On the Complexity of Computing Markov Perfect Equilibrium in General-Sum Stochastic Games

• URL: http://arxiv.org/abs/2109.01795v1
• Date: Sat, 4 Sep 2021 05:47:59 GMT
• Title: On the Complexity of Computing Markov Perfect Equilibrium in General-Sum Stochastic Games
• Authors: Xiaotie Deng, Yuhao Li, David Henry Mguni, Jun Wang, Yaodong Yang
• Abstract summary: Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. We derive an approximate Perfect Equilibrium (MPE) in a finite-state SGs Game within the exponential precision of textbfPPAD-complete. Our results indicate that finding an MPE in SGs is highly unlikely to be textbfNP-hard unless textbfNP=textbfco-NP.
• Score: 18.48133964089095
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive that computing an approximate Markov Perfect Equilibrium (MPE) in a finite-state discounted Stochastic Game within the exponential precision is \textbf{PPAD}-complete. We adopt a function with a polynomially bounded description in the strategy space to convert the MPE computation to a fixed-point problem, even though the stochastic game may demand an exponential number of pure strategies, in the number of states, for each agent. The completeness result follows the reduction of the fixed-point problem to {\sc End of the Line}. Our results indicate that finding an MPE in SGs is highly unlikely to be \textbf{NP}-hard unless \textbf{NP}=\textbf{co-NP}. Our work offers confidence for MARL research to study MPE computation on general-sum SGs and to develop fruitful algorithms as currently on zero-sum SGs.

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