Evolutionary dynamics of reactive partner strategy in stochastic games

Jing Zhang, Yixin Yang, Zhihai Rong and Zhi-Xi Wu

Chaos, Solitons & Fractals, 2026, vol. 208, issue P1

Abstