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_cc_2024_Conference
Published: 2024-05-15 07:23:44

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.

Main paper: 
 introduction: 
 User-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, TikTok) and many more, count on algorithmic recommendation algorithms [36, 5] to help content consumers (i.e., users) navigate the vast ocean 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.Recent studies have begun to explore how a platform's algorithmic decisions, such as 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 or 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 dynamics. In fact, there are evidence suggesting that traffic received directly influences creator productivity [31, 56] . A 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, a statistically significant positive correlation exists between content viewership and the corresponding creator's productivity 2 .Motivated by real-world evidence and the research gap in modeling production frequency within content creation competition, we introduce a new game-theoretical model, named Cournot Content Creation Competition (C 4 ), aiming to study the impact of a platform's recommendation strategy on creators' production willingness. Our C 4 framework builds upon the Content Creator Competition (C 3 ) framework introduced in [52, 54, 55] , assuming that creators compete for platform-allocated user traffic [27, 29] . However, unlike C 3 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 to 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.Our C 4 framework offers a 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 4 '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 exploration strength at a per-user basis. We formulated this mechanism design challenge as a 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 a new game-theoretical framework, C 4 , to investigate how recommendation algorithms affect content creation frequency among creators; (b) conceptually, we reveal a 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 C 4 framework and its derived solution serve as a pre-deployment audit tool for platforms, assessing the effects of algorithmic choices on creator and user engagement. 
related work: 
 The study of online content creation economy has captured the attention of machine learning community 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 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 C 4 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 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. A recent study [53] also explored competition between human and Generative AI creators within a 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.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes]Justification: We have discussed our limitations in the Conclusion section as well as in Theorem 2. We are not able to prove the most general claim with m > 1 and have to demonstrate our idea in a simplified setting (m = 1). However, our empirical study shows our theory is applicable to a much broader scenario.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
the cournot content creation competition: 
 In this section, we introduce the formulation of Cournot Content Creation Competition (C 4 ), which models the competition among creators for traffic on UGC platforms. This model considers the potential impact of the platform's traffic reallocation mechanisms, such as their deployed recommendation algorithms, where creators strategically choose their production frequencies to optimize their allocated traffic. Each C 4 game instance G is characterized by a tuple (n, m, M, {c i } n i=1 , {β i } m i=1 ). We detail each component of this tuple as follows:1. Basic setups. There is a set of content creators denoted by [n] = {1, • • • , n}, and a set of users denoted by {u j } m j=1 . 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 (i, j)-th entry w ij ∈ [0, 1] denoting the strength of user j's preference over creator i's content. Each creator determines a production frequency x i ∈ R ≥0 in a unit amount of time (e.g., one week/one month). For the purpose of our analysis, x i can be interpreted interchangeably as either the production frequency or volume, provided there is no ambiguity 3 . Follow the terminology of game theory literature, x i is referred to as the action or pure strategy of creator i. Each creator i is associated with a cost function c i , which characterizes the cost for creating content at frequency x i . We have two assumptions about c i : 1. c i is increasing in x i and c i (x i ) → +∞ as x i → +∞, which reflects that content creation is always not free. 2. c i is convex in x i , indicating a non-decreasing marginal cost of improving production frequency.2. Platform intervention. We assume that each user u j contributes a unit amount of traffic, and the platform redistributes the total user traffic based on a relevance-based recommendation algorithm that adheres to certain probabilistic principle. Specifically, the recommendation algorithm matches u j to each piece of content produced by creator i with a probability proportional to exp(β j σ ij ), where σ ij = w ij + ϵ ij represents the algorithm's estimated relevance score. This score combines the true preference score w ij with independent Gaussian noise ϵ ij ∼ N (0, σ 2 ). The parameter β j ≥ 0 governs the exploration of the matching for user u j : a higher β j results in a more precise matching, while a lower β j introduces more exploration into the matching results 4 . In this work, we analyze intervention mechanisms that operate under this Personalized Probabilistic Matching (PPM) principle, parameterized by β = {β i } m i=1 , and refer to it as PPM(β) for ease of notations. 3. 