this case, there must exist distinct indices i * j such that 8; = 8;; ek, with corresponding utilities u, and uj. If 8, changes its action from ey to e1, the new utilities of the agents are denoted as uf and u'y. respectively. From this, we obtain the following inequalities:
u/ Wis u/j uu, Uj
1/ + u/j us UT.
Thus, in s", st sll, conclude that 91 1.
Next, suppose 8j ek, with utilities and uj for agents and j. respectively. Since 2 1, there must exist a k' * 1 such that qje = O. If s; changes its action from e₁ to ex' the new utilities the agents are denoted by of and v/.. respectively. Again, the following incqualities hold:
nf > ui, un 222
4i nly us + Uj-
Thus, in s", s s", it follows that q < 1 for all i 1.
Finally, in the TvN game, for any K < and * 1, we have:
n2 n+11
0n (91) > (n)
> (1).
2n
2n
Therefore, any individual creator will choose e as their strategy. Since individual creators will all select e,, it follows that
sl "!
A.3. Proof for Theorem 4.7
Proof. (1) When ne 1, Based on Lemma A.1,
qi E {0,1) for i + 1, so the general user welfare is
n + min(K.91)
((s)
Ft +
(8)
2n
2n
According to Lemma A.1, for the vanilla equilibrium 8" {8: = = for all E [n]], for any {re) the optimal welfare achieved when K = m:
argmaxx W (8", K) = n.
And when r1 12 -... T'
((s) = n 1
min(K, K, K,n).
2n
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
So (s) is maximized when K n1, and W mmxx
2+1
(2) When ne n, we have
Qc(s) 5
The equality the above inequality holds when
= ==s" {s: for i [n]}.
Under this equilibrium, the user welfare W W(s!) = 1.
(3) When +
0,
if q: = 0,
(x))))
Pi
if q. 2
9:
Let the number of creators in the group choosing ei be 9
(c), Q1 (c) 2 1, and we have
Qc(g((c)) = #+
(c(c)
+ 2n
(n. 21 (c)).
2n n + (c())
Maximize (c() and we got
qi(c)* or I 1)(n ne) - (n -neel or [v 1)(n ne) -n ne]]
When B + 00,
if q: 0,
vy vx())))
if 2 1.
(c) (c)
ne (c)
n 2n
Maximize Qc(n1) and we got (c))* = Combining Qn (c)) with Eq. 8, we complete the proof.
A.4. Additional results for Theorem 4.7 with more general p
Theorem A.2. Consider a bandit C game with exposure rewards, where the user distribution satisfies p1 2 1, + (n
1)p2 = 1, and p2
Let P1.2 01 Then, st, Moreover, if = 12 TK = 1, the following
results hold:
1. Individual case (n. 1): If 3 + 0, the vanilla equilibrium satisfies P1,2 - 1 of S P1.2 and
W(s", K) = =PI + p2(n 94' 2 (n² + 2n 1) +
2n 1.
P2
B + 00,
W(s", K) = P1 K,
and the optimal welfare is W Waax max,,K K (s,, K) nnn.
2. Full group case (n. = nt): When all creators form single group.
W(s K) 1.
3. Partial group case (1 < ne < n): 3 + O, two cases arise: (i) If of S ne- which is guaranteed when
P2 2 I. then o q.. (ii) If q > then
H < max
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms? and the welfare loss is
Wmax W(s (p1 P2) of-)-
B -+ 0o, we have off and W max = ).
Theorem A.2 can be proved analogousty to the proof of Theorem 4.7.
A.5. Proof for Theorem 4.9
Proof. Based on Lemma A. we have (c) 2 and Øj E (0, for j * 1, meaning individual creators select distinct strategies ej. Additionally, qi - qi (c) in this game, where individual creators have restricted action sets. The group utility is defined as follows:
For S 91 I K, the group utility is:
2 exp(3-1) ai exp(8-1) + 92) Pa( -1)-
Qc(a)) Pı
(9)
Let = exp(8-1)- - 1 E (0, oo). We compute the derivative of Qo( with respect to qı:
(((a) = n+ 1
(b+ + 1)K
2n (g1b b + K)² 2n'
By selecting a sufficiently large 3, we ensure (c(2)) > 0 for S q S K. For q1 2 K + 1, the group utility simplifies to:
Qo(ii) = P1 + P2(ne 91).
Thus, when 1 1 qi S K, Qo(qi) increases as dı increases; when qi 2 K + 1, Qe(gi) decreases qi increases. Therefore, the optimal value of K maximizes the group utility. Combining this result with Eq. 8, we complete the proof.
Note that for more general unbalanced user distribution satisfying P1 2 1, P1 + (n l)p₂ 1, and p2 Ps Pro the results still hold when pi > Kp2. Moreover, when p is uniform, the value of K no longer affects user welfare in this setting.
A.6. Restricted MTvN Game
In the Restricted MTvN game, there are L groups, each of size h, with user distribution pr = n(L+i] for E E [L] and PL+1 = _.... = Pa = m((+1)- Each group specializes in specific topics: for group E E [Z]. the action set is restricted to {ee) U {ELL1, e.+ }. This setup models scenarios where creators with expertise in specific topics form groups to maximize their collective utility.
Corollary A.3. In a Restricted MTvN game, the following results hold:
1. When r1 = 12 = = rk- 1, if B - O, then Wss K) 1. Bf + oo, then W(8 K) = max
2. rf = -... rr = and r++1 = ... = =ra = 0, and h > then:
(n+1)4 K n-KL KST,
W(s K)
n(L+1) n(L+1)'
(n+1)] a-KL n(1++) T+ a(I+1))
K<t
A.7. Proof for Theorem 4.12
Proof. For each group L [L], let (E({) denote the number of creators in group & selecting strategy e₁. If the group
pure Nash equilibrium { differs from the vanilla equilibrium {q) J there exist j, E [m] such that qj < of and qe > %% We focus on the group utility for users j and k. As 3 + 0, the vanilla equilibrium {2) y satisfies:
Pj
Pk
P5
Pk
(10)
9
+
95 +
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Next, compute the reward increment when creator in group & switches from strategy eg ey:
+ (,,
Qr (g,()))))))))))))))))))) (2,(t),
(11)
- (1)-+()))))++11111)) + (g 9 (t) + (k( - 1) (qxx(() - 1) -v+(()) (x(
dj + (8((+)+))
Pj +1)
22 ()) +
Pk
(qx(t) - -1) Pk (E)
qk
Pj (1 (1-b(())
(1- (x(()
Ph
4 + qj
9k -1
ql
For every group [Z] with (x({) 1, q, (6( 0, then based on (10) and the conditions qj S -
-11 11 and @h 2 9% 1,
we have:
Qe(g; (1) 1.
Qr(g, (x)) O.
This implies that a creator in this group can increase the group utility by switching from es to Ej. contradicting the assumption that {q 1 is a multi-group PNE. Therefore, for every E [L] with 9 (f) 2 1, we have gy({) 2 1.
Let Cj.k denote the of groups where (e) 2 1. Since no group has incentive to change strategies, for every & E Cj.ks (11) S O. As (t) qu. |Cj,al 2 Summing over all E Cj.b. we obtain:
Σ (e(g(())+ + (1) 1) - Qe (g)(t). 0 0. REC,
Given that Eieos (i(() S qi and Ereo,N (b( qk. we derive:
Pj
Pk
(12)
43 +
46
Combining the vanilla equilibrium conditions (10) with (12), and noting that Qj S oz - -1 and Qk 2 o + 1, we have:
Ph
Pj
Pj
Pk
Pk
<
9j
+
9k
9k
This implies Ql 9% We now consider two cases:
(1) If there exists l E [m]] such that yk- oh 2, then:
Pk
Pk
Pk
<
(13)
0
+1
9j
4h
9h
+
All inequalities in (13) must hold as equalities, implying dj = 13
1
(2) If for all e [m] satisfying Ok < Th Qk
0% combining (10) and (12), we have:
Pj
Pk
Pk
Pj
96
9
Ph
Thus, 9j 2 9f
Pi
pt
Since dj = of + (0 -;), there are at least (a) - 4j) strategies es with oh = 1, each involving at least 2 groups.
Given that 93 (e) 2 for every & E [L], there are at least 2 - 95) distinct groups in ej. Therefore:
f 2 2(4 4
This yields 0 2 30., completing the proof.
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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
B. Proofs for Section 5
B.1. Submodularity user welfare
Lemma B.1. [Submodularity of Welfare] For any a = (...... ,n), let S {11, ........ ,.,) Then the social welfare
function defined in Eq (2) is submodular as a set function, i.e, for any S. 82, Sy holds that
U {s=}) - ((S) 2 W(S (z 8yt) W(S (8y}).
(14)
Proof. is sufficient prove that for any fixed K and any fixed user Vzj.
Ty U {s+))) (T)( 2 サ, (T) (8,, sy))))
Case 1: If 8.. $ TT U ). then LHS = 0 RHS.
Case 2: If 8, & (S U (Sn, sy)), then LHS 2 and RHS = 0.
Next we assume that 8,r E (S {8., 8y)). We denote the relevance scores of 8x, By toward this user as og and By-
Case 3.1: If By $ (J {s then RHS LHS.
Case 3.2: If By & U {s., {2}) and 8y (S {sy}). so rt ranks the last one in ( ($2. sy1).
we have
LHS RHS = T -
-oo) 20. 0.
Case 3.3: If sy E ( U (s., sy}) and σy 2 o", and we suppose that ṭt replace the original relevance score in By (S U {sz]) index i", then
K-1
LHS RHS = (re= 1o=+ - -o+) +
Σ (n. - -0- - + 20 1=
Case 3.4 If Sy E TT(S sy1) and ṭ² < o", and we suppose that R replace the original relevance score in
By E (S U (8z; my}) at index 1V, then
LHS RHS
K
= - - -wv) - -Tx 0d) + rav+1 - 0x411) Fo+11 0x++1) +
Σ
141 - o(41) r44 -0+11)
t=
ro' -xx) + +r - 0,041) F/x (0" 0i+)+ + Σ
T0+1 - -0+22 0(+2)
t=
2 rww - -0w) - ro - - = (ri - ( - o 2.
We can further extend (14) to more general version: For any S, S' it holds that
W(SUS") W(S) 2 w(SuS'us") -W(Su) w(SUS).
(15)
It is sufficient to prove that for any S, By holds that
W(SU (8,, 8, W(S) 2 U(S
(8,, 8,)) -
Based on Lemma 1. we have
LHS = W(S U WSS.
2 W(SUS' (rgSs//ShseeeeessSSsSsSSSsusussS
((SUS uS -W(SUS)))))))
W(SUS)
RHS.
17

