Unveiling User Satisfaction and Creator Productivity Trade-Offs in Recommendation Platforms
Authors: Fan Yao
Yiming Liao
Jingzhou Liu
Shaoliang Nie
Qifan Wang
Haifeng Xu
Hongning Wang
Venue: NeurIPS 2024 poster (2024)
Keywords: Mechanism Design
Content Recommendation Platform
Content Creator Competition Game
Creator Productivity
Primary area: algorithmic_game_theory

Abstract: On User-Generated Content (UGC) platforms, recommendation algorithms significantly impact creators' motivation to produce content as they compete for algorithmically allocated user traffic. This phenomenon subtly shapes the volume and diversity of the content pool, which is crucial for the platform's sustainability. In this work, we demonstrate, both theoretically and empirically, that a purely relevance-driven policy with low exploration strength boosts short-term user satisfaction but undermines the long-term richness of the content pool. In contrast, a more aggressive exploration policy may slightly compromise user satisfaction but promote higher content creation volume. Our findings reveal a fundamental trade-off between immediate user satisfaction and overall content production on UGC platforms. Building on this finding, we propose an efficient optimization method to identify the optimal exploration strength, balancing user and creator engagement. Our model can serve as a pre-deployment audit tool for recommendation algorithms on UGC platforms, helping to align their immediate objectives with sustainable, long-term goals.

Unveiling User Satisfaction and Creator Productivity Trade-Offs in Recommendation Platforms
Fan Yao"
Yiming Liao Meta yimingliao@meta. com
Jingzhou Liu Meta j jingzho ctttcho@@met..comm com
University of Virginia ty4bcovirginia, edu
Shaoliang Nie Meta snie@meta.com com
Qifan Wang Meta
Haifeng Xu
Hongning Wang
University of Chicago
University of Virginia
wqf wnfcrmmetaccom com
haiifengxuuuchicagooo edu
hw5x@virginia edu
Abstract
On Eser-Genereted Content (UGC) platforms, recommendation algorithms sig- nificantly impact creators' motivation to produce content they compete for algorithmically allocated user traffic. This phenomenon subtly shapes the volume and diversity of the content pool, which is crucial for the platform's 's sustainability. In this work, we demonstrate, both theoretically and empirically, that a purely relevance-driven policy with low exploration strength boosts short-term user sat- isfaction but undermines the long-term richness of the content pool. In contrast, more aggressive exploration policy may slightly compromise user satisfaction but promote higher content creation volume. Our findings reveal a fundamental trade-off between immediate user satisfaction and overall content production on UGC platforms. Building on this finding, we propose an efficient optimization method to identify the optimal exploration strength, balancing user and creator engagement. Our model can serve as pre-deployment audit tool for recommen- dation algorithms on UGC platforms, helping to align their immediate objectives with sustainable, long-term goals.
1 Introduction
llser-generated content (UGC) platforms have become an indispensable component of our daily lives [5, 45]. Those platforms, including various social media (e.g., Facebook, Instagram), streaming services (e.g., YouTube,, TikTook and many more, count on algorithmic recommendation algorithms of content generated by creators. Unlike other content recommendation platforms such as Netflix and Spotify, user experience on UGC platforms critically relies on the active participation of creators [58], as the goal of enhancing user engagement is inherently linked to the abundancy and diversity of the content pool.
[36, to help content consumers (i.e., users) navigate the vast
Recent studies have begun to explore how platform's 's algorithmic decisions, such their employed recommendation algorithms and revenue sharing agreements, might influence the behavior of content creators and subsequently affect user welfare [52, 54, 55, 34, 30, 33, 32, 43). A common technique used in these works is to model the competition among creators who strive to establish their brand and comparative advantages by selecting topics that maximize the traffic rewards from the platform. While these competition models offer valuable insights into how platforms' interventions could lead to suboptimal outcomes in terms of content diversity and issues related to popularity bias, they ignore the dimension of content creation volume - an equally critical aspect of such competition
algooort
Research conducted during intersship at Meta. Corresponding author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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dynamics. In fact, there are evidence suggesting that traffic received directly influences creator productivity [31, 56]. recent study on a leading video recommendation platform found that creators whose content received boosted exposure significantly increased their video production without compromising quality [31]- And a recent field experiment on a large-scale video sharing social network showed that while popularity-based recommendation strategies boost content consumption, they can reduce content production [56]. The similar effect has also been documented on Instagram. For instance, when the recommender system allocates more traffic to targeted groups of creators, their production frequency increases, as indicated by metrics such as the number of daily active creators and the daily average creation volume per group. However, disproportionately boosting traffic to certain creator groups can negatively impact others; for instance, directing more traffic to popular, or "head", creators often diminishes engagement from less prominent, or "tail", creators. And overall, statistically significant positive correlation exists between content viewership and the corresponding creator's productivity?.
evidence and the research gap in modeling production frequency within content creation competition, we introduce new game-theoretical model, named Cournot Content Creation Competition (C*), aiming to study the impact a platform's 's recommendation strategy on creators' production willingness. Our C' framework builds upon the Content Creator Competition (C9) framework introduced in [52, 54, 55], assuming that creators compete for platform- alloccate user traffic [27, 29]. However, unlike C and similar previous models, our approach models the competition where creators are aware of their expertise and consistently produce within their niche, but strategically adjust their production frequency balance gain and cost, which is often observed on mature platforms such as YouTube and Instagram. Our proposed competition model resonates with the well-established Cournot competition [14] in economics, where firms compete for revenue by strategically setting their production quantities. Hence, it inherits its name.
Motivated by
Our Ca framework offers powerful tool for analyzing the competition dynamics among creators, as it always yields a unique Pure Nash equilibrium (PNE) that enables a precise prediction of the total content creation volume under any specific recommendation strategy. Furthermore, our in-depth analysis of C*'s 's equilibrium reveals a critical and interesting insight: while increased recommendation accuracy boosts immediate user satisfaction, it simultaneously reduces creators' motivation to produce content, potentially compromising long-term user engagement. This finding, supported by both theoretical analyses and simulations, suggests the necessity to balance user and creator engagement through a careful control over the recommendation algorithm's 's exploration strength at a per- user basis. We formulated this mechanism design challenge bi-level optimization problem and tackled it using a projected gradient descent approach with an efficient gradient approximation scheme, providing an effective method to achieve the optimal trade-off between user satisfaction and creator productivity.
In summary, our contributions are threefold: (a) modeling-wise. we introduce new tteoretheott framework, C+,, to investigate how recommendation algorithms affect content creation frequency among creators; (b) conceptually, we reveal new insight that managing the exploration strength of the recommendation algorithm can balance between short-term user satisfaction and long-term creator engagement at equilibrium; and (c) technique-wise, we reformulate the mechanism design problem of identifying the optimal engagement trade-off at the equilibrium into a solvable offline optimization problem, tackled using approximated gradient descent. Our CA framework and its derived solution serve as pre-deployment audit tool for platforms, assessing the effects of algorithmic choices on creator and user engagement.
2 Related Work
The study of online content creation economy has captured the attention of machine learning commu- nity recently, leading to a diverse collection of models addressing the dynamics of content creator
competition [25, 24, 3, 54, 52, 57, 32, 34, 30, 16]. In these models, creators strategically select the type [49], topic [30, 34, 52], or quality [25, 32] of their content, competing for resources such as traffic [30, 2, 24], user engagement [52], or platform-provided incentives [57, 54]. Some models
aim to explore the properties of creator-side equilibrium, investigating how creators specialize at
Further details regarding the Instagram findings are protected under a non- di---isslouuee agreement (NDA) and may be disclosed in future versions of this work.
2