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(β) and when each creator i produces x i copies of content, the platform will allocate to i the amount of traffic fromu j proportional to E ϵij ∼N (0,σ 2 ) x i e βj (wij +ϵij ) = x i e βj wij • e σ 2 β 2 j 2. Here we should note that x i does not suggest the creator would create x i pieces of identical content, but amount of content following his/her expertise. Therefore, we formulate creator i's utility function as the following:EQUATIONwherex -i ∈ R n-1≥0 denotes the strategy profile of all creators except i.The C 4 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, our 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 traffic allocation algorithm. In addition, while Cournot competition typically incorporates only linear cost functions, the C 4 game accommodates general convex cost functions, offering a more nuanced reflection of the real cost faced by creators. These distinctions highlight the unique aspects of our model, while maintaining a conceptual link to traditional economic theories of competition.Research questions: Under the C 4 framework, an important and natural research question is how we can predict creators' strategic choices in the competition. This is a fundamental question in game theory and we employ the concept of Pure Nash Equilibrium (PNE) [40] to characterize the outcome of C 4 games. The definition of PNE is given by the following: Definition 1. A joint strategy profile of all creators x * = (x * 1 , • • • , x * n ) forms a pure Nash equilibrium (PNE), if for every creator i, x * i is a best response strategy that maximizes u i given other creators' strategy x -i ; formally,EQUATIONIn other word, a PNE represents a stable state when everyone is satisfied with their strategies and does not want to deviate. As we will demonstrate in the subsequent section, a PNE always exists in C 4 under any PPM(β) 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(β). We will explore these issues in the upcoming technical discussions.some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results. 
the pnes of c 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, C 4 always admits a unique PNE.Theorem 1. For anyC 4 instance G(n, m, M, {c i } n i=1 , β). If each c i is convex in x i , G admits a 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 in such games is a classic result from [44] . Theorem 1 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 w 11 = • • • = w n1 . Second, the fact that C 4 games are monotone is significant because it is wellknown that the PNE of strictly monotone games can be found efficiently. For example, many natural multi-agent online learning dynamics such as mirror descent [7] , accelerated optimistic gradient [8] , and payoff-based learning [47] guarantee the last-iterate convergence to the unique PNE in strictly monotone games, even 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 a plausible prediction of real-world competition but also paves the way to our simulation-based studies in our experiments, where we use multi-agent mirror descent with perfect gradient to numerically solve the PNE of C 4 .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 * (β) of any G(n, m, M, {c i } n i=1 , β) satisfies the following first-order condition:EQUATIONSince we have already shown the existence and uniqueness of G's PNE, Corollary 1 follows immediately according to Definition 1. Corollary 1 is useful for establishing further properties of C 4 games in Section 5. 
the trade-off between user and creator engagement: 
 We have established that a unique PNE exists in any C 4 game under any PPM(β) and can be naturally achieved by competing content creators. This raises a crucial question for platform designers: how should the quality of the PNE be evaluated? For any mature UGC platform, it is essential to balance user satisfaction, which is key to short-term prosperity, with creator engagement, which is crucial for long-term sustainability. Within our C 4 framework, this requires the platform designer to generate matching results that not only guarantee high user satisfaction (by improving the average matching quality at PNE) but also stimulate substantial content creation volume (by encouraging creators to increase their production frequency x * at PNE). We define these two objectives as follows: Definition 2. For anyC 4 instance G(n, m, M, {c i } n i=1 , β), let x * (β) = (x * 1 , • • • , x * n )be the unique PNE under PPM(β). Then the (short-term) total user satisfaction is defined asEQUATIONand the (long-term) total content creation volume is defined asEQUATIONThe social welfare of the whole system is measured by a linear combination of U and V , defined asEQUATIONIf we denote π* j (x * (β), β) = n i=1 wij x * i e β j w ij n k=1 x * k e β j w kjas the indicator of an individual user's satisfaction or utility, which is the expected matching scores of user j at the PNE under PPM(β). And the total user satisfaction measure U = m j=1 π * j is 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 a specific instance of matching outcomes but does not capture the dynamics of user engagement over time. This overlooks the crucial fact that sustained user engagement on a platform requires a 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 {x * i }, indicating that it fails to reflect changes in 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 an indicator of the long-term welfare of the platform.For the platform designers, it is essential to develop metrics that balance both short-term and longterm 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 U (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 β, 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 anyC 4 game with m = 1. If the elements of M = [w 1 , • • • , w n ] ⊤ are not identical, it holds that:1. U (β) defined in Eq. ( 4) is strictly increasing in β.2. V (β) defined in Eq. ( 5) is strictly decreasing in β ∈ [β 0 , +∞) for some β 0 > 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 a strong observation because it holds without relying on 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 x * i does not align with a creator's capability w i , the metric U is still monotonically increasing with respect to β. 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 an 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 β 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 β → +∞, 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 β = 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 a 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 m = 1 as a representative snapshot of how creators compete for a single unit of user traffic (i.e., homogeneous user population), extending the time frame to encompass a sequence of heterogeneous 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 > 1 and with various complex user distributions.The proof of Theorem 2, while delivering a clear message, is far from trivial. Since the dependencies of U and V on β are indirectly linked through x * , which lacks a closed form, the derivation of their derivatives with respect to β necessitates the use of the implicit function theorem [37] to articulate the derivative of x * with respect to β. This involves a 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 a novel first-order optimization approach to address the hybrid social welfare optimization discussed in Section 7. Detailed proofs are provided in Appendix A.2.Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?Answer: [Yes] Justification: We provide the code and data in the supplementary material.Guidelines:• The answer NA means that paper does not include experiments requiring code. • Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. 
