Cooperation Dynamics In Multi-agent Systems: Exploring Game-theoretic Scenarios With Mean-field Equilibria

Abstract

Cooperation is fundamental in Multi-Agent Systems (MAS) and Multi-Agent Reinforcement Learning (MARL), often requiring agents to balance individual gains with collective rewards. In this regard, this paper aims to investigate strategies to invoke cooperation in game-theoretic scenarios, namely the Iterated Prisoner's Dilemma, where agents must optimize both individual and group outcomes. Existing cooperative strategies are analyzed for their effectiveness in promoting group-oriented behavior in repeated games. Modifications are proposed where encouraging group rewards will also result in a higher individual gain, addressing real-world dilemmas seen in distributed systems. The study extends to scenarios with exponentially growing agent populations (\(N \longrightarrow +\infty\)), where traditional computation and equilibrium determination are challenging. Leveraging mean-field game theory, equilibrium solutions and reward structures are established for infinitely large agent sets in rep

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