---

Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
B.2. Proof for Theorem 5.4
Proof. We set ((s) (w)s), ((,,)) (s, Under a rescaling of constant B, it is without loss of generality consider scoring function 0. the user utility function, and the social welfare function in the following form.
(S; K) represents the strategies with the top-K relevance scores for user æ.j, where $ = 81,". 8n- If [S] < K, we complement S with strategy O to ensure |S| = K, as this does not affect the result. We prove the theorem for the fixed K. We ignore K in (S), and write as (S) in abbreviation.
m
exp (o6,, (8T( exp (o(s',
(-(8)881))= = Σ
iEC, 1=1
K
W(S) = ( [S(
j,(())
j=1
3=1 Km
We need to prove that
Q0() 2 K -W())-
(16)
It is sufficient to prove that for any [m]]
exp exp (o(88, kz)) EE)T(s)) exp (a 2z))
(Tz(S) Σ Tse (S))
2 B K (T((S) (S){)
(17)
sECg
When s; (S) for any i Ce, (17) is trivially held because LHS RHS 0. With little abuse of notation, next assume that there are h content of group e in (S). Next we let
2x)) 8 E TT())) = [ (2,,02,... Uh Uh+ UK
and
(exp(o(s, 2;)) E (S(S)))) (1/, ubr..., th wn....... vk), where v 2 of for é E [h], and h I min [c and & E [1,e
We let
S, ... Uh SK Ui +... Up + uh+1 UK. SK = St - Sh Pa 01 2 U/
1, P/- 1/22 ... 1/. Pk = 0102 UK PK-h PK/PP
So we can rewrite (17) as
S₁ log Pk 2 Sx
1
[log Ph log P%]
K
Noticed that PA 2 1, is sufficient to show that
Sh log PK 2 log Pn.
(18)
Sx
K
Let
f(1 (Uk)) = Sn log Pk
Sx log Ph
i E [h K].
0f
Sh
1 S₁ log P
Ov:
log Ph
(Sx)²
18