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 4 : how can we identify the optimal trade-off between these two factors by optimizing any given welfare metric W λ ? Generally, the welfare metric W is influenced by three factors: the platform's algorithmic recommendation policy PPM(β), the resulting content creation profile x * at the PNE induced by β, and the relevance matrix M . Thus, we can formulate the resulting optimization problem (OP) as follows:Find arg maxEQUATIONs.t. x * (β) is the PNE of G.In general, OP (7) presents a formidable challenge, as solving for a PNE of a game is known to be difficult [15] . Fortunately, the nice structure of C 4 allows us to utilize the implicit characterization of the PNE detailed in Corollary 1 to tackle OP (7) effectively. In the subsequent section, we demonstrate that the gradient of W λ w.r.t. β can be explicitly computed.According to the chain rule, the first-order gradient of W λ w.r.t. β can be expressed asEQUATIONThe evaluation of the gradient of W λ relies on the calculation of three vectors, ∂U ∂x * , ∂V ∂x * ∈ R 1×n , and ∂U ∂β ∈ R 1×m , as well as a Jacobian matrix dx * dβ ∈ R n×m . The computations of ∂U ∂x * , ∂V ∂x * and ∂U ∂β are straightforward and computationally light, which position the main challenge as the computation of dx * dβ . Fortunately, the first-order characterization of x * by Corollary 1 enables us to express the gradient of x * w.r.t. β using implicit function derivation [37] as dx * dβ = -∂F ∂x * -1 • ∂F ∂β , where F (x, β) = ∂ui ∂xi n i=1is an n-valued function, and both ∂F ∂x * and ∂F ∂β are matrices of dimensions n × n and n × m, respectively. The following proposition provides the exact formula for the gradient. The calculation is straightforward and we omit the detailed derivation.Proposition 1. Let x * = (x * 1 , • • • , x * n ) be the PNE of G(n, m, M, {c i } n i=1 , β).Then, the Jacobian matrix of x * as a function of β isEQUATION)where D is an n × n diagonal matrix given byEQUATIONand B, Y, Z are R n×m matrices calculated as follows (1EQUATIONwhere c ′′ i is the second-order derivative of creator i's cost function, andP ij = x * i exp(βj wij ) n k=1 x *k exp(βj w kj ) is the probability that creator i is matched with user j at the PNE under PPM(β).Proposition 1 together with Eq. ( 8) offers us a possibility to directly apply gradient-based approaches for solving OP (7) . However, the gradient computation requires the inversion of an n × n matrix, whose time complexity is O(n 3 ) and thus too cumbersome. To reduce the computational burden, we propose to approximately compute the gradient using the Sherman-Morrison-Woodbury formula [46] to approximate the matrix inverse, inspired by the specific structure of the RHS of Eq. ( 9). According to Sherman-Morrison-Woodbury formula, it holds thatEQUATIONand the computation of the RHS of Eq. ( 12) now requires a time complexity of O(n 2 m + nm 2 + m 3 ). However, the size of the user population m in practical scenarios is often even larger than n. To efficiently compute the RHS of Eq. ( 12), we propose a method to "sketch" the matrices Y and Z by sampling a subset of users. Initially, each column of Y and Z corresponds to a user index j. We begin by sampling a sub-population of X , indexed by I, with |I| = m = [δm], where δ ∈ (0, 1] denotes the sampling rate. With this sampled index set I, we construct matrices Ỹ , Z ∈ R n×m , where the (i, j)-th entries are defined as follows:EQUATIONwith j ′ being uniformly sampled from I. Given that Ỹ , Z now possess reduced ranks of [δm], the computational complexity of evaluating (D + Ỹ Z⊤ ) -1 is significantly lowered to O(n 2 m + n m2 + m3 ). Algorithm 1 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 δ, learning rate η, initial mechanism PPM(β). for t ∈ [T ] do Find the PNE x * of G under PPM(β) using Algorithm 2, Uniformly sample [δm] users from X and use them to compute matrices Ỹ , Z in Eq. ( 13), Compute the approximated gradient dW λ dβ using ( 8),( 9), (12) with sketched matrices Ỹ , Z,Update β = β + η dW λ dβ .Algorithm 1 requires solving for the PNE of G each time when β is updated. To accomplish this, we employ the multi-agent mirror descent method, as proposed in [7] and detailed in Algorithm 2 in Appendix, to serve as a subroutine 5 . To accelerate the convergence of Algorithm 1, the PNE strategy x * obtained under the previous β is used as the initial strategy for computing the new PNE after updating β. Further implementation details are provided in the experiment section.Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?Answer: [Yes]Justification: Experiment details are listed in Section 7.Guidelines:• The answer NA means that the paper does not include experiments.• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. • The full details can be provided either with the code, in appendix, or as supplemental material. 
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-1m dataset [28] . In our experiments, Algorithm 2 is 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 {c 1 , . . . , c 50 }, from the unit sphere S d-1 . For each center c i , users belonging to cluster-i are generated by sampling independently from a Gaussian distribution N (c i , 0. [22] to train user and movie embeddings (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 a 5-fold cross-validation and obtained an averaged RMSE=0.739 on the test sets. With the same hyper-parameter, we train the 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 ∈ R n×m 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.7.1 The Empirical Trade-Offs Between U and V Figure 1 illustrates the content creation frequency x * i , user utility π * j , and their corresponding aggregated values U = j π * j , V = i x * i under the PNE induced by different homogeneous β (i.e., all users share the same β). The result in the right panel shows that a larger β enhances overall user satisfaction U but undermines total content creation V . As β 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 i's creation frequency x * i and each user j's utility π * j at the PNE, such that both x * i and π * j are rearranged in descending order. They show that when β is shared across all users, its change affects x * i and π * j in the same direction.Next, we use Algorithm 1 to find the optimal PPM(β) and investigate the properties of the optimal β. We set λ = 0.5 and aim to maximize the objective W λ = U + 0.5V , more results under different choices of λ can be found in Appendix B. The initial β is set to (100, • • • , 100), representing a nearly deterministic matching for every user. Algorithm 1 is then run to update β. The sample rate and learning rate are set to δ = 0.1, η = 200. In addition to searching for personalized β j for each user j, we also attempt to find a homogeneous β (i.e., a fixed β j for each j) using Algorithm 1 6 .The first and third panels in Figure 2 show the evolution of W λ during the optimization process in both synthetic and MovieLens environments. As illustrated, Algorithm 1 successfully finds a better PPM(β) 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 β leads to a slightly better outcome compared to homogeneous β.The second and fourth panels depict the optimal β j for each user j, arranged in descending order. These panels provide insights into how such a mechanism achieves better trade-offs. For each user index j on the x-axis, we also plot the average and the standard deviation of the relevance scores {w ij } n i=1 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 are considered more "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 are less selective and more open to exploration. The results show that the optimal β tends to increase the exploration strengths (by deploying smaller β j ) for less selective users. This approach is intuitive, as it safely increases exploration while minimizing losses in user engagement.Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [Yes]Justification: We provide error bars in all figure in our experiments.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.• The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). • The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors). • It should be clear whether the error bar is the standard deviation or the standard error of the mean. 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conclusion: 
 In this work, we introduced a new game-theoretical model C 4 (Cournot Content Creation Competition) to explore how creators strategically determine their creation frequency under a UGC platform's recommendation algorithm. Our investigations reveal a critical balance between user satisfaction and creator engagement, mediated by the exploration strength of the recommendation. The existence and uniqueness of the PNE of C 4 games provide a 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 as a pre-deployment audit tool for optimizing recommendation algorithms to balance platforms' long-term and short-term objectives.While our C 4 model offers insights into strategic differentiation among creators regarding production quantity, it relies on a simplified assumption that creators maintain a 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 as topic variety, content quality, and production quantity-would be a valuable direction for future research. We leave this intriguing problem for future work. 
broader impacts: 
 Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?Answer: [Yes]Justification: It has been discussed at Abstract and Section 1.Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations. • The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
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 Appendix: A Omitted Proofs A.1 Proof of Theorem 1Proof. First of all, we argue that given any G(n, m, M, {c i }, β), for any creator i, there exists an δ i > 0 such that any x i ∈ [0, δ i ] cannot be an equilibrium strategy. This is because given any x -i ∈ R n-1 ≥0 , u i as a function of x i has a continuous and strictly positive gradient at x i = 0, meaning that there exists a δ i > 0 such that ∂ui ∂xi xi=t > 0, ∀t ∈ [0, δ i ] regardless of what other creators' strategies are. In other word, for any x i ≤ δ i , creator i can always increase her strategy to strictly improve her utility. As a result, any potential PNE x * must satisfy that x * i ≥ δ i . On the other hand, since c i (x i ) → +∞ when x i → +∞ but the traffic gain for each creator is at most m, we haveu i (x i , x -i ) → -∞, ∀x -i ∈ R n-1≥0 when x i → +∞. As a result, any equilibrium strategy must also be upper bounded by a uniform constant ∆ > 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 [δ i , ∆].For any fixed β = (β 1 , • • • , β m ), let a ij = exp(β j w ij ) and Eq. ( 1) can be simplified toEQUATIONFor simplicity we denote g j (x) = n k=1 x k a kj and u i can be expressed asu i (x i , x -i ) = m j=1 xiaij gj (x) -c i (x i ).Our proof starts from a sufficient condition from [44] for a 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 λ = (λ 1 , • • • , λ n ) such that the Hessian matrix given byEQUATIONis strictly negative-definite. In [44] , it is shown that any game satisfying λ-DSC condition has a unique pure Nash equilibrium (PNE); such a game is often referred to as monotone games.First of all, we already argued that each creator i's strategy set is [δ i , ∆], which is a convex set. Core to our proof is to show that game G is 1-DSC under the theorem conditions. Direct calculation shows that for any1 ≤ k ≤ l ≤ n, ∂ 2 u k (x) ∂x k ∂x l = a kj a lj g 3 j • (-g j + 2a kj x k ), ∂ 2 u l (x) ∂x l ∂x k = a kj a lj g 3 j • (-g j + 2a lj x l ),and therefore the Hessian matrix of G specified by the RHS of Eq. ( 15) is equal toEQUATIONwhere g j in the above expressions denotes g j (x), vector a j = (a 1j , • • • , a nj ) ⊤ . We can see that if all the cost functions are strictly convex, the second diagonal matrix H 0 in the RHS of Eq. ( 16) is strictly positive-definite (PD). Therefore, it suffices to show that (1) for all j ∈ [m], H j is PD. To see this, let z i = x i a ij and we show that for any y = (y 1 , • • • , y n ) ∈ R n , y ⊤ H j y ≥ 0, and the equality holds if and only if y = 0. In fact, note thatEQUATION)Because x i and a i are all strictly positive, each z i must also be strictly positive. Hence, Eq. ( 17) can take value zero if and only ify i = 0, ∀i ∈ [n].Therefore, H j is PD for any j ∈ [m], which completes the proof.First let's recall the definition of U, V when m = 1:EQUATIONEQUATION)In the following, we prove the monotonicity of U (β) and V (β) by showing d ln U dβ > 0 and dV dβ < 0, 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 x * and simply use x to refer to the PNE of G. When m = 1, the creator utility function writesEQUATION)LetP i = xiai n k=1x k a k , where a i = e βwi . First of all, we claim that it is without loss of generality to consider the regime where P i ≤ 1 3 . To see this, consider the following two C 4 instances:G 1 (n, m = 1, w = (w 1 , • • • , w n ), c = (c 1 , • • • , c n ), β), G 2 (3n, m = 1, [w, w, w], [c/3, c/3, c/3], [β, β, β]).Clearly, both games G 1 , G 2 have unique