PPA-Game: Characterizing and Learning Competitive Dynamics Among Online Content Creators
Authors: Renzhe Xu, Haotian Wang, Xingxuan Zhang, Bo Li, Peng Cui
Organizations: MoE Key Laboratory of Interdisciplinary Research of Computation and Economics, Institute for Theoretical Computer Science, Shanghai University of Finance and Economics, Shanghai, China · College of Computer Science and Technology, National University of Defense Technology, Changsha, China · Department of Computer Science and Technology, Tsinghua University, Beijing, China · School of Economics and Management, Tsinghua University, Beijing, China
In this paper, we present the Proportional Payoff Allocation Game (PPA-Game), which characterizes situations where agents compete for divisible resources. In the PPA-game, agents select from available resources, and their payoffs are proportionately determined based on heterogeneous weights attributed to them. Such dynamics simulate content creators on online recommender systems like YouTube and TikTok, who compete for finite consumer attention, with content exposure reliant on inherent and distinct quality. We first conduct a game-theoretical analysis of the PPA-Game. While the PPA-Game does not always guarantee the existence of a pure Nash equilibrium (PNE), we identify prevalent scenarios ensuring its existence. Simulated experiments further prove that the cases where PNE does not exist rarely happen. Beyond analyzing static payoffs, we further discuss the agents' online learning about resource payoffs by integrating a multi-player multi-armed bandit framework. We propose an online algorithm facilitating each agent's maximization of cumulative payoffs over T rounds. Theoretically, we establish that the regret of any agent is bounded by O(log1+ηT) for any η>0. Empirical results further validate the effectiveness of our online learning approach.
Figures & tables
Figure 1: Graphical overview of our algorithm: Utilizes hyper-parameters c1 , c2 , c3 , and η , with counter s progressing through natural numbers. Initially, the algorithm enters an Exploration Phase for c1K rounds ( Section 4.3.1 ), followed by a Learning and Exploitation phase ( Section 4.3.2 ), where it alternates between Learning PNE and Exploitation Subphases based on the counter s . Specifically, in round s , the Learning PNE Subphase spans c2sη rounds, and the Exploitation Subphase spans c32s rounds.
Figure 2: Curves showing the average regret and the number of rounds where players do not follow the most efficient PNE. Note that SelfishRobustMMAB could not be applied to scenarios when N>K .
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 3: An improvement cycle in a game with no PNE.
Strategy profile
PNE?
Least reward change by deviation if PNE
δ′ -Nash equilibrium if not PNE
(1,1,1)
✗
0.518 . Deviated strategy (1,1,2)
(1,1,2)
✗
0.022 . Deviated strategy (1,2,2)
(1,2,1)
✓
0.052 . Deviated strategy (1,2,2)
(1,2,2)
✗
0.052 . Deviated strategy (1,2,1)
(2,1,1)
✓
0.133 . Deviated strategy (2,1,2)
(2,1,2)
✗
0.133 . Deviated strategy (2,1,1)
Appendix
Table 1: A showcase that δNE>δNoNE . Set N=3 and K=2 . Assume the resources’ payoffs to be [1,0.7] . Suppose each player has the same weights on the resources (as per Condition (2) in Theorem 3.2 ), with weights [1,0.8,0.4] , respectively. We list all strategy profiles and find that δNE=min{0.052,0.133}=0.052>0.022=min{0.518,0.022,0.052,0.133,0.356,0.873}=δNoNE .
Strategy profile
PNE?
Least reward change by deviation if PNE
δ′ -Nash equilibrium if not PNE
(1,1,1)
✗
0.389 . Deviated strategy (1,1,2)
(1,1,2)
✓
0.040 . Deviated strategy (1,2,2)
(1,2,1)
✓
0.068 . Deviated strategy (1,2,2)
(1,2,2)
✗
0.068 . Deviated strategy (1,2,1)
(2,1,1)
✓
0.126 . Deviated strategy (1,1,1)
(2,1,2)
✗
0.215 . Deviated strategy (2,1,1)
Appendix
Table 2: A showcase that δNE<δNoNE . Set N=3 and K=2 . Assume the resources’ payoffs to be [1,0.6] . Suppose each player has the same weights on the resources (as per Condition (2) in Theorem 3.2 ), with weights [1,2/3,4/9] , respectively. We list all strategy profiles and find that δNE=min{0.040,0.068,0.126}=0.040<0.068=min{0.389,0.068,0.215,0.360,0.874}=δNoNE .
User interactions in online recommendation platforms create interdependencies among content creators: feedback on one creator's content influences the system's learning and, in turn, the exposure of other creators' contents. To analyze incentives in such settings, we model collaboration as a multi-agent stochastic linear bandit problem with a transferable utility (TU) cooperative game formulation, where a coalition's value equals the negative sum of its members' cumulative regrets. We show that, for identical (homogenous) agents with fixed action sets, the induced TU game is convex under mild algorithmic conditions, implying a non-empty core that contains the Shapley value and ensures both stability and fairness. For heterogeneous agents, the game still admits a non-empty core, though convexity and Shapley value core-membership are no longer guaranteed. To address this, we propose a simple regret-based payout rule that satisfies three out of the four Shapley axioms and also lies in the core. Experiments on MovieLens-100k dataset illustrate when the empirical payout aligns with -- and diverges from -- the Shapley fairness across different settings and algorithms.
The Kelly or proportional allocation mechanism is a simple and efficient auction-based scheme that distributes an infinitely divisible resource proportionally to the agents bids. When agents are aware of the allocation rule, their interactions form a game extensively studied in the literature. This paper examines the less explored repeated Kelly game, focusing mainly on utilities that are logarithmic in the allocated resource fraction. We first derive this logarithmic form from fairness-throughput trade-offs in wireless network slicing, and then prove that the induced stage game admits a unique Nash equilibrium NE. For the repeated play, we prove convergence to this NE under three behavioral models: (i) all agents use Online Gradient Descent (OGD), (ii) all agents use Dual Averaging with a quadratic regularizer (DAQ) (a variant of the Follow-the-Regularized leader algorithm), and (iii) all agents play myopic best responses (BR). Our convergence results hold even when agents use personalized learning rates in OGD and DAQ (e.g., tuned to optimize individual regret bounds), and they extend to a broader class of utilities that meet a certain sufficient condition. Finally, we complement our theoretical results with extensive simulations of the repeated Kelly game under several behavioral models, comparing them in terms of convergence speed to the NE, and per-agent time-average utility. The results suggest that BR achieves the fastest convergence and the highest time-average utility, and that convergence to the stage-game NE may fail under heterogeneous update rules.
Younes Ben Mazziane, Cleque-Marlain Mboulou Moutoubi, Eitan Altman +1
LIA, Avignon university, Avignon, France · INRIA, Sophia Antipolis, France
The rise of AI amplifies the economic phenomenon of positive spillovers: when creators contribute content that can be reused and adapted by LLMs, one creator's effort may improve the content quality of others through recombination. While such spillovers can improve content quality, they also reshape incentives, as creators may reduce effort when they can benefit from others' contributions. We introduce the Content Creation with Spillovers (CCS) model, a game between a platform and strategic creators. In this game, each creator chooses an effort level, and qualities are jointly determined by all creators' efforts. The platform contracts on qualities while seeking to maximize social welfare. We show that standard contest mechanisms can be unstable, and propose a parametrized family of Provisional Allocation mechanisms that guarantee a Pareto-dominant equilibrium. Although optimizing welfare within this family is hard to approximate in general, we develop approximation algorithms whose guarantees hold either deterministically across structured spillover classes or with high probability under random instances.