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equilibrium [34], the impact of creators' strategic behaviors on social welfare [52], and the design of
optimization methods for long-term welfare considering these behaviors [2, 3, 54, 57, 32, 33, 39]. Unlike these works, which generally assume equally paced creation frequency among creators, our proposed Cs games consider scenarios where creators strategically control their creation quantities, allowing us to analyze how recommendation algorithms influence overall content creation volume at the equilibrium.
Our model of the platform's is recommendation algorithm draws inspiration from the proportional allocation concept in game theory, applicable to resource distribution [9, 41] and contest design [48]. We assume that each user contributes a unit of traffic, which is allocated to creators based on both of their merit and effort (content creation frequency). This modeling is closely related to the Tullock contest [48], also known as the lottery contest, where the probability of winning a fixed prize is proportionate to the effort expended relative to the total effort by all contestants. While the Nash equilibrium of the one-dimensional Tullock contest with homogeneous costs is well-understood [20, 21], our work extends this framework to include heterogeneous convex costs. recent study [53] also explored competition between human and Generative AI creators within similar setup, examining its impact on total content creation volume. However, they did not address the influence of different recommendation algorithms, which we investigate in our work.
In a broader sense, our work contributes to a line of research evaluating the impact of recommender systems on individuals, specifically exploring how deployed algorithms shape user and content creator behavior [16, 12, 11, 38, 17, 35, 19] and how we can design new algorithms to address these effects [10, 50, 6, 51, 4, 43, 1]. Our study introduces a key insight: recommender algorithms optimized solely for user satisfaction can unintentionally reduce content creators' willingness to engage, thereby impacting long-term user engagement. We address this challenge by proposing a solution that balances creator engagement and user satisfaction through imposing exploration strengths tailored to individual users.
3
The Cournot Content Creation Competition
In this section, we introduce the formulation of Cournot Content Creation Competition (C*), which models the competition among creators for traffic on UGC platforms. This model considers the potential impact of the platform's 's traffic reallocation mechanisms, such as their deployed recommen- dation algorithms, where creators strategically choose their production frequencies to optimize their allocated traffic. Each CH4 game instance G is characterized by tuple (n, m, M, J (1.) We detail each component of this tuple as follows:
1. Basic setups. There is a set of content creators denoted by (1, , ne). and set of users denoted by {u,} We assume each user j has a stable preference over creators and such relationship is captured by an n-by-m matrix M with its (ith) entry way E [0, 1] denoting the strength of user j's preference over creator i's content. Each creator determines production frequency I; E R20 in a unit amount of time (c.g., one week/one month). For the purpose of analysis, z; can be interpreted interchangeably as either the production frequency volume, provided there is no ambiguity Follow the terminology of game theory literature, 2; is referred as the action or pure strategy of creator i. Each creator is associated with cost function C, which characterizes the cost for creating content at frequency Ey. We have two assumptions about c: 1. G is increasing in i; and cx(x;)) - t00 as x; + +00, which reflects that content creation is always not free. 2. G is convex in I; indicating a non-decreasing marginal cost of improving production frequency.
2. Platform intervention. We assume that each user uy contributes a unit amount of traffic, and the platform redistributes the total user traffic based on relevance-bate based recommendation algorithm that adheres to certain probabilistic principle. Specifically, the recommendation algorithm matches uj to each piece of content produced by creator i with probability proportional to cxp(B) where oi = Wig + Gjj represents the algorithm's 's estimated relevance score. This score combines the true preference score Wij with independent Gaussian noise Eg (O, o²). The parameter 3, 2 0 governs the exploration of the matching for user uy: a higher 33 results in more precise
$ For the elegance of our theoretical analysis, we treat x; as a continuous variable, although the key messages and insights of this paper are preserved if 2;; is discrete.
3

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matching, while lower 3, introduces more exploration into the matching results In this work, we analyze intervention mechanisms that operate under this Personalized Probabilistic Matching (PPM) principle, parameterized by B (3: V and refer to it as PPM(3) for ease of notations.
Creator utility. Creators are reward-seeking individuals who try to maximize the expected traffic for their created content while carefully balancing the costs. Under PPM((3) and when each creator produces 24 copies of content, the platform will allocate to the amount of traffic from
x .²p
Here should note that 2; does not suggest the creator would create x; pieces of identical content, but amount of content following his/her expertise. Therefore, we formulate creator i's utility function the following:
"j proportional Beg~W(0,00)) [maeli(ws
m
E E
(x x2113) =
- (2(2)
W (
j=1
24 S
c((T)),
T3 k= The
where v- E 1220" denotes the strategy profile of all creators except i.
The Ca game models the scenario where creators are aware of their expertise (i.e., what topic to create), and compete purely on creation quantity. This concept is akin to the extensively studied Cournot competition [14] model in economics, where firms independently determine the output of homogeneous products at different costs. However,
model diverges from the classic Cournot competition in several key aspects. First of all, they have different revenue functions: in Cournot competition, the revenue for each firm is calculated as the product of price and production quantity, and the price only depends on all firms' joint strategy. In contrast, in the C'4 game, the gain of a creator not only relies on other creators' decision but also hinges on the platform's 's traffic allocation algorithm. In addition, while Cournot competition typically incorporates only linear cost functions, the Ct game accommodates general convex cost functions, offering the real cost faced by creators. These distinctions highlight the unique aspects of our model, while maintaining conceptual link traditional economic theories of competition.
nuanced reflection of
Research questions: Under the Cdd framework, an important and natural research question is how we can predict creators' strategic choices in the competition. This is fundamental question in game theory and we employ the concept of Pure Nash Equilibrium (PNE) [40] to characterize the outcome of O games. The definition of PNE is given by the following:
Definition 1. A joint strategy profile of all creators x² (si,... ,=+) forms a pure Nash equilibrium (PNE), if for every creator x, is a best response strategy that maximizes u, given other creators' strategy s; formally,
u, u,( x=.)) 2
for every E R20. Vi E [n).
In other word, a PNE represents stable state when everyone is satistied with their strategies and does not want to deviate. As we will demonstrate in the subsequent section, PNE always exists in 4d under any PPM(3) and can be computed efficiently. This finding forms the basis for our further theoretical analysis and empirical simulations.
In addition to the predictability and stability of creators' production strategies, it is equally crucial for platform designers to develop metrics that encourage the prosperity of the content ecosystem. They must also devise algorithmic solutions to optimize these metrics, balancing the trade-off between engagement of users and creators, using the available "knob" PPM((3). We will explore these issues in the upcoming technical discussions.
4 The PNEs of 4H Games and Their Properties
As widely known, the PNE does not always exist [18, 23, 26]. However, our first main result establishes that, under mild assumptions, Ct always admits unique PNE.
"The randomness in matching results may stem from either the imperfect estimation of the preference score Wi or intentionally injected exploration strength based on the intervention mechanism. In this paper, we focus on the latter source of randomness and analyze how such exploration strength might affect the outcomes.

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Theorem 1. For any Ca instance (n,, m. M, M, If each is convex in Iú G admits unique PNE.
Note that the primary challenge in proving Theorem 1 is to show G is a strictly monotone game, whereas the existence and uniqueness of PNE such games a classic result from [44]. Theorem is interesting from multiple perspectives. First, it strictly generalizes previous equilibrium existence results in classic Tullock contest [42, 13], which corresponds to the special case when m = 1 and W11
monotone is significant because it is well- known that the PNE of strictly monotone games can be found efficiently. For example, many natural multi-agent online learning dynamics such mirror descent [7]. accelerated optimistic gradient [8], and payoff- payoff-based learning [47] guarantee the last-iterate convergence to the unique PNE in strictly monotone games,
Wn1. Second, the fact that C* games
when players have mere zeroth order feedback about their utility functions. These results suggest that the PNE of G is achievable if all creators use a reasonable update rule in their strategies. This observation not only makes this equilibrium plausible prediction of competition but also paves the way to our simulation-ban studies in our experiments, where we use multi-agent mirror descent with perfect gradient numerically solve the PNE of C*.
In addition to the existence and uniqueness properties, the following corollary characterizes the first-order characterization of G's PNE.
Corollary 1. The unique PNE x= (B) of any ((n, m, M, {GH! 3) satisfies firt condition:
Ou:
=0, Isisn.
0z, (
Since we have already shown the existence and uniqueness of G's PNE, Corollary follows immedi- ately according to Definition 1. Corollary is useful for establishing further properties of Cal games in Section 5.
5
The Trade-Off Between User and Creator Engagement
We have established that unique PNE exists in any C2 game under any PPM((3) and can be naturally achieved by competing content creators. This raises crucial question for platform designers: how should the quality of the PNE be evaluated? For any mature UGC platform, it essential balance user satisfaction, which is key short-term prosperity, with creator engagement, which is crucial for long-term sustainability. Within our Cdd framework, this requires the platform designer to generate matching results that not only guarantee high user satisfaction (by improving the average matching quality PNE) but also stimulate substantial content creation volume (by encouraging creators to increase their production frequency x² at PNE). We define these two objectives follows:
Definition 2. For any CA instance G(n, m, M, 1.)), let x" (B) (zi, ,,,,,, be the umique PNE under PPM(3). Then the (short-term) total user satisfaction defined as
Wiy exuus
=
ΣΣ
E
(4)
1
and the (long-term) total content creation volume is defined
"
V(x = Σ
(5)
The social welfare of the whole system is measured by linear combination Of and V, defined as (x( U(=" (B): (Vx=(()):))
(6)
If we denote (x (8), Σm_ EE= P Pa as the indicator of an individual user's satis-
faction or utility, which is the expected matching scores of user j at the PNE under PPM(3). And the total user satisfaction measure U = Σm 7H the accumulated user utility. We argue that U primarily serves as a metric for short-term welfare evaluation, since it focuses solely on user satisfaction at specific instance of matching outcomes but does not capture the dynamics of user
5

