2025/02/28 by Meli̇h İşeri̇, Erhan Bayraktar, İşeri, Melih +1
Psychology · #Computer Science and Game Theory (cs.GT) #Educational Games and Gamification #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #I.2.6 #J.4 #Optimization and Control (math.OC) #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2503.00227
openalex publication_date 2025/02/28 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
This work introduces a unified framework for analyzing games in greater depth. In the existing literature, players' strategies are typically assigned scalar values, and equilibrium concepts are used to identify compatible choices. However, this approach neglects the internal structure of players, thereby failing to accurately model observed behaviors. To address this limitation, we propose an abstract definition of a player, consistent with constructions in reinforcement learning. Instead of defining games as external settings, our framework defines them in terms of the players themselves. This offers a language that enables a deeper connection between games and learning. To illustrate the need for this generality, we study a simple two-player game and show that even in basic settings, a sophisticated player may adopt dynamic strategies that cannot be captured by simpler models or compatibility analysis. For a general definition of a player, we discuss natural conditions on its components and define competition through their behavior. In the discrete setting, we consider players whose estimates largely follow the standard framework from the literature. We explore connections to correlated equilibrium and highlight that dynamic programming naturally applies to all estimates. In the mean-field setting, we exploit symmetry to construct explicit examples of equilibria. Finally, we conclude by examining relations to reinforcement learning.