---

Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Since v 1, for Vj [1, e1, so St > log Pk when es So we have the partial derivative of e greater than on 2/ 1:
f ev;
Sh. S log Ps
(1
u = 1.... uK) log Ps.
(Sx)²
Since S. - log Pk is non- -on-increasing in Uú the value of function f in non non- non-decreasing or increases first and then decreases 34 with variable 2 increases, only boundary values of will minimize f.
Thus when we intend to minimize f. v orr e for i [h + K. Suppose that there are us's equal to ed. Then
S = K w + w e
w 3
log Pk- =
So
S
log P/: +
log Ph. (Sn K h w
6
And noticed that for [0, h).
0 < 0 or
0f
2 0.
dw
dw
Therefore, only boundary values of w will minimize f. So 0 or w K h.
(i) When 0 or K h, then
Sh log Ph
Sh
h 1
(Sh. + K h) log Ph.
Sh. K
h K h
K
(ii) When w- K h 2 then:
Sh (log(Ph) + k="
Sh + (K -))ed log(Pn) Ph))
Simplify it we have
Sh f == Sn + (K- h)et
Sp(K - h)
Sn
3 S + (K h)e log(Pr)
B S (K n)ee
log( Ph)
By GM-AM inequality, we have Ph S (Sa/h)/. So
S₁.
Sn.
3 Sn + (K- - N)ed log(Pr)
Bh
Sn + (K - n)e log(Sn/1
We let =
Sn. h. so we have
S₁
(19)
8h
Sr. + (K- - h) log(Sn/h)
B h (K - n))dtt1) logt
3 (1 (1+ (K - 1edd logt
define
G(t) = 3000((11 (K -1e log t.
We only need to prove that G(t) < K. We first take the derivative G(t),
G'(t) t + (K
1)e (1 log
19

---

Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Define Htt) = (K- 1)e (1 logtt). Then we calculate the derivative of (t).
(t) = 1 (K - 1)e
1 S 0.
For (() and B 2
H(t = 1) = 0,
H(t = e = e - (K - 1)e
1 3 0.
So H() > 0 for E [1,e7]. So G(I) non-decreasing for E [1, [1, so G(I) maximized / e
Therefore
- = K. G(L) Gmax (1)
Let (st) and 8" = (87) be different strategy profiles, where 8, represents group f's strategy. First, based on Lemma B.1 and (15), for every e E [4] we have
W([ 8-)) ((s W(( ,6611,88, - (( ((
8))
Summing over all group 1 we obtain
Σ (W((s)),_e)) - ((( 2
Σ (WS) 88-11, W([s), (1)))111)))))
t=1
[[s** 8]) ((8)
2 ((*)) - (s),
where the last inequality holds because the top-K relevance scores are elementwise non-decreasing with the addition of more items (strategies), resulting in non-decreasing user welfare. From the Incqulity (16), we have
Q1(5):811) 2 K
s- -
(20)
And therefore
n
" 8-1)) W(s
Σ 21())8811)
i=1
W(8 W(s)
K
Then we can take expectation over 8 a and obtain
Σ (0(37:00))
1 [W(s") Ee~a [W>o][
(21)
K
Therefore, combining the definition of GCCE, we have
Es~a [W = Egra Σ Qr(s)
E=1
> Eynal
ie(s)i8_1))
[=1
1
E W W([s}, 8- =]]]
Ryna ( +)]
K
1
(W(s*) Exra W [s))]]
K
20

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Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Rearranging terms we obtain
max, ((s)
S 11+ K. PoA(g) aiCCE E. a [[s)]
(22)
B.3. Proof for Theorem 5.5
ed +
Proof. We construct a game instance of the bandit C game with user engagement rewards. Let pt
P2
20 +k-1
and = K. A vanilla equilibrium of this game is s = {s, - e2 for i E [n]], since
2n77 --
u;(s") = P2 = K -1
us(s: = E1. s"
The welfare this equilibrium is W(s*) K2 For the joint strategy 8* Thus, the PoA satisfies
{8i ei). the welfare is W(s*) Kp
PoA(g) W(s*)
Pr
et
K -
W(s") P2 ed
B.4. Proof for Proposition 5.6
Proof. Based on the proof of Theorem 5.4, it suffices to show that for any j E [m].
exp (3- (8,,
(S) Iss TS))
2z)(S) (S- E EVET,(S) exp (B 10 (s' x.)))
(23)
iEC
As B 0 and a E {0, 1}, assume that r1 72 Ty 1 and r++1 Tn 0. If o4 $ T,(S) for any E C..
(17) holds trivially since LHS RHS 0.
Let
{o(s, E TS()) = =00, 02... .h. Oh11.
and
(o(8, 8 E (T((5))) =o] og..., o. oht
where 01 02 ... -.. 1, $ for E [h], and S min [C]]]. Since 3 0 and a E {0, 1}. we have
exp ( 1.)))
Σ [[s E (y() ICCa
EX'ET(S)) exp (B
x
where v is the number of relevance scores equal to 1 in TS)), and æ = T,( Let y = (S-.)) Noting that 2 we obtain for the LHS and RHS of (23):
h LHS = r 2 -r-1 RHS.
The proof of Proposition 5.6 can then be completed analogously to the proof of Theorem 5,4 in Appendix B.2.
C. Supplementary Material for Section
C.1. LBR algorithm (Yao et al., 2024a;e)
21

---

Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Algorithm 2 (LBR) Local Better Response update at time step /
1: Input: Learning rate 7, the joint strategy profile s(t) (s)") s..h) the current step
2: Generate random direction 9i Sd.
3: if (,(s(() 799; ( 2 (s)) then
4: (++1) 8; + gg:.
(e+ 5: Find 8; ((+1) as the projection of 8;
in S,.
6: else
7: #; ((++1) :
8: end if
C.2. Creators' final strategies visualization
Figure presents a visualization of the creators' final strategies under constant attention scores.
Final Positions Exposure
Final Engagement
0.5
0.
0.4
A
0.4
Dinersion
0.0
Dimemiion
0.0
User Proportin
-0.2
-0.4
-0.6
-0.8
Group Creators
00.8
Group Creators Other Creators
Other Creatora
Dinonsion
Dimension 1
(a) Exposure reward
(b) Engagement reward
Figure Visualization of creators' final strategies under constant attention scores, n. 10
C.3. User welfare comparison under different K values
We further validate Theorem 4.9 through simulations with varying values of K, using the same user proportions as in the TvN game but with users no longer orthogonal to each other. All group creators are initialized near user æ,, while the remaining individual creators are each assigned a different user Zy, where o 1. We set n 30, 3 100, and define the attention scores p1 72 Л3 and r; 0 for i 3 (r 3). The group size is fixed at n. 10, and the time horizon set to T = 1000. All other parameters follow the simulation setup in Section 6.
We evaluate K over the set {1, 2, 6, 10, 15). Results for K = 1 and K = 2 are not presented graphically. The final user welfare values for welfare increases with larger K. For K > r, user welfare slightly declines as increases. These results align with and further validate the theoretical results of Theorem 4.9.
and K = 2 are 0.9726 + 0.0019 and 1.9416 + 0.0073, respectively. When K < 7 = 3, user
22

---

Beyond Seif-Interest! How Group Strategies Reshape Content Creation in Recommendation Platforms?
User Welfare under different K values
Final User Welfare under different K Values
k:3
K-16
K-30
2.13300026
2.055
Final User Welfere
3105
User Welfare
2.000
2,800
2.775
2.775
724000014
Round
Value
Figure User welfare under different values
C.4. User welfare comparison under different 3 values
User Welfare Comparison: Different Values (Constant Attention)
USer Viluur
Peremcters 2-0.1
$-10
Figure 4: User welfare under different 3 values
proportions in the TvN game but with users no longer orthogonal to each other. The number of creators is set to n 30, with constant attention scores = 1 for all i E [n], and K n, T' = 2000. We test two values of 3: B = 0.1 and 8 = 10. All other parameters follow the simulation setup in Section 6. A larger 3 leads to higher user welfare, which aligns with the theoretical findings of item in Theorem 4.7.
We also conduct simulations to validate item 3 of Theorem 4.7. We the
C.5. Addiioonal simulations on Zipf-like user distributions
We further strengthen the practical relevance and credibility of our results by using more general based on Zipf-like or pawer-law distribution, where Pj x f.2 with a 1. Such distributions are well-doeumented in real-world platforms and capture the skewed nature of user preferences (Chowdhury Makaroff, 2013; Cameron, 2022; Chris & Simon, 2022).
23

---

Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?
Our setup in the main already follows similarly skewed pattern. The additional results under this new p yield similar results and insights, further supporting conclusions. We present results for 3 different values of a. In these simulations, we first set w = max jo, 0.01 ). and then normalize the user distribution by setting Pj x wy.
Table 1: User welfare under different group sizes and reward types for a 1.1, a 1.5, and a = 1.8.
1.1
1.5
1.8
Size
Exposure
Engagement
Exposure
Engagement
Exposure
Engagement
10
4.72
4.81++0.03
4.80
4.86++001
0.02
4.89:10.02
15
4.65::0.05
4.79:10.4
4.75+0.04
4.87=0.02
4.84=0.02
4.9010.01
20
4.59::0.07
4.81=0.02
4.68:00.6
4.87=0.02
4.73=0.05
4.89+:0011
25
4.52:10.08
4.82:1..03
4.65:10.03
4.87+
4.70=0.03
4.89
30
3.26::0.02
4.77
3.54
4.84
3.75=0.01
4.88
C.6. User welfare comparison under a different creator initialization
Average
Average
Log
23
Average User Wefore
Reaard
Group Size
Group Size
(a) Constant attention
(b) Log cutoff attention scores
Figure 5: User welfare under different reward types, group sizes, and attention scores.
We also examine the impact of alternative creator initialization where all creators initialized around users 2 to 10. Under this initialization, the resulting user welfare under exposure rewards is worse. The simulation results are presented in Figure 5.
24


Reviews:
[{"review_id": "Tq5i1s45sz", "reviewer": "Reviewer_dTVP", "summary": "The paper is attempting to answer : How do group strategies among content creators impact recommendation systems, specifically focusing on content distribution and user welfare? The paper examines how content creator groups impact recommendation systems, contrasting with individual creator behavior. Particularly, they show that  large groups can significantly harm user welfare, especially with exposure-based rewards.\n\nFurthermore, the authors quantifies inefficiency, showing the price of anarchy (PoA) can be arbitrarily large with exposure rewards but is bounded with engagement rewards. They argue and demonstrate that engagement-based rewards better mitigate negative group effects and improve user welfare. \n\nEmpirical results from simulations further support the effectiveness of the user engagement rewarding mechanism.", "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": ">The paper primarily uses synthetic data for simulations. Including empirical validation with real-world data from online platforms would further strengthen the claims and demonstrate the practical relevance of the findings.\n\nThank you for the thoughtful suggestion. We will further strengthen the practical relevance and credibility of our results by using a more general $p$ based on a Zipf-like or power-law distribution, where $p_j \\propto \\frac{1}{j^\\alpha}$ with $\\alpha > 1$. Such distributions are well-documented in real-world platforms and capture the skewed nature of user preferences [1][2][3]. Our current setup already follows a similarly skewed pattern, and we will clarify this in the revision. The additional results under this new $p$ yield similar results and insights, further supporting our conclusions. We present results for two different $\\alpha$ values below.\n\n[1] Chowdhury et al. Popularity growth patterns of youtube videos-a category-based study.\n \n[2] Cameron, S. Zipf’s Law across social media. \n\n[3] Mosaic Ventures. The creator economy: a power law. https://www.mosaicventures.com/patterns/the-creator-economy-a-power-law.\n\n$\\alpha=1.1$\n|Group Size|Exp|Eng|\n|-:|:-:|:-:|\n|10|4.72±0.04|4.81±0.03|\n|15|4.65±0.05|4.79±0.04|\n|20|4.59±0.07|4.81±0.02|\n|25|4.52±0.08|4.82±0.03|\n|30|3.26±0.02|4.77±0.01|\n\n$\\alpha=1.8$\n|Group Size|Exp|Eng|\n|-:|:-:|:-:|\n|10|4.85±0.02|4.89±0.02|\n|15|4.84±0.02|4.90±0.01|\n|20|4.73±0.05|4.89±0.01|\n|25|4.70±0.03|4.89±0.01|\n|30|3.75±0.01|4.88±0.01|\n \n\n\n>The model relies on certain simplifications and assumptions (e.g., relevance function, user attention scores, specific game setups). The paper could discuss the limitations of these assumptions and their potential impact on the results.\n\nWe appreciate your valuable suggestion. \nOur model does make several stylized assumptions as many works in this line also do (Jagadeesan et al., 2023, Hu et al., 2023, Yao et al. 2024a;b). However, we do not see it as a major weakness but rather a necessary simplification to better unveil the theoretical insights. Below, we clarify the rationale and limitations associated with our assumptions:\n1. **Relevance function**: \nThe results in Section 4 are based on the dot product relevance score, which is for the simplification of presentation, and our results also hold for other reasonable relevance functions (e.g., $\\sigma$ depending on $||s - x||$). And our general results—Theorems 5.3, 5.4, and 5.5—do not rely on specific assumptions about the form of the relevance function.\n2. **User attention scores**: \nThese two types—constant and diminishing—represent common user behaviors corresponding to slow-decay and rapid drop-off attention, respectively, providing results and insights under these two kinds of user attention. \n3. **Specific game setups**: \nThe bandits $C^3$ game simulates the fundamental scenario where every creator must select a topic to create content. And, the TvN game, where the user distribution is unbalanced, is recognized as a good example for worst-case analysis (Yao et al., 2024a). While generalizing Section 4's results to broader environments is a meaningful and challenging direction for future work, we highlight that Section 5 already addresses the general case: it makes no orthogonality assumptions about user population vectors and does not constrain the parameter $p$.\n\nWe will include a dedicated discussion about the limitations and potential impact of these assumptions in our revision.\n\n>In the simulations, were the differences in user welfare between exposure and engagement rewards statistically significant?\n\nYes, as shown in Figure 1, engagement reward consistently maintain higher user welfare, while exposure rewards lead to a notable decline. Each experiment is run 5 trials to avoid the randomness. We also emphasize that our simulations do not consider the worst-case group behavior under exposure reward. Under such behavior the user welfare could be even lower than reported. Under an alternative initialization where all creators are intialized around users 2–10, the resulting user welfare under exposure reward is worse. We present the empirical results here:\n\n|Group Size|Exp|Eng|\n|:-:|:-:|:-:|\n|10|4.20±0.07|4.53±0.21|\n|15|4.19±0.12|4.54±0.10|\n|20|4.25±0.17|4.69±0.03|\n|25|4.13±0.22|4.81±0.10|\n|30|3.80±0.04|4.95±0.01|\n\nFurthermore, it is important to note that even small improvements in user welfare can have meaningful consequences in practice. For example, platforms like TikTok serve billions of content impressions daily. Thus, marginal gains in user welfare—achieved through better reward design—can translate into substantial improvements in user satisfaction, engagement, and platform revenue.", "claims_and_evidence": "The paper provides theoretical arguments and examples (like the TvN game) to show that group behavior can significantly alter content distribution and user welfare, especially with exposure rewards. This is supported by mathematical formulations and the concept of group equilibria.\n\nThe argument that engagement rewards are better for user welfare is supported by the PoA analysis and the simulation results, which show higher user welfare under engagement rewards.", "methods_and_evaluation_criteria": "The game-theoretic framework provides a solid foundation for analysis, PoA offers a quantitative measure of inefficiency, and simulations validate the theoretical findings. The focus on user welfare and the comparison of reward mechanisms are central to the research questions. Therefore, the proposed methods and evaluation criteria make sense for the problem at hand.", "theoretical_claims": "I briefly looked at the formulations in the main paper. Do not see any obvious issues.", "experimental_designs_or_analyses": "The experimental designs and analyses are generally sound and appropriate.  The simplifications and assumptions are acknowledged but could be discussed more thoroughly.", "relation_to_broader_scientific_literature": "The TvN game was introduced by Yao et al. (2024a) to model the dilemma faced by creators in choosing between popular trends and niche topics.  The paper uses the TvN game to illustrate the specific impact of group behavior on content distribution and user welfare. It shows how groups can lead to a significant deviation from the individual creator case, especially with exposure rewards. This provides a concrete example of the general theoretical findings.", "essential_references_not_discussed": "The author discussed related work mostly in the study of game-theoretic aspects in recommendation systems. Probably it would be interesting to touch the prior work on empirical studies of creator behavior on content platforms.", "other_strengths_and_weaknesses": "Strengths:\n\n* The paper is generally well-structured with examples that help to clarify the concepts and arguments.\n* The combination of theoretical results and simulations strengthens the paper's claims.\n* The paper clearly demonstrates the advantages of engagement rewards in mitigating negative impacts of group behavior.\n* The paper makes a significant contribution by shifting the focus from individual creator strategies to group strategies in recommendation systems.\n\nWeakness:\n* The paper primarily uses synthetic data for simulations. Including empirical validation with real-world data from online platforms would further strengthen the claims and demonstrate the practical relevance of the findings.\n* The model relies on certain simplifications and assumptions (e.g., relevance function, user attention scores, specific game setups). The paper could discuss the limitations of these assumptions and their potential impact on the results.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "In the simulations, were the differences in user welfare between exposure and engagement rewards statistically significant?", "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": "vSHRjjXZo5", "reviewer": "Reviewer_vc1Y", "summary": "The paper studies how strategic behaviors of a group of creators can affect user welfare with game-theoretic analysis. In particular, they adopt the content creation competition (CCC) game-theoretic framework introduced in prior works, where users and content creators both derive utilities from the recommender system, with a specific definition of utility for both sides. And they assume there are groups of content creators who collaboratively maximize their group utility. \n\nThey conducted game-theoretical analysis under various settings. They found that (1) when the group size is small, groups do not affect the equilibrium much; (2) when group size is large,  user utility suffers a lot. (3) the equilibrium can be quite different under different parameters in the CCC framework, (3) the price of anarchy can be arbitrarily bad when the reward for the creators are exposure (rewarded when created items exposed to users), when the reward for the creators are user engagement( rewarded when created items get user engagement), then the PoA is bounded, suggesting that we might want to use engagement reward to improve user welfare.", "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": ">The paper focuses a bit too much on settings that are not algined with real-world applications. For instance, I think content creators are rewarded for engagement, but the paper focuses a lot on the setting where creators are rewarded for exposure.\n\nAs mentioned in the paper (Lines 144-148), the exposure reward mechanism is widely used in both theoretical and empirical settings (Ben-Porat et al., 2019; Hron et al., 2022; Jagadeesan et al., 2023; Meta, 2022; Savy, 2019), making it an important aspect to study in the context of recommendation systems. Furthermore, both exposure and engagement metrics are used in practice: user engagement tends to be used more often as a reward metric for established creators, while exposure is typically used for new creators (Yao et al., 2023). Thus, our focus on exposure rewards reflects a commonly encountered scenario in many platforms.\n\n>Another example is that users do have limited attention, but the paper focuses a lot on the case where users have infinite attention.\n\nThank you for your valuable comment. We would like to clarify that our analysis does not assume infinite user attention.\n\n1) The constant attention model we use does not imply infinite attention. This attention truncated by the parameter $K$ and it assumes users allocate a fixed amount of attention uniformly across the top-$K$ items they are shown—e.g., $r_1 = r_2 = \\dots = r_K = 1$. This setting is relevant in practice, particularly in user interfaces where content is displayed in fixed-sized, unordered blocks (e.g., a “For You” page with $K$ equally weighted items). Thus, the model captures a common real-world recommendation scenario without assuming that users consider all available content.\n\n2) Our paper also considers another setting with *diminishing attention*, modeled as $r_1 = \\dots = r_\\tau = 1$, $r_{\\tau+1} = \\dots = r_n = 0$, which captures the case where users only pay attention to the top $\\tau$ items. These two types—constant and diminishing—represent common user behaviors corresponding to slow-decay and rapid drop-off attention curves, respectively.\n\n3) The theoretical results in Section 4 can be extended to more general attention profiles $\\{r_i\\}_{i=1}^n$. In particular:\n   - Slow decay attention will lead to results akin to those in Theorem 4.7, implying that large group strategic behavior negatively impacts user welfare.\n   - Under rapid drop-off attention, Theorem 4.9 and Corollary 4.10 hold similar results demonstrating that tuning $K$ and $\\beta$ can help mitigate user welfare loss.\n\n4) In our simulations, we also test *log cutoff attention scores* as an intermediate setting. These results are consistent with our theoretical findings, reinforcing the robustness of the insights under various attention models.\n\nWe chose to present constant and diminishing attention as representative cases to improve the readability and clarity of the exposition. We will clarify this modeling choice and its implications in our revision.", "claims_and_evidence": "I do not find problems", "methods_and_evaluation_criteria": "The paper focuses a bit too much on settings that are not algined with real-world applications. \n\nFor instance, I think content creators are rewarded for engagement, but the paper focuses a lot on the setting where creators are rewarded for exposure. \n\nAnother example is that users do have limited attention, but the paper focuses a lot on the case where users have infinite attention.", "theoretical_claims": "I did not check the proofs.", "experimental_designs_or_analyses": "I did not find issues.", "relation_to_broader_scientific_literature": "It adopts prior frameworks on game-theoretic analysis in recommender systems with strategic behaviors. This paper specifically focuses on a new aspect where content creators might form groups to compete strategically.", "essential_references_not_discussed": "I am not aware of any", "other_strengths_and_weaknesses": "Strengths\n\n1. The paper studies a very interesting problem----the impact of strategic behaviors of content creators on user welfare in recommender systems. It might have many real-world implications. \n\n2. The paper provided theoretical analysis on the game-theoretic dynamics of grouped content creators and user welfare under various scenarios. \n\n3. The paper draw conclusions and insights from these theoretical analysis which make sense to me. \n\nWeaknesses\n\n1. I think the paper's analysis focuses too much on unrealistic settings as I mentioned above. \n\n2. The writing can be improved.  See below.", "other_comments_or_suggestions": "1. In introduction, it might be good to talk about the findings in this work earlier. \n\n2. Many notations are used without definition. e.g. n, K, \\beta in introduction. \n\n3. Acronyms used without explanation, e.g., PNE.", "questions_for_authors": "No", "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": "xLyoxjS5hg", "reviewer": "Reviewer_5tLb", "summary": "This paper investigates group strategic behaviors among content creators in recommendation systems. Specifically, the authors assume that creators within a group can strategically deviate to maximize their collective reward. Using bandit C3 games, they theoretically demonstrate that user welfare can suffer significant losses due to such group strategic behaviors. In more general cases, they analyze the price of anarchy (PoA) of coarse correlated equilibria. Furthermore, they show that user engagement-based reward mechanisms can mitigate these issues compared to exposure-based mechanisms. Simulations support the theoretical findings.\n\n---\n\nI have updated the score to 3 after rebuttal.", "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": ">One major issue is the definition of group deviations. \n\nAs we discussed in the paper (Lines 270-274), suppose that all creators have reached an equilibrium, and then some creators decide to form a group. Joining such a group becomes a dominant strategy because the group utility is at least as high as the individual case—at the very least, it remains unchanged if the creators continue their previous actions. If the group generates additional rewards, the bonus can be allocated among the group members, ensuring that each creator receives a reward greater than or equal to their original reward. Given this allocation rule, the formation of such groups is reasonable. Even if a creator deviates from the group strategy, they have an incentive to re-join the group. Furthermore, in the real world, groups of creators often exist and are typically united by a media company, such as an MCN (Lines 28–33).\n\n>When the users are not orthogonal or the creator strategy set is more general, it is unclear how the results would extend.\n\nWe use this simplified game to better unveil the theoretical insights. In Section 5, we address the general case, where the user population vectors are not orthogonal, and no assumptions are made regarding the parameter $p$. Theorem 5.3 demonstrates that the PoA under exposure reward can be arbitrarily bad, which aligns with the results in Theorem 4.7. Additionally, we provide bounds on the PoA under engagement rewards in the general case. Furthermore, our empirical results in Section 6 and Appendix C further support the theoretical claims in the general cases, where the user population vectors are not orthogonal and the creator strategy set is continuous.\n\n>In Theorems 4.7 and 4.9, the findings seem highly dependent on the choice of $p$. It would be helpful to understand how the results hold for different choices of these parameters.\n\nThank you for your valuable suggestions.\n1) To emphasize the potential negative impact of group strategic behavior on user welfare, we consider the TvN game as an example for worst-case analysis (Yao et al., 2024a). The TvN game, although stylized, reflects user distributions in real-world online content platforms, which are often highly skewed and unbalanced. \n2) Our choice of this representative $p$ is also primarily for clarity and simplification of presentation. Analogous to the proof of Theorems 4.7 and 4.9, we can extend our results to a more general unbalanced case, where the largest user proportion in the TvN game can vary, and this will provide a more smooth transit from the extreme case to the even case. We will incorporate these results into the revision. And we will expand the discussion to explicitly cover how the results extend to general $p$. In particular:\n    - Under unbalanced $p$, similar welfare loss results hold, and group strategic behavior remains impactful.\n    - Under more evenly distributed $p$, the impact of group behavior diminishes, as also implied by Theorem 4.6 and Theorem 4.12. For example, when $p$ is uniform, in Theorem 4.7, the welfare under both the individual case and the $n_c = n$ case equals 1, and the $K$ will no longer affects the user welfare in Theorem 4.9. \n\n\n>I would expect the authors to conduct experiments under varying choice of the vector $p$.\n\nThanks for your thoughtful suggestion. We will further strengthen our results by using a more general $p$ based on a Zipf-like or power-law distribution, where $p_j \\propto \\frac{1}{j^\\alpha}$ with $\\alpha > 1$. Such distributions have been widely observed in user preferences across online platforms[1][2][3]. Our current $p$ already follows a similarly skewed pattern, and we will clarify this in our revision. The additional experiment results under this new $p$ yield similar results and insights, further supporting the robustness of our conclusions. Please refer to the empirical results provided in our response to reviewer dTVP.\n\n\n[1] Chowdhury et al. Popularity growth patterns of youtube videos-a category-based study.\n\n[2] Cameron, S. Zipf’s Law across social media.\n\n[3] Mosaic Ventures. The creator economy: a power law. \n\n>What is the optimistic tie-breaking rule in Line 203, ...?\n\nThank you for pointing this out. It refers to selecting $s_{-c}$ in a way that is most favorable to the group. This rule is specific to the equilibrium introduced in Line 203 and is unrelated to the tie-breaking rule mentioned in Theorem 4.6.\nIn Theorem 4.6, the tie-breaking rule applies to individual creators when their utilities are equal for selecting different strategies. In such cases, a more general and consistent rule is to assume that creators will choose the user with the smaller index, which is generally used in game theory literature. This deterministic rule avoids ambiguity and is suitable for all cases discussed in the paper. In our revision, we will remove the optimistic tie-breaking rule and adopt this general tie-breaking assumption for clarity and consistency.", "claims_and_evidence": "**(Pro)** The theoretical results are generally sound.\n\n**(Con)** One major issue is the definition of group deviations. The formation of such groups is questionable, as some players in the group may be worse off due to their inclusion. Consequently, the stability of these groups is unclear, and some players may have an incentive to deviate from the group strategy. A more reasonable setting would introduce an additional requirement ensuring individual rationality—i.e., players should not be worse off by following the group strategy.\n\n**(Con)** Another major issue is the simplification of theoretical results in the bandit C3 game. The theoretical results in Section 4 rely heavily on this specific game structure. For example, when the user population vectors are not orthogonal or the creator strategy set is more general (e.g., continuous), it is unclear how the results would extend. Additionally, in Theorems 4.7 and 4.9, the findings seem highly dependent on the choice of $p_1, p_2, \\dots, p_n$. It would be helpful to understand how the results hold for different choices of these parameters.", "methods_and_evaluation_criteria": "N/A", "theoretical_claims": "I did not check the details of the theoretical claims, but the results appear to be generally sound.", "experimental_designs_or_analyses": "**(Con)** Similar to the claims section, I would expect the authors to conduct experiments under more general settings, such as varying the choice of the vector $p$. Additionally, incorporating a real-world dataset with user features would strengthen the analysis.", "relation_to_broader_scientific_literature": "**(Pro)** The paper's major contribution is the consideration of group strategic behaviors in recommendation systems.", "essential_references_not_discussed": "No essential references appear to be missing.", "other_strengths_and_weaknesses": "No additional strengths or weaknesses were identified.", "other_comments_or_suggestions": "1. What is the optimistic tie-breaking rule in Line 203, and how does it relate to the tie-breaking rule in Theorem 4.6?\n\nSome typos were found:\n1. The notation $\\sigma$ is inconsistent throughout the paper, appearing in three different forms: $\\sigma(\\cdot, \\cdot)$, $\\sigma_{\\cdot, \\cdot}$, and $\\sigma_{\\cdot}(\\cdot)$.\n2. Line 172: ${q_j^v}$ and $q_j^{eq}$ are not consistent.\n3. Line 214: \"for for\" → \"for\"\n4. Line 224: One of $s_{1,2,4}$ or $s_{4,5}$ in $S^{II}$ appears to be incorrect.", "questions_for_authors": "See the cons listed 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": "m8SHl9UP2n", "reviewer": "Reviewer_SsRd", "summary": "The paper studies group strategies in content creation games: a game framework in which individual creators in a recommender system can form groups. This can lead to interesting scenarios, such as a creator deviating from its strategy in the \"vanilla\" Nash equilibrium, even though this reduces its individual utility, it increases the group’s utility. They provide game classes, such as the bandit $C^3$ and TvN games, under which the vanilla Nash equilibrium and the $C^3$ game with group creators result in the same or different equilibria. They then analyze general $C^3$ games and the Price of Anarchy under exposure and engagement rewards, showing that it can be unbounded with exposure but bounded for engagement. Finally, they provide simulations supporting their theoretical claims on user welfare.", "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": ">For the Bandit C3 game, to get $PNE(G, s)$ you initialize all creators in the group $c$ with $s_c$, wlog say these are 1 to $n_c$; now from $n_c$ to $n$ you follow Algorithm 1?