Symmetric equilibrium of multi-agent reinforcement learning in repeated prisoner's dilemma

Abstract

We investigate the repeated prisoner's dilemma game where both players alternately use reinforcement learning to obtain their optimal memory-one strategies. We theoretically solve the simultaneous Bellman optimality equations of reinforcement learning. We find that the Win-stay Lose-shift strategy, the Grim strategy, and the strategy which always defects can form symmetric equilibrium of the mutual reinforcement learning process amongst all deterministic memory-one strategies.

arXiv comment29 pages, 6 figures

References in corpus (3)

• Deterministic limit of temporal difference reinforcement learning for stochastic games
• Reinforcement Learning Produces Dominant Strategies for the Iterated Prisoner's Dilemma
• Emergence of Exploitation as Symmetry Breaking in Iterated Prisoner's Dilemma

Cited by in corpus (4)

• Intrinsic fluctuations of reinforcement learning promote cooperation
• Emergence of Cooperation in Two-agent Repeated Games with Reinforcement Learning
• Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoners' dilemma game
• Controlling conditional expectations by zero-determinant strategies