PNE. Let the PNE of G 1 be denoted by x * 1 . In G 2 , since its 3n players are divided into three identical groups, its PNE can be represented as(x * 2 , x * 2 , x * 2 ), where each group of n players follow the same strategy. Moreover, for any 1 ≤ i ≤ n, it is straightforward to observe that the i-th player's utility functions in G 1 and G 2 differ only by a multiplicative constant of 3. Consequently, we have x * 1 = x * 2 . Therefore, for any C 4 instance G 1 with m = 1, we can always construct an equivalent instance G 2 that shares the same PNE structure, while ensuring P i ≤ 1 3 . This justifies the assumptions that, without loss of generality, we can take P i ≤ 1 3 . Another property we need is that the PNE strategy x i of any player i in G 1 is bounded in a compact region [0, L] for some constant L, regardless of the values of β. To see this, note that c i (x i ) is increasing in x i and goes to infinity as x i → +∞ while P i is upper bounded by 1. As a result, for any x i such that u i (x i , x -i ) ≤ 1 -c i (x i ) < -c i (0) = u i (0, x -i ), x i cannot be a PNE strategy as switching to 0 increases player i's utility. Therefore, if we takeL = max i∈[n] {inf x {x ≥ 0 : 1 -c i (x i ) < -c i (0)}}, it holds that x i ≤ L, ∀i ∈ [n]. Let F (x, β) = ∂ui ∂xi n i=1be an n-value function. From Corollary 1 we know x, β satisfy F (x, β) = 0. And Theorem 1 guarantees that for any β ≥ 0, the x implicitly determined by F (x, β) = 0 exists and is unique. Therefore, by the implicit function theorem [37] , the derivative of x w.r.t. β can be written asdx dβ = - ∂F ∂x -1 • ∂F ∂β ,where ∂F ∂x n×n is the Jacobian matrix (which is also the Hessian of G when λ = 1, see Eq. ( 15)) and ∂F ∂β ∈ R n×1 is the partial derivative of F w.r.t. β. The first-order derivative of u i can be calculated asEQUATIONand we can use it to further obtain the following explicit expressions in terms of the derivatives of F :EQUATIONLet's define a positive definite diagonal matrixD = diag P 2 1 x 2 1 + c ′′ 1 , • • • , P 2 n x 2 n + c ′′ n .Since c ′′ i > 0, we can introduce variablesEQUATION)In addition, let's also defineEQUATIONthen we have ∂F ∂x = D + yz ⊤ and from Sherman-Morrison formula [46] , it holds thatEQUATION)whereD -1 = diag δ 1 x 2 1 P 2 1 , • • • , δ n x 2 n P 2 n , D -1 y = δ 1 x 1 (1 -2P 1 ) P 1 , • • • , δ n x n (1 -2P n ) P n ⊤ , z ⊤ D -1 = δ 1 x 1 P 1 , • • • , δ n x n P n . Since P i ≤ 1 3 , we have 1 -2P i ≥ 1 3 > 0.With all the notations introduced so far we are now ready to give the formal proof of Theorem 2.Proof. We prove the monotonicity of U (β) and V (β) by showing d ln U dβ > 0 and dV dβ < 0. The monotonicity of U (β): The first-order derivative of ln U w.r.t. β is given byEQUATION)where ∂U ∂x ∈ R 1×n is the partial derivative of U w.r.t. x. Let a i = e βwi , we will first showEQUATIONFrom Cauchy-Schwarz inequality, it holds that n k=1w 2 k x k a k • n k=1 x k a k ≥ n k=1 w 2 k x k a k • x k a k 2 = n k=1 w k x k a k 2 .Therefore, the RHS of Eq. ( 27) is greater than or equal to 0. Hence, it suffices to showEQUATIONAlso note thatEQUATIONand substitute Eq. ( 22), (25) , and (29) into the LHS of Eq. ( 28), we obtainEQUATIONwhereEQUATIONSince 1 -2P i > 0, from Cauchy-Schwarz inequality it holds thatn i=1 δ i (1 -2P i )(w i -T ) 2 • 1 + n i=1 δ i (1 -2P i ) = n i=1 δ i (1 -2P i )(w i -T ) 2 • n i=1 δ i (1 -2P i ) + n i=1 δ i (1 -2P i )(w i -T ) 2 ≥ n i=1 δ i (1 -2P i )(w i -T ) 2 + n i=1 δ i (1 -2P i )(w i -T ) 2 > n i=1 δ i (1 -2P i )(w i -T ) 2 ,where the last inequality holds because {w i } are not identical so there exists at least one j ∈ [n] such that δ j (1 -2P j )(w j -T ) 2 > 0. Therefore, Eq. ( 31) holds and we have d ln U dβ > 0. The monotonicity of V (β): Next we show dV dβ < 0. Since ∂V ∂β = 0, this is equivalent to showEQUATIONNote that dV dxi = 1, we haveEQUATIONTo show the RHS of Eq. ( 33) is positive, it suffices to showEQUATIONPlugin T = n i=1 P i w i into Eq. ( 34), it is equivalent to show that1 + n i=1 δ i (1 -2P i ) n i=1 δ i x i (1 -2P i )w i P i - n i=1 P i w i n i=1 δ i x i (1 -2P i ) P i < n i=1 δ i x i (1 -2P i ) P i n i=1 δ i (1-2P i )w i ,and note that 1 =EQUATIONLeta i = δixi(1-2Pi) Pi , b i = δ i (1 -2P i ) + P i , then Eq. (35) is equivalent to n i=1 b i • n i=1 a i w i < n i=1 a i • n i=1 b i w i ⇐⇒ i>j (w i -w j ) b i a i - b j a j > 0.Next, without loss of generality we show that for any 1 ≤ i < j ≤ n, if w i > w j then it also holds that bi ai > bj aj for sufficiently large β. In fact, fromP i = xie βw i n k=1x k e βw k and Eq. ( 23) we obtainb i a i • a j b j = δ j (δ i (1 -2P i ) + P i )(1 -2P j ) δ i (δ j (1 -2P j ) + P j )(1 -2P i ) • e β(wi-wj ) = 1 + P i δ i /(1 -2P i ) 1 + P j δ j /(1 -2P j ) • e β(wi-wj ) = 1 + P 3 i (1-2Pi)(P 2 i +x 2 i c ′′ i (xi))1 +P 3 j (1-2Pj )(P 2 j +x 2 j c ′′ j (xj ))• e β(wi-wj ) .On the one hand, because 1-2P i , 1 -2P j ∈ [ 1 3 , 1], x i , x j ∈ [0, L],and c ′′ i (x i ), c ′′ j (x j ) > 0, the first terms of the LHS of Eq. ( 36) is a positive number lower bounded away from zero. On the other hand, w i > w j ensures that the second term e β(wi-wj ) can be arbitrarily large as long as β is sufficiently large. Therefore, there must exist a β 0 > 0 such that for any β > β 0 , bi ai • aj bj > 1 holds for any i > j. As a result, (w i -w j ) bi ai -bj aj > 0 holds, which completes the proof.We use the following Multi-agent Mirror Descent (MMD) algorithm as the PNE solver of C 4 , whose convergence is guaranteed by [7] . Since each creator's strategy set X i = [0, +∞), we can simply choose a projection mapping Proj Xi (x) = (max(x i , 0)) n i=1 . The gradients of utility functions can be implemented directly since they have closed forms. Through our experiment, the default T = 10000, η = 0.1, ϵ = 1e -2, x (0) i = 1.0. Algorithm 2 is a simplified version of Algorithm 1 in [7] where we replace the gradient estimation to the exact gradient. According to Theorem 5.1 in [7] , Algorithm 2 converges to the unique PNE of any C 4 game with probability 1.Algorithm 2: Multi-agent Mirror Descent (MMD) with perfect gradient Input: Maximum iteration number T , step size η, each player i's utility function u i , error tolerance ϵ, initial strategyx i = x (0) i . for t ∈ [T ] do if ∥(g 1 , • • • , g n )∥ 2 < ϵ, then Break Compute gradient g i = ∇ i u i (x i , x -i ), for i ∈ [n], Update x i ← Proj Xi (x i + ηg i ), ∀i ∈ [n]. Output :(x 1 , • • • , x n ).Figure 3 illustrates the trade-off between U and V in the MovieLens environment, and Figure 4 plots the same information as shown in Figure 2 but with a different value of λ = 0.1. As we can see, the optimal PPM(β) found by Algorithm 1 conveys a consistent message: it prioritizes the recommendation accuracy for users with more determined preferences while increasing the exploration strength for less selective users. Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.Further details regarding the Instagram findings are protected under a non-disclosure agreement (NDA) and may be disclosed in future versions of this work.For the elegance of our theoretical analysis, we treat xi as a continuous variable, although the key messages and insights of this paper are preserved if xi is discrete.The randomness in matching results may stem from either the imperfect estimation of the preference score wij 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.In[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.The gradient of W λ with respect to a homogeneous β can be readily obtained by summing all the partial derivatives of W λ with respect to βj. 