\n\nWe initialize the group of creators with $s_c = (s_1, s_2, \\dots, s_{n_c})$, which are not necessarily identical across all members. As you mentioned, once the group strategy $s_c$ is selected, Algorithm 1 is applied to the remaining $n - n_c$ creators, who then sequentially choose their strategies to complete the profile.\n\n>In the Type 1 and Type 2 equilibria, and more generally for the theorems in Sections 4.1 to 4.4, each individual in the group c plays the same strategy $s_c$, right? \n\nNote that $s_c = (s_1, s_2, \\dots, s_{n_c})$. Creators within the group are allowed to adopt different strategies (actions), and these strategies are not necessarily identical. In both the Type 1 and Type 2 equilibria, the strategies of group members can differ—the equilibrium does not assume a single shared strategy across all group members. And in Figure 2 of the appendix, the group creators (represented by red triangles) indeed employ different strategies. \n\n\n\n>Can you specify how gradient descent is used to approximate the optimal group strategy at each round?\n\nThank you for pointing this out. The group aims to select $s_c = (s_1, s_2, \\cdots, s_{n_c})$ in order to maximize its group utility, defined as $Q_c(s_c, s_{-c}) = \\sum_{i \\in \\mathcal{C}} u_i(s)$. To approximate the optimal group strategy at each round, the group can perform multiple steps of gradient descent on the objective $Q_c(s_c, s_{-c})$ with respect to the group strategy $s_c$, assuming that the group has full knowledge of the game environment. In more realistic scenarios, the group can instead adopt trial-and-error approaches to iteratively improve its group utility over time. Alternatively, heuristic methods may be employed—for example, assigning certain creators to dominate the exposure of the largest user while others are allocated to target remaining users. This structured, adaptive strategy allows the group to improve utility even with limited information. We will include this clarification in our revised version.\n\n\n>I believe there’s a typo on line 175, column2: “… shapes the same”, I think you mean equal up to permutation of strategies?\n\nYes, we mean they are equal up to permutation of strategies.\n\n> Can you provide more insights on the importance reweighting method mentioned on line 356?\n\nThank you for pointing this out. The importance reweighting method, as proposed in (Yao et al., 2024b), enables the platform to steer creator incentives toward under-served users by modifying the reward structure. Specifically, the platform defines the creator's utility as \n\n$$\nu_i(s) = \\mathbb{E}_{x \\in \\mathcal{X}} \\left[ w(x) \\pi(x, s) P_i(s, x) \\right],\n$$\nwhere $w(x)$ represents the *importance weight* of user $x$. When the platform detects that a user is being under-served under the current content distribution, it increases $w(x)$ for that user. This effectively amplifies the reward for creators who target such users, encouraging them to shift their content in that direction. Over time, this reshapes the content distribution and improves overall user welfare. As a concrete example, consider the game instance in Appendix B.3. In that case, we can set the reward as \n\n$$u_i(s) = w(x_1) \\pi(x_1, s) P_i(s, x_1) + w(x_2) \\pi(x_2, s) P_i(s, x_2),$$ \nand choose $w(x_1)$ to be large and $w(x_2)$ small. This encourages all creators to shift from $s_i = e_2$ to $s_i = e_1$, \nleading to a new PNE where user welfare is optimal. Once this equilibrium is reached, the platform can reset the weights to $w(x_1) = w(x_2) = 1$, and creators will no longer deviate. We will include a detailed explanation and discussion of this method in revision.", "claims_and_evidence": "Yes, the theorems and lemmas are clearly stated and have proofs in the Appendix.", "methods_and_evaluation_criteria": "Yes, the polarized synthetic dataset and experiments with LBR algorithm support the theoretical claims namely Theorem 4.7, 4.9 and 5.4", "theoretical_claims": "Yes, I’ve checked the correctness of Lemma 4.3, Thm 4.6 and 4.7. \n\nA quick clarification on the last statement in section A.1:  For the Bandit C3 game, to get $PNE(G, s_c)$ you initialize all creators in the group $c$ with $s_c$, wlog say these are 1 to $n_c$; now from $n_c$ to $n$ you follow Algorithm 1?", "experimental_designs_or_analyses": "Yes, the experiments are sound and support Theorems 4.7, 4.9, and 5.4. However, some details are missing:\n-  Can you specify how gradient descent is used to approximate the optimal group strategy at each round?\n-  According to Figure 2 in the appendix, the group creators (red triangles) are dispersed. Just to clarify, this is not for the fixed group strategy as in Section 4.1; here, group creators can have different strategies within a group.", "relation_to_broader_scientific_literature": "This paper is a good contribution to the literature on content creation games. The concept of producers forming groups is novel and has not been considered in prior work. The technical results are solid and provide a theoretical characterization of new kinds of equilibria, namely: Single-Group Stackelberg Equilibrium (Definition 4.4), Single-Group Nash Equilibrium (Definition 4.5), and scenarios in which they differ from the \"no-group\" individual creators' Nash equilibrium. The paper also provides Price of Anarchy bounds for general $C^3$ games with group strategies and builds on the PoA characterizations in Yao et al.", "essential_references_not_discussed": "Although not an essential reference, I wonder if the authors considered connections to the literature on Algorithmic Collective Action in Machine Learning, https://proceedings.mlr.press/v202/hardt23a.html. Here, too, individuals can form groups to achieve a collective goal.", "other_strengths_and_weaknesses": "Overall, I enjoyed reading this paper, and it has clear theoretical contributions and corresponding practical takeaways:\n\ni) The insights from Theorem 4.7 demonstrate how welfare under the single-group Nash equilibrium $s^{II}$ has a drastic decrease compared to individual creators.\n\nii) The insight from Theorem 4.9, shows how welfare varies with the topK value and that the platform should avoid very large $K$ due to diminishing attention spans.\n\niii) The Price of Anarchy under exposure and engagement rewards is analyzed and provides a good follow-up to the literature on $C^3$ games PoA from Yao et al., now with group strategies.\n\nThe only weakness is in the description of Section 6, and it would improve the paper if the experimental design description were expanded in Section 6 or Appendix C, as I highlighted earlier.", "other_comments_or_suggestions": "I believe there’s a typo on line 175, column2: “… shapes the same”, i think you mean equal up to permutation of strategies?", "questions_for_authors": "1. In the Type 1 and Type 2 equilibria, and more generally for the theorems in Sections 4.1 to 4.4, each individual in the group c plays the same strategy $s_c$, right? This is different from the example in the paragraph on line 172. I believe the results in Theorem 5 do not require this single group strategy. \n2. Can you provide more insights on the importance reweighting method mentioned on line 356?", "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: The paper deals with strategic content providers, raising the novel aspect of group strategies. The theoretical contributions are interesting and non-trivial, and the experimental validation helps to demonstrate further how coalition formation shapes content creation.  While the reviewers had their concerns (e.g., assumptions, synthetic experiments), the authors' rebuttal seems to have cleared them all. 

I recommend accepting this paper and hope it will impact the "strategic content providers" line of work.
Decision: Accept (poster)