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engagement over time. This overlooks the crucial fact that sustained user engagement on a platform requires continuous supply of relevant content, as users can hardly be satisfied by their previously consumed material. This limitation is also evident in U"s mathematical formulation: its value remains unchanged with a rescaling of {a;)- indicating that fails to reflect changes content volume or frequency that might affect long-term user engagement. On the other hand, the long-term prosperity of a UGC platform is fundamentally linked to the engagement of content creators. Therefore, we introduce the total content creation volume V as indicator of the long-term welfare of the platform.
For the platform designers, is essential develop metrics that balance both short-term and long- term considerations. Thus, we propose a hybrid social welfare metric, W, which combines U and V to reflect both user satisfaction and content supply sustainability. However, understanding the mechanisms to optimize U and V independently is critical. In the following sections, we will explore the optimal matching mechanisms tailored to the exclusive objectives of (short-term) and V (long-term), and then present an efficient algorithm designed to optimize W.
Interestingly, our findings suggest that both U and V exhibit monotonicity with respect to the parameter B, even in scenarios involving a homogeneous user population. This uniform behavior of U and V offers valuable insights into how the adjustment of exploration strength could potentially impact platform performance. Our forthcoming theorem formally characterizes these observations.
Theorem 2. Consider any C* game with m = 1. If the elements of M = [[11,'" " [ are not identical, it holds that:
1. (B) defined in Eq. (4) is strictly increasing in 3.
2. (() defined in Eq. (5) is strictly decreasing in 3 E |So. +00) for some 30 > 0.
Theorem 2 conveys two significant insights. The first one, though perhaps unsurprising, reveals that improving matching accuracy corresponds to an increase in expected user satisfaction. Despite its intuitiveness, this is strong observation because it holds without relying any specific structural assumptions about creator cost functions. This means that regardless of the potential complexity in equilibrium structures due to creator costs, and even when the order of 5 does not align with creator's ' capability wi, the metric U is still monotonically increasing with respect to B. The second insight may surprise some readers: it suggests that while keep increasing the matching accuracy motivates some creators to produce more content, it demotivates others, resulting in a net decrease in the overall volume of content creation. This finding illustrates intrinsic trade-off between short-term matching accuracy and long-term content supply: strategies that enhance short-term user satisfaction can inadvertently reduce content creation frequency across creators. To the best of our knowledge, this result is novel and has not been discussed in similar studies.
Here is an intuitive explanation for why a large 3 diminishes creators' willingness to produce content. As the traffic allocation becomes more deterministic, the marginal gain from increasing production frequency diminishes because the amount of traffic accrued is largely determined by the relevance score, rather than volume. In the extreme case where / - +00, only the most relevant creator captures all the user traffic, regardless of her production volume. Consequently, due to the presence of production costs, this creator, and others, will only sustain the minimum viable productivity. Conversely, in the other extreme scenario where / = 0, i.e., user traffic is distributed uniformly among creators irrespective of relevance, the gain for each creator depends solely on their production frequency, prompting productivity arms race. Clearly, both extremes are suboptimal, but they effectively illustrate the rationale behind our theoretical findings.
Although in Theorem 2 we consider the game instance G with = 1 as representative snapshot of how creators compete for a single unit of user traffic (i.c., homogencous user population), extending the time frame to encompass sequence of hetcrogeneous users suggests that the observed trade-off between U and V remains consistent. In our experiments, we will demonstrate this trade-off in broader settings through simulations, e.g. when m I and with various complex user distributions.
The proof of Theorem 2, while delivering a clear message, far from trivial. Since the dependencies of U and V on , are indirectly linked through x², which lacks a closed form, the derivation of their derivatives with respect to 33 necessitates the use of the implicit function theorem [37] to articulate the derivative of x" with respect to B. This involves complex matrix inverse, which we simplify using the Sherman-Morrison formula [46] due to its structure being a diagonal matrix with a rank-one update. This proof technique not only supports our theorem but also inspires novel first-order

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optimization approach to address the hybrid social welfare optimization discussed in Section 7. Detailed proofs are provided in Appendix A.2.
Finding the Optimal Trade-off through Optimization
Our theory thus far indicates that optimizing both user satisfaction U and creator engagement V is non-trivial, even when the user population is homogeneous, as achieving the optimal of U and V simultaneously is impossible. Consequently, an essential and intriguing question arises within any specific competitive environment C*: how can we identify the optimal trade-off between these two factors by optimizing any given welfare metric W
Generally, the welfare metric W influenced by three factors: the platform's algorithmic recommen- dation policy PPM(3), the resulting content creation profile x" at the PNE induced by 3, and the relevance matrix M. Thus, we can formulate the resulting optimization problem (OP) as follows:
Find
arg max (x (3), BER
8.t.
(G) is the PNE of G.
In general, OP (7) presents a formidable challenge, solving for PNE of a game is known to be difficult [15]. Fortunately, the nice structure of C# allows us to utilize the implicit characterization of the PNE detailed in Corollary I to tackle OP (7) effectively. In the subsequent section, demonstrate that the gradient WA w.r.t. 3 can be explicitly computed.
6.1 The Derivation of Exact Gradient
According to the chain rule, the first-order gradient of W,, w.r.t. B can be expressed as
dW> (U'x" (U),) +
dV (xxx OU
JV
dx
OU
(8)
d3
d3
dB
ax
Ox
dB
03
The evaluation of the gradient of W2 relies the calculation of three vectors, au av R lxn. and aU
8m
03 E 1= as well as Jacobian matrix dg E _R=xm The computations of Dw dæ and äp
de-
DV a0
are straightforward and computationally light, which position the main challenge as the computation of de dg
Fortunately, the first-order characterization x by Corollary enables us to express the
gradient of x= w.r.t. f using implicit function derivation [37] as dæz
OF ar where dz
03
F(x, = n X n and n x m, respectively. The following proposition provides the exact formula for the gradient. The calculation is straightforward and we omit the detailed derivation.
aug
is an n-valued function, and both aF and aF are matrices of dimensions Væ
Jz.
Let xx = ;h) be the PNE of G(n, m, M, ( B). Then, the Jacobian matrix of x" a function of ß is
Proposition
dx
(D+YZT) B BER"X",
d3
where is an n diagonal matrix given by
P2
p2
D = diag &
+
3 +
Σ
nj
(10)
+2
j=1
and B, Y.Z are Ruxm matrices calculated as follows (1 dliss, n2,s,15si m):
Y = Pi 2P,))
=
Ps
B
(1 1 2Pr;)
U6ij
Σ k=
Wky Pki
x
(11)
where of is the second-orde order derivative of creator i's cost function, and P.j the probability that creator is matched with user j at the PNE under PPM(3).
2, exp(3, wss)
Dim "f exp(23 (0, mm))
7

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6.2 Optimization with Approximated Gradients
Proposition together with Eq. (8) offers us a possibility directly apply gradient- based approaches for solving OP (7). However, the gradient computation requires the inversion of an matrix, whose time complexity is O(n²) and thus too cumbersome. To reduce the computational burden, we Morrison-ooddbrry formula [46]
propose to approximately compute the gradient using the to approximate the matrix inverse, inspired by the specific structure of the RHS of Eq. (9). According to Sherman-Morrison- Woodbury formula, it holds that
(D +
(1- Z
(12)
and the computation of the RHS of Eq. (12) now requires a time complexity of (n nm? + m However, the size of the user population efficiently compute the RHS of Eq. (12), we propose a method to "sketch" the matrices and Z by sampling subset of users. Initially, each column of Y and Z corresponds to user index j. We begin by sampling a sub-population of X, indexed by I, with [I] = m = [6m], where ō E (0, 1] denotes the sampling rate. With this sampled index set I, we construct matrices Y, E RR where the (ith) entries are defined as follows:
in practical scenarios is often even larger than n. To
Yu 1g.11-PPp) 27
Ps 27
Zij-
(13)
with j' being uniformly sampled from I. Given that Y, 2 now possess reduced ranks of [ōm]] the computational complexity of evaluating (D + Y --1 is significantly lowered to O(n²m m + mm² m)). Algorithm describes the steps for addressing OP (7).
Algorithm 1: Approximated Gradient Descent for Solving OP (7).
Input:
The environment specified by G, maximum iteration number T,, sample rate ô, learning
rate 1), initial mechanism PPM(3).
for 1 E [T) do
2
Find the PNE xx of 9 under PPM(33) using Algorithm 2,
Uniformly sample [8m] users from X' and use them to compute matrices Ý, 7, in Eq. (13), Compute the approximated gradient dWa using (8).(9)(112) with sketched matrices Y, Z, d3
Update 3 = 9 n dW> 43
Algorithm I requires solving for the PNE of each time when ,3 is updated. To accomplish this, we employ the multi-agent mirror descent method, as proposed in [7] and detailed in Algorithm 2 in Appendix, serve subroutine'. To accelerate the convergence of Algorithm 1, the PNE strategy x" obtained under the previous 3 is used as the initial strategy for computing the new PNE after updating B. Further implementation details are provided in the experiment section.
Experiments
To validate our theoretical findings and demonstrate the performance of Algorithm 1, we conduct simulations on instances of G constructed from both synthetic data and the MovieLens-Inn I dataset [28]. In our experiments, Algorithm 2 employed to solve the PNE for each instance of G. Below, we first outline the specifications of these two simulation environments and then present our results.
Synthetic environment For the synthetic environment, we construct the user population X' by setting an embedding dimension d 32 and independently sampling 50 cluster centers, denoted as fc....., c from the unit sphere gd11 For each center C, users belonging to cluster-i are generated by sampling independently from a Gaussian distribution ((c,, 0.5²I.) The sizes of the 50 user clusters are determined uniformly random, ensuring the total size of X' is m 1000. Similarly, = 200 creators are generated, and the relevance matrix M E Raxm is defined by the dot product between each user-creator pair, which are then normalized the range [0, 1]. This synthetic
'I [7]. the algorithm is guaranteed to converge to PNE under zeroth order feedback. Here we use the perfect gradient as input and thus the convergence is also guaranteed.
8

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Individual
Individuai user utilit
Aggregated Engagement Netrics at PNF
2.0
5.5
8
8 50.0
V. Content Creation User Satisfaction
28
200.0
creator
user Index
Figure I: The left and the middle panel: the empirical distributions of content creation frequency xf and each user's individual utility xj. Different colors represent results for PNEs induced by different B. Right: the total content creation V and total user satisfaction U obtained under different (3. Error bars obtained from 10 independently generated environments.
dataset encapsulates class of clustered user and creator preference distributions. On the creators' side, their cost functions are set (2(2) c,a², with the default p 1.5. The marginal costs {<i are randomly sampled from uniform distribution U/ (0.1, 0.5).
dataset We deep matrix factorization [22] to train user and movie emheddings (with dimension set to 32) by fitting the observed ratings in the range of 1 to 5. To ensure the quality of the trained embeddings, we performed 5-fold cross-validation and obtained an averaged R.MSE= on the test sets. With the same user/item embeddings with the complete dataset. We randomly select m 1000 user embeddings to construct the population X' and n 200 movie embeddings as the creator profiles. Similarly, The relevance matrix M E Raxm is given by the dot product between each user-creator pair normalized to [0, 1] and creators' cost functions are the same as we specified in the synthetic environment.
Environment constructed from MovieLens
we train the
7.1 The Empirical Trade-Off's Between U and V
Figure 1 illusttrtee the content creation frequency xt, user utility Tj. and their corresponding aggregated values U = E3 Tj. V = -;; z under the PNE induced by different homogeneous (i.e., all users share the same (9). The result in the right panel shows that larger /3 enhances overall user satisfaction U but undermines total content creation V. As / increases, the drop in V becomes more significant. This empirical finding supports Theorem 2 and suggests it holds under broader settings without the assumptions on creator cost function and user population structure. The left and middle plots illustrate each creator v's creation frequency x; and each user j's ss utility xÿ at the PNE, such that both z and Tī are rearranged in descending order. They show that when 3 is shared across all users, its change affects x; and æī in the same direction.
7.2 The Optimal (B Found by Algorithm 1
Next, we use Algorithm to find the optimal PPM(3) and investigate the properties of the optimal B. We set X = 0.5 and aim to maximize the objective W, U + 0.5V, more results under different choices of \ can be found in Appendix B. The initial set to (100, .... 100), representing a nearly deterministic matching for every user. Algorithm is then run to update B. The sample rate and learning rate are set to = 0.1, 7) = 200. In addition to searching for personalized 33 for each user j. we also attempt to find a homogeneous (i.e., fixed (3 for each j) using Algorithm 19.
The first and third panels in Figure show the evolution of Wx during the optimization process in both synthetic and MovieLens environments. As illustrated, Algorithm successfully finds better PPM(33) compared to the baseline of exact matching for all users, with a significant gain of over 20% in the welfare metric. Furthermore, in both environments, personalized B leads to slightly better outcome compared to homogeneous B.
The second and fourth panels depict the optimal By for each user j. arranged in descending order. These panels provide insights into how such a mechanism achieves better trade-offs. For each user
'The gradient of W₂ with respect to homogeneous 3 can be readily obtained by summing all the partial derivatives of Wx with respect to B3.

---

Socil
Cytimal 79961 Found
Sacidd ptafir onde duaiviaaiion
Cptiaa Prag:
er d6. Ng
189e
Figure 2: Panel 1.2: social welfare improving curve under Algorithm 1, and the distribution of the obtained optimal B, in the synthetic environment, Panel 3,4: the same plots the MovieLens environment. À 0.5.
index the a-axis, also plot the average and the standard deviation of the relevance scores [wsgh= associated with each user j over all creators, shown as orange and green lines. Based on the definition, users with smaller average scores and higher standard deviations "picky" or selective, indicating high relevance scores with a small group of creators and low scores with many others. Conversely, users with higher average scores and smaller standard deviations less selective and more open to exploration. The results show that the optimal /3 tends to increase the exploration strengths (by deploying smaller (3)) for less selective users. This approach is intuitive, as it safely increases exploration while minimizing losses in user engagement.
considered more
8 Conclusion
In this work, introduced new game-theoretical model Cd (Cournot Content Creation Competi- tion) to explore how creators strategically determine their creation frequency under UGC platform's 's recommendation algorithm. Our investigations reveal critical balance between user satisfaction and creator engagement, mediated by the exploration strength of the recommendation. The existence and uniqueness of the PNE of Cd4 games provide predictive framework for assessing the effects of algorithmic choices on content diversity and volume. Through both theoretical analysis and empirical simulations, we demonstrated how varying the exploration strength can either enhance user engagement at the cost of reduced content diversity or encourage richer content creation at the expense of immediate user satisfaction. These findings disclose the delicate trade-offs platform designers face and highlight the utility of our model pre-deployment audit tool for optimizing recommendation algorithms to balance platforms' long-term and short-term objectives.
While our C* model offers insights into strategic differentiation among creators regarding production quantity. it relies on a simplified assumption that creators maintain fixed niche, consistently producing content on the same topic with similar quality. This assumption, though useful for modeling purposes, may be restrictive in real-world scenarios where creators dynamically adjust topics, vary content quality, and scale production quantity. Exploring the dynamics where creators compete across heterogeneous dimensions such topic variety, content quality, and production quantity-would would be valuable direction for future research. We leave this intriguing problem for future work.
This work is supported in part by the NSF Award IIS-2128019, NSF Award CCF-2303372, A12050 program at Schmidt Sciences (Grant G-24-66104) and Army Research Office Award W911NFF23-1-0030
Acknowledgment.
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13

---

Appendix to Unveiling User Satisfaction and Creator Productivity Offs in Recommendation Platforms
A Omitted Proofs
A.1 Proof of Theorem
Proof. First of all, we argue that given any G(n, m, M, (c),,)) for any creator there exists an [0, 6,] cannot be an equilibrium strategy. This is because given any n- U4 function of z; has continuous and strictly positive gradient at = 0, meaning
5; 0 such that any
--; E R
that there exists 6 > such that
Das U2
0, [0,5,] regardless of what other creators'
= d, creator can always increase her strategy to strictly
strategies are. In other word, for any 24 improve her utility. As a result, any potential PNE x must satisfy that x; 2 6,.
On the other hand, since (2(2)) + too when 2; + too but the traffic gain for each creator is at most m, have (z,, x=-) (= -oo, V 20 when H; too. As result, any equilibrium strategy must also be upper bounded by uniform constant A > 0.
To argue the existence and uniqueness of PNE of G. in the following we may with out loss of generality restrict each creator i's strategy set to a convex set [6,, A].
For any fixed [ (31, ,,,m) let Oij exp(33 (xp())))))) and Eq. (1) can be simplified to Bm,,
I;0;J k=1 TEaKj ) -
wilri x 1i Σ jml
cx(x))
(14)
For simplicity we denote 9, (x) En- Tzaki and can be expressed as u,(x;, Ej=1 ووتy
(5(æ) (z;). Our proof starts from sufficient condition from [44] for game to be monotone. A game is said to satisfy the diagonal strict concavity (DSC) condition if (1) each player has a concave utility function in his own strategy in a convex strategy space; and (2) there exists some non-zero parameter À= = (Ai,-.. An.) such that the Hessian matrix given by
Hsa A) 2 d Pul(x) X Pul(x) Orgam
(15)
strictly -efuiiie In [44], it is shown that any game satisfying X-DSC condition has unique pure Nash equilibrium (PNE); such a game is often referred to as monotone games.
First of all, already argued that each creator i's strategy set is [6,, A]. which is convex set. Core to our proof is to show that game G is 1-DSC under the theorem conditions. Direct calculation shows that for any 1 < l < <lS
(z) Okj9yj (-9) + 22kj
9
axj 93
(-gj + 201z21))
Or,0r
and therefore the Hessian matrix of G specified by the RHS of Eq. (15) is equal to
8g Oz7
2 2ini Iiaij Eie(1 Isais
Eie(1 Ijdi 2 i2 Tilli
01j (2j
m
-[H(())
Σ 9j
[aij a.j.
+
0
8
ax3
j=1
m
Σ
93 3 aa H Ho:
(16)
1=1
14

---

where 9j in the above expressions denotes (z), vector a; = (a15. any)) We can see that if all the cost functions are strictly convex, the second diagonal matrix Hg in the RHS of Eq. (16) is strictly positive-definite (PD). Therefore, it suffices to show that (1) for all j E [m]] H2 is PD. To see this, let 2; Izd,y and we show that for any y = (y1, ;nn E IR", y H2y 2 0, and the equality holds if and only if y = 0. In fact, note that
y T H3y = 2
Σ Vi
Σ
2j
+
2
Villi
Σ 2k
1=1
AEf
2 Vi
Σ iNi
+ Σ
Σ 2j
+ 2
>
yill
Σ Z6 RELLE
1m
im
jtii
i
11
Σ z
+ Σ 2k
Σ
y5
+2
Σ
yilli
jti
1=1
Vi
2
Σ
Zj
+ i=1
Σ jzi
Mj
O.
(17)
1=1
jæ
Because x, and a, are all strictly positive, each e, must also be strictly positive. Hence, Eq. (17) can take value zero if and only if y = 0, Vi E [ni] Therefore, H, is PD for any j E [m], which completes the proof.
A.2
Proof of Theorem 2
First let's recall the definition of U, when m 1:
W.s e.r Bur
((x = Σ
(18)
n
k= e
i=1
V(x*) =
xx.
(19)
In the following, we prove the monotonicity of U33 and V(3) by showing dlaU > 0 and dV
da < 0,
d3 respectively. Before presenting the detailed proof, we first derive some relevant definitions and their properties that will be used in the proof.
For simplicity we omit the superscript in xt and simply use æ to refer to the PNE of G. When 1, the creator utility function writes
Sw: Ek Bye (x(x), [n]]
u. (2,
(20)
Let P.
where a; @o., First of all, claim that it is without loss of generality to consider the regime where P. < 3. To see this, consider the following two C4 instances:
B,a. E ZeoL
(n, m 1, (Wi, Wr), (c 3),, G2(3n, m = 1, [w, w, w). [c/3, c/3, c/3) [3, 3, B)).
Clearly, both games G1, Gy have unique PNE. Let the PNE of G1 be denoted by x;. In G2, since its 3n players are divided into three identical groups, its PNE can be represented as (æ), ax, at)), where each group of players follow the same strategy. Moreover, for any 1 < i S n, it is straightforward to observe that the i-th player's utility functions in 91 and G2 differ only by a multiplicative constant of 3. Consequently, we have æi æz. Therefore, for any C instance G with = 1, we can always
15

---

construct an equivalent instance G2 that shares the same PNE structure, while ensuring P. S 3. This justifies the assumptions that, without loss of generality,
can take P. 3--
Another property need is that the PNE strategy 2 of any player in 91 is bounded in a compact region [0, L] for some constant L, regardless of the values of B. To see this, note that (x(z;) is increasing in 2, and goes infinity as 2; + +o00 while P; is upper bounded by 1. As a result, for any such that (z --)) S (2,) < (0) u, (0, x x-i), I2 cannot be a PNE strategy as switching to 0 increases player i's utility. Therefore, if we take
L max [in (ar 0: ( -c (0))}
3E|n]
holds that x2 S Li E [n].
Let B),
Ou: be an n-value function. From Corollary we know a; satisfy F(ar, (3) 0. And Theorem guarantees that for any 2 O, the implicitly determined F F(x,, (3) exists and is unique. Therefore, by the implicit function theorem [37], the derivative of æ w.r.t. 3 can be written
dx
0F
OF
d3
3x:
0
and OF nxn is the Jacobian matrix (which is also the Hessian of & when À Eq. (15))
where [FF]
03 E R=xl is the partial derivative of F w.r.t. B.
The first-order derivative of us can be calculated as
Ou:
Sw,
Buy
c<(x))
(21)
Ek=1 Tge
k= eee
and we can use further obtain the following explicit expressions terms of the derivatives of F:
OF;
1 (1--1PP)) 1 -
P? (x.),
0x;
I3
OF;
P.P3 (1-2P.) -P.)) +
0z,
OF.
P.
(1 (1-)
wi Σ PRIOR
(22)
03
k=1
Let's define positive definite diagonal matrix
p2
p2
D diag
+
x2
Since of 0, we can introduce variables
p2
p2
8 E (0, 1) such that
xt
C
5,
(23)
In addition, let's also define
y Pi - 2P,)
P. -P(1)
P
P
(24)
31
In
then we have aF az
D + yz and from
formula[46], it holds that
(0
(D + yz T-
dx
D-1yz D-1
D-1
(25)
1 2T -lyy"
16

---

where
810
n a p
D-1 = diag
P
6, (1 2PP)
T (1 2P,)) T
D- y
Pt
Pn
81.11
D
Pi
Pn
Since P. S 3. we have 2P, 2 to give the formal proof of Theorem 2.
0. With all the notations introduced so far we are now ready
Proof. We prove the monotonicity of U(3) and ((3) by showing d d3
> and
dv dg < O.
The monotonicity of (B): The first-order derivative of In U w.r.t. 8 is given by
d U
0U dæ
au
+
d3
U
dx
d3 03
1
OU
OF -1
OF
1 au U
(26)
U
Ox
dx
03
0s
where aU E RR'x is the partial derivative Uf w.r.t. œ. Let a; Baws we will first show In fact, calculation shows
:.
au
0.
08
1 a0 E akas U
EE wBZ Tbak) EE w2zxax)?
08
k=1 WKttak
(Eh= xzaH)²
k=1 whaxaK
Ek=1 WKKKakk
(27)
Ek= WKIAOK
E 2z
From Cauchy-Schwarz Schwarz inequality, holds that
2
2
12
n
n
Σ
wffaaa Tgak
Tbak
W ag
Therefore, the RHS of Eq. (27) greater than or equal to Hence, it suffices show
1
OU
OF
-1
oF
(28)
8x
Ox
03
Also note that
1 00
Σ k= Fg
W;4; E Tb(kk)
0; ΣR= W.FKKR
U 0r:
Σ 11 WKTT
(2 TACA)²²
W1a;
a
Σ m
Aml WKZKKR
Ekm TKak
Wydg
P.
(29)
Eksn WyZEEa
and substitute Eq. (22), (25), and (29) into the LHS of Eq. (28), we obtain
OU
OFF)
OF
dx
Ox
03
P.
D D-1 yz 1-1
P
D
(1 2P.)
Wi
wk
WgT
Tr je(m]]]
1 z D-1
[E(x)
(E 5:(1 - 2P:)(w; - -)))
Σ
6,(1 - 2P:) - 2
(30)
T
T(1 + Σ 1 (111-P,
1=1
17

---

where T = D
= =E== P.ws. Therefore, it suffices to prove
kkst Syau
2 -i=1 8,(1 - 2P:) ( T))
Σ - ((l1-PP)((u)) -T)²
0.
(31)
1 Σi= 6;(1 2P:)
Since 1 - 2P; 0, from Cauchy- Serrhh--S inequality it holds that
Σ 6,(1 2P:)( - -))
1+ Σ 8,(1 (P.1))))
Σ 8,(1 (P))(u: - -T)2
Σ
6,(1 2P,) + Σ
2P.)( 6,(1 (11)22:)(w 272
==1
i=1
==1
2
Σ 6,(1 - (w;) (
+
Σ 6, - TT,
i=1
i=1
2
7
Σ 5:(1 2P:) ( -T)
where the last inequality holds because [w;] are not identical so there exists at least one j E [n] such that (1 - (mg - -T)² > 0. Therefore, Eq. (31) holds and we have d ln >
d3
The monotonicity of V(8): Next show
dv d3
0. Since
0v 83
0, this is equivalent show
OF
-1
OF
> 0.
(32)
Ox
0x:
03
Note that da;
1, we have
av
OF
OF
dx
0x
03
11,1, .... .1] D D- yz T 1-1
P
(1 - 2P,)
Σ PAWE
1 D-1y
k=
ii(nn]
8,1;(1
2P.)(w: T)
1
n
8, 2P.)
P. +
8,(1 2P.)( T).
1+ Σ4 8,(1 -2P)
P
(33)
To show the RHS of Eq. (33) is positive, it suffices to show
Σ d1 (1 -2P.) - T) d,z;(1 (1 2P.)
1 1 Σ 61 - 2P:)
Σ
6.(1-2P)((u:-1))
P.
P;
i=1
(34)
Plugin Σn PAWx into Eq. (34), it is equivalent to show that
8, (1 - 2P.) w
8, (1 - -2P))
8, - -PP)
1+ 2=1
8,(1 - 2P.))
Paws
(1-2P.))..
P.
P:
P.
A=
1=1
im
and note that
Σi
Ps. it equivalent show
8,z; -2P.)
8,0 (1 2P.)
Σ 8,(1 - 2P.) + P.)
16,(1 2P.) + P.Ju,. (35)
P.
P:
18

---

Let a; (1-P(1))P))
b, = =0,(1 -PP:) + P., then Eq. (35) is equivalent to
P.
b. O4
bj Ug
a:W;
Σ wj)
0.
Next, without loss generality we show that for any S i < S n, if wi wy then also holds that b. 21 for sufficiently large B. In fact, from P. Ei=1 #xening and Eq. (23) we obtain
2,0
a;
bi jj -1- + P.)(1 2Pj)
02 by 61(6,(1-2P)) + +1)(11 (P)) -eB(w;))))
1+ (10/(11 - 2P.) (ww
1 (10,/(1-225 2P;)
1 2223)(((+t((" ((w
(36)
pa
(1-2P;)(P (25
On the one hand, because - 1 2P, E 1 11. H4 E (0, f.J. and dy (x)), terms of the LHS of Eq. (36) is positive number lower bounded away from zero. On the other hand, Wi > w ensures that the second term @0(,,wr can be arbitrarily large as long as /3 is sufficiently large. Therefore, there must exist a So > 0 such that for any 3 > So- b. ai > 1 holds for any i > j. As result, (w: - w;) A bi
0, the first
> holds, which completes the proof.
B Additional Experiments
We use the following Multi-agent Mirror Descent (MMD) algorithm as the PNE solver C'4, whose convergence is guaranteed by [7]. Since each creator's strategy set X; [0. +oo), we can simply choose a projection mapping Projæ, (a) = (max(#;, 0)) The gradients of utility functions can be implemented directly since they have closed forms. Through experiment, the default
10000, 7 0.1, 1 - 2, (0) 1.0. Algorithm is a simplified version of Algorithm in [7] where replace the gradient estimation the exact gradient. According to Theorem 5.1 in [7], Algorithm converges to the unique PNE any Cr4 game with probability
Algorithm 2: Multi-agent Mirror Descent (MMD) with perfect gradient
Input:
Maximum iteration number T, step size 77, each player i's utility function u,, error tolerance e, initial strategy æ; x; (0)
for / [T) (g...... -9n)ll2 < c, then
Break
Compute gradient 9: = (a,, x x-.). for [n]. Update x; Projx, (m:; vggi), Vi [n].
Output: (æ1.-.. v.
Figure 3 illustrates the trade-off between U and V in the MovieLens environment, and Figure plots the same information as shown in Figure 2 but with a different value A 0.1. As we can the optimal PPM(3) found by Algorithm conveys consistent message: it prioritizes the recommendation accuracy for users with more determined preferences while increasing the exploration strength for less selective users.
19

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Aggrepated Engagement Metrics PNE
Individual creation
utiiity
1-00
10.0
f 30.0
V. Cortent Creation
index
Figure 3: The left and the middle panel: the empirical distributions of content creation frequency x;
and each user's individual utility zÿ. Different colors represent results for PNEs induced by different 3. Right: the total content creation V and total user satisfaction U obtained under different B. Error bars obtained from 10 independently generated environments.
Sacal We
Socal Ihfrr Optriiattee
Figure 4: Panel 1.2: social welfare improving curve under Algorithm 1, and the distribution of the obtained optimal B, in the synthetic environment, Panel 3,4: the same plots in the MovieLens environment. 0.1.
20

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Reviews:
[{"review_id": "9vKREboxfT", "reviewer": "Reviewer_GVPh", "summary": "The authors propose a new game-theoretical model Cournot Content Creation Competition ($C^4$), that studies the relation between the matching strategy of user-generated content (UGC) platforms and the production willingness of the platform’s content creators. Under certain assumptions, the authors show that the game has a unique Pure Nash equilibrium, and show that increasing matching accuracy elevates user satisfaction but also decreases the overall volume of content creation. Building on this tradeoff, the authors propose an optimization approach that balances the two objectives, providing both theoretical analysis and empirical simulations.", "questions": "- Can the authors elaborate on the point on short v.s. long-term goals in the weakness section above? Specifically, why is user satisfaction short-term concern and content generation frequency long-term concern. \n- In practical scenarios when an increase in content comes with quality degradations and topic differentials, are there intuitions on whether and under what scenarios the result can continues to hold?\n- Is collusion between content creators a potential problem here?", "limitations": "The authors adequately addressed the limitations.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Overall well-written.\n- Interesting insight on the tradeoff between user satisfaction and creator engagement shown by theoretical analysis.", "weaknesses": "- (Main) Model might be too simplistic - authors assume users consistent produce work of same topic & quality and only changes the production volume.\n\n- (Minor) The authors associate user satisfaction as a short-term goal for the platform and creation volume as a long-term goal for the platform. The authors make an argument for this in line 188-197, although I’m still not fully convinced:\n   - The main imbalance that I feel comes from the fact that when I think of *long-term* goals of a platform, it's fundamentally intertwined with the ability for platforms to attract new and keep existing users, which comes from a user standpoint and not from a \"content volume\" standpoint. I get the authors argument when they mention how content creation frequency might harm user satisfaction (line 192 “users can hardly be satisfied by their previously consumed material”). However, given individual's limited attention span, I think this only happens when the number of creators are quite limited, and that it's unclear that a decrease of production frequency from say 2 weeks -> 3 weeks will result in a significant harm to the *long term* viability of a platform causing users to drop out in the long-term.\n   - In general, this seems to point to an alternative model where the content volume *comes in* the user's utility model, where users’ utility are not only determined by how they liked the recommended content (which is the utility considered in the paper) but also by the availability of content on the platform, and they might drop out of the platform when their utility falls below a certain level. From this lens, it's less clear that this is a short-term v.s. long-term issue.\n\n- Typo: i =1 -> j=1 in line 92, third and fourth -> second and fourth in line 347", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for appreciating the insights of our problem setting and results. For our response to the suggested main weakness and question 2, please refer to our common response above. Below, we address the remaining questions.\n\n**Why total content volume affects long term user engagement** It is not a surprise that long-term user engagement on a platform is crucially dependent on the total content creation volume due to the following reasons.\n\n- First, Regular and abundant content updates provide users with a better experience of personalization, encouraging them to return to the platform more often or new users to join the platform, which increases engagement time and user satisfaction, and thus long-term success of the platform. \n\n- Even though active creators and users are usually large in number on leading UGC platforms, the creator-to-user ratio is typically small. For example, TikTok has billions of viewers but only around 1 million active creators. As a result, most users are highly loyal to specific creators and eagerly consume whatever they create. This user stickiness means that even a small increase in content creation frequency by these creators can significantly boost total user engagement. Therefore, while minor fluctuations in overall content creation frequency might not drastically affect user churn rates, a consistent decrease in content creation from active creators will have a significant negative impact on user engagement.\n\nIn addition, we acknowledge that emphasizing the contrast between short-term and long-term goals might be a bit misleading. Our key point is to highlight the tradeoff between recommendation relevance and overall content creation volume in optimizing user engagement. Both factors are clearly important to the engagement target but we show that they are inherently conflicting when considering content creators' strategic responses. We will clarify this point in revision.\n\n**Alternative model that accounts for volume in utility** This is a very constructive and interesting idea, however, to justify such a user utility model that correlates with the volume of available content on the platform (even if they do not consume them), we need to introduce an ad-hoc user behavioral assumption describing how users' satisfaction or return to the platform  relates to the amount of available content. And oftentimes, ordinary users do not even know the amount of available content on a particular platform (think about YouTube and Instagram),  although a positive correlation might empirically exist. We recognize this as an intriguing direction and intend to investigate it in future work.\n\n**Collusion among creators** Indeed, many creators today are not working as individuals but as representatives of a team (e.g., belonging to the same studio or society). In our model, a player can be regarded as a team rather than an individual for such situations. However, if the reviewer is referring to collusion among different players to game the system, this is beyond the scope of our current framework and we might need a new model for studying such an intriguing phenomenon.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "ttlN0X1pRz", "reviewer": "Reviewer_1ynk", "summary": "This paper studies the problem of the tradeoff between users’ satisfaction and creators’ engagement. Authors first define the traffic competition of creators on user-generated content platforms as a Cournot Content Creation Competition (C4) and establish corresponding PNEs. Based on PNEs, this work identifies the tradeoff between users’ and creators’ engagement and proposes the offline optimization solution to achieve the maximum social welfare by adjusting the exploration level of matching. Theoretical and empirical results are provided to support the effectiveness.", "questions": "1.\tHow is the efficiency of the proposed solution when the dataset includes millions of users? \n2.\tWhat are the differences between C4 and previous C3 game? How does C4 benefit from the additional “Cournot” setting?", "limitations": "1.\tLimited practical value. The assumption is too strong, and the experiments are constrained on small dataset with 1,000 users.\n2.\tUnclear distinct contributions compared with previous works.", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.\tAuthors theoretically model the traffic competition among content creators as a C4 game, identify the tradeoff of user and creator engagement based on their theory, and finally find the optimal platform intervention to maximize the social welfare with the optimization method. Necessary proofs are provided with details. \n\n2.\tBased on the synthetic and real-world datasets, authors validate the phenomenon of the user-creator tradeoff (Figure 1) and the benefit of optimizing \\beta (Figure 2). Authors also provide the results in Appendix with different $\\lambda$ in the objective $W_\\lambda$ to investigate the sensitivity of their solution when the target is changed. \n\n3.\tThe manuscript is well-organized and easy to follow.", "weaknesses": "1.\tSome assumptions are too strong, including (a) basic setups: Creators are producing contents with the same frequency and the same cost (only relate to the frequency) all the time. (b) platform intervention: all users contribute one unit amount of traffic, neglecting the dominant position of active users. \n2.\tAlthough the effectiveness is guaranteed by the theory and empirical study on small datasets, authors should also present the potential of the solution to be applied in the practical scenarios, e.g., how is the efficiency of the optimization, how to conduct the daily update of intervention strategy. \n3.\tExisting works have studied the C3 game. Authors may declare their unique contribution and improvement by considering “Cournot Competition” in their theory establishment and compare with previous methods in empirical validation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for pointing out the concerns and raising the clarification questions and we respond to them below accordingly.\n\n**Response to weakness 1: unit user traffic** First, we have to clarify that our model does not assume each user contributes only one unit of traffic. Since we do not impose any assumptions on the user distribution, we can easily represent active users by incorporating multiple instances of such a user in the formulation of creator utility function. For concerns regarding the assumption of homogeneous creation, please refer to our common response above.\n\n**Response to weakness 2 and question 1: computational efficiency** Thank you for these great suggestions. We discussed computational efficiency in detail in Section 6.2, providing a computational complexity upper bound of $O(n^2m + nm^2 + m^3)$, where one can cluster users and creators to share parameters within the same cluster ($n$ and $m$ represent the number of clusters for creators and users, respectively). By appropriately setting $n$ and $m$, we can tune the resolution of clustering and balance between the accuracy and efficiency of the optimization process described in Algorithm 1. Moreover, this optimization process does not need to be run frequently (e.g., on a daily basis), as every time Algorithm 1 identifies the optimal treatment for each user group based on the current user and creator preference distribution. It is only necessary to rerun the algorithm if there is a significant change in the global user or creator preference distribution. Therefore, the intervention strategy computed by Algorithm 1 does have strong potential for practical applications.\n\n**Response to weakness 3 and question 2: Difference from $C^3$ game** We highlighted the main differences between $C^4$ and $C^3$ in lines 32-41. First of all, we clarify that $C^4$ is NOT an extension of $C^3$, despite the similarity between their names. In fact, these two models correspond to entirely different competitive environments and assumptions about creator behavior. In $C^3$, creators have fixed creation frequencies and their strategy is to choose topics for producing content. In contrast, in $C^4$, creators' content has a stationary topic distribution, and their strategy is to determine the creation frequency. These two settings represent different stages of online content sharing platforms: $C^3$ models the early stage when creators are new to the platform and explore various possibilities to find their identity, while $C^4$ models a mature stage where creators are aware of their expertise and consistently produce within their niche, strategically adjusting their production frequency to balance gain and cost. Therefore, the formulation of $C^4$ addresses a very different practical problem and should be considered a complementary setting to $C^3$, and the results obtained in the previous $C^3$ setting do not provide any analytical insight for $C^4$.\n\n**Response to limitation 1: experiment scale** As explained in Section 6.2, the number of users is not the bottleneck for the scalability of our algorithm because we can cluster the user population and update $\\beta$ at the group level (this is also a practical treatment in large-scale real-world systems). Therefore, we believe that our experiment with 1,000 users is representative and should be sufficient for larger-scale experiments.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "74bjJ6IYzG", "reviewer": "Reviewer_1Tuv", "summary": "This paper studies a model of content creation and consumption on arbitrary online user-generated content platforms (e.g., YouTube, TikTok). It focuses on a type of Cournot competition in which creators mainly modify their creation volume. The paper provides a description of this model, a theoretical analyses of the Pure Nash Equilibria in this setting, an analysis of how platform designers might use mechanism design to balance consumer and creator utility, a framing of this balancing problem as an optimization problem solvable via (approximated) gradient descent, and experiments using purely synthetic data (sampled \"users\" with Gaussian preferences) and empirical data (users with preferences from the MovieLens dataset, popular in recommender systems).", "questions": "A few very specific questions about the model (with the caveat that of course anything along the lines of using empirical data from major platforms and/or trying to frame this model as predictive for an entire spectrum of platform types is probably out of scope)\n- What is the strongest evidence that any of these major platforms follow Cournot competition like dynamics?\n- What is the impact of platform-as-creator dynamics, such on Netflix?\n- More generally, it would be helpful to explicitly state how resource heterogeneity amongst creators or budget heterogeneity amongst consumers may or may not cause issues for the use of this model.\n- To what extent would we expect results to hold if we did have access to MovieLens-style observational data from e.g. YouTube?\n\nOverall, these are not \"existential\" questions per se, but some attempt to clarify could strengthen the draft quite a bit.", "limitations": "I do think the current draft could do more to justify the strength of the conceptual claims and/or hold a bit more space to explicitly discuss limitations (primarily, how well requisite assumptions hold across the platforms of interest). See above (Questions).", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "Overall, this paper provides a strong overall contribution and number of results and insights that will be of interest to a number of different communities -- researchers interested in UGC and online communities, mechanism design, ML for social media, etc.\n\nThe clarity is high throughout. The paper begins with strong and well argued motivation, the organization is helpful, and in general the overall narrative of the paper is clear.\n\nIn terms of novelty, this paper directly builds on a previous modelling work, but is very upfront about highlighting what the main differences and additions are in terms of contribution. The experiments seem to especially build off the design of [40] (esp. in terms of the synthetic data + MovieLens combination), which might be worth mentioning if that is intentional.\n\nOverall, the potential significance of this work seems potentially high.", "weaknesses": "Overall, I expect readers won't have any major concerns with the theoretical results or experiments (see some minor questions below in the Questions section). \n\nRather, the main threat to the significance of this paper is making the case that that a Cournot-style is actually common in the UGC platforms being invoked here. Of course, even if only a few platforms really end up being well-described by the model, the contribution is still very meaningful. That said, a few specific concerns with the current draft:\n- a number of specific platforms are mentioned by name: YouTube, TikTok, Netflix, Spotify, and MovieLens. \n- Only data from MovieLens is used (which is very reasonable -- it's a very popular dataset for academic work for good reason).\n- However, the named platforms vary quite a bit in terms of their actual creator competition, i.e. one would expect the incentives of a platform like Netflix (which also acts a creator agent, sometimes with substantially higher budget than other creators) to differ quite a bit from TikTok\n\nSee \"Questions\" section below for some specific questions about this concern that I think are likely to be in scope of a revision.\n\nWith this critique in mind -- that certain platforms might violate the assumptions needed for the model to work well -- I think the current draft may overstate the generality of the conceptual insight.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We greatly appreciate the reviewer's suggestion for additional justification of our problem setting. Below, we respond to the questions raised.\n\n**Evidence of volume competition**\nMajor UGC platforms, such as YouTube, TikTok, and Instagram, primarily generate profits through ad impressions, which are directly correlated with content impressions. Given this revenue model, it is logical that platform incentives are designed to encourage creators to compete for more impressions. By fostering an environment that motivates creators to increase their content visibility, platforms can maximize their ad revenue. This setup inherently triggers Cournot competition-like dynamics in UGC platforms, where creators compete for audience attention by producing more content.\n\nOur work is done in collaboration with a world-leading content recommendation and sharing platform with billions of users. We do observe Cournot competition-like dynamics from offline data analysis, and we will include such evidence in the revision once authorized by the company to disclose this information. Generally, we observed two phenomena:\n- Content embeddings from the same creators are clustered around a small region, indicating that most creators consistently produce content within the same topic.\n- Creator productivity is significantly influenced by the platform’s incentivizing plan; when the platform allocates more user traffic to a group of creators, the average production frequency of this group increases.\n\nThese observations motivate the formulation of the $C^4$ framework. \n\n**How our model handles heterogeneity** We do allow for heterogeneity in budgets, as the cost function can be creator-dependent. For the discussion of heterogeneity in terms of content creation, please refer to our common response above.\n\n**How general is our model to different platforms** Our $C^4$ framework is applicable to mature content recommendation and sharing platforms where creators are aware of their expertise, consistently produce within their niche, and strategically adjust their production frequency to balance gain and cost. As discussed in lines 36-41, many existing leading platforms, such as YouTube and Instagram, exhibit these characteristics. On these platforms, most influential creators have clear and consistent branding and target specific user interest groups. Consequently, the platform’s recommendation strategy primarily impacts their willingness to engage, i.e., their content production frequency.\nHowever, our framework is less applicable to platforms like Netflix, where a different platform-as-creator dynamics prevail. The dynamics under such an environment is also interesting but is beyond the scope of our work. We have clarified this scope in the first paragraph of the introduction (see line 18), where we exclude non-UGC platforms like Netflix from our discussion.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:
**Common response**

We appreciate the reviewers' overall positive evaluations about our work, especially the acknowledgement of the significance of the problem setting, novelty of our analysis and insights from our theoretical and empirical results. We are happy to integrate the reviewers’ suggestions for improving the current version. In the following, we first respond to a common question regarding our modeling assumption raised by reviewers, and then answer each reviewer’s questions separately. 

**Assumption about homogeneous creation** Reviewers raised a common concern that our model relies on the assumption that creators consistently produce content of the same topic and quality, only varying the production volume. However, our setting is more nuanced than the reviewers suggested. Rather than assuming creators are homogeneous in their creations, our framework incorporates variances  in quality and topics by the random variable  $\epsilon_{ij}$, which reflects the uncertainty of the matching score between user-$i$ and creator-$j$'s content. This means each creator in our model can produce multiple pieces of content with varying topics and qualities. The key assumption is that the average matching score of these contents to each user does not depend on  the creation volume. Essentially, the content from a creator can be drawn from a fixed distribution, and the variance of this distribution does not significantly impact the creator's utility function as long as it is not too large (e.g., not to be flat), given we consider the expected traffic each creator collects.

Moreover, our data analysis on a world-leading content creation and sharing platform indicates that most creators tend to stick to a specific topic (e.g., reflecting their expertise or identity), meaning that their produced content is indeed drawn from a static and well-concentrated distribution. This is not a surprise as such a strategy helps them build brand identity and uniqueness among their followers and also maximizes their chances of being favored by the platform's algorithm. However, due to company policy, we are unable to disclose specific details but can only provide a qualitative discussion in lines 36-41. We can add more data analysis results regarding this finding to further support our modeling assumptions once we obtain the legal permission of the company.

Meta-review: The paper investigates the dynamics between user-generated content (UGC) platforms and content creators, particularly focusing on the impact of recommendation algorithms on creator behavior. The authors propose a game-theoretical model, the Cournot Content Creation Competition (C4), to study the trade-offs between short-term user satisfaction and long-term content diversity. The paper introduces an optimization approach to balance these competing objectives, providing both theoretical insights and empirical validation using synthetic data and real-world datasets.

Generally, reviewers agree that the research question of modeling the content generation/consumption of UGC is well motivated and that the results are technically solid overall. Many of the questions and concerns raised revolve around the justifications of the models and objectives. We encourage authors take the reviewer comments into account in preparing their final version.

One additional comment that's raised during the discussion phase: The research question of modeling and analyzing UGC from game theory and learning perspectives has been explored for quite some time, however, most of the citations in this work are from the past few years. It would help if the authors can include the discussion to these earlier works to better contextualize their contributions. As examples, below are two of the papers along this line:

- Incentivizing High-quality User-Generated Content. Arpita Ghosh, Preston McAfee. WWW 2011.
- Learning and Incentives in User-Generated Content: Multi-Armed Bandits with Endogenous Arms. Arpita Ghosh, Patrick Hummel. ITCS 2013.
Decision: Accept (poster)