Decision: 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.

Reviews: review: paper_summary: paper_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.
strength_weakness: strength_weakness: - (Main) Model might be too simplistic - authors assume users consistent produce work of same topic & quality and only changes the production volume.

- (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:
   - 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.
   - 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.

- Typo: i =1 -> j=1 in line 92, third and fourth -> second and fourth in line 347
questions: 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. 
- 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?
- Is collusion between content creators a potential problem here?
limitations: limitations: The authors adequately addressed the limitations.
paper_summary: paper_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.
strength_weakness: strength_weakness: 1.	Some 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. 
2.	Although 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. 
3.	Existing 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.
questions: questions: 1.	How is the efficiency of the proposed solution when the dataset includes millions of users? 
2.	What are the differences between C4 and previous C3 game? How does C4 benefit from the additional “Cournot” setting?
limitations: limitations: 1.	Limited practical value. The assumption is too strong, and the experiments are constrained on small dataset with 1,000 users.
2.	Unclear distinct contributions compared with previous works.
paper_summary: paper_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).
strength_weakness: strength_weakness: 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). 

Rather, 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:
- a number of specific platforms are mentioned by name: YouTube, TikTok, Netflix, Spotify, and MovieLens. 
- Only data from MovieLens is used (which is very reasonable -- it's a very popular dataset for academic work for good reason).
- 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

See "Questions" section below for some specific questions about this concern that I think are likely to be in scope of a revision.

With 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.
questions: 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)
- What is the strongest evidence that any of these major platforms follow Cournot competition like dynamics?
- What is the impact of platform-as-creator dynamics, such on Netflix?
- 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.
- To what extent would we expect results to hold if we did have access to MovieLens-style observational data from e.g. YouTube?

Overall, these are not "existential" questions per se, but some attempt to clarify could strengthen the draft quite a bit.
limitations: 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).

Comments: title: Reminder to Reviewer 1ynk
Re: Response
Re: Official Comment by Reviewer 1Tuv
Response
comment: Dear Reviewer 1ynk, as the discussion phase is coming to a close, we wanted to gently remind you to review our response and consider reevaluating our paper in light of the additional information provided. If you have any further suggestions or concerns, we would be more than happy to engage in further discussion to improve our work.
We are pleased that our response has addressed the reviewer's main concerns. We are currently working on providing an anonymized version of the offline data to strengthen our model assumptions, which will be included in the next version as additional supporting results. If you have any further suggestions for improving our work, please feel free to share them, and we would be more than happy to engage in further discussion.
We sincerely thank Reviewer 1Tuv for their positive evaluation of our work and response. We particularly appreciate your accurate understanding of the contributions and potential of our research. We are currently working on providing an anonymized version of the offline data used to support our model, which will be included in the next version as additional justifying data. If you have any further questions, we would be more than happy to engage in further discussion.
I thank the authors for their response. Most of my concerns are addressed, and I'm happy to keep my score, leaning towards acceptance of the paper.
Thanks to the authors for this additional information.

In my original review, I stated the view that even absent specific evidence about a particular UGC platform that the framework contribution of this work could be a meaningful reason to accept the paper.

IMO the addition of offline data from a major platform will really boost the impact of the paper. While I understand it seems there is a still a chance the data cannot be shared, this reflects positively on the work.

Beyond the potential of adding specific justifying data, the common response was also very helpful in clarifying concerns shared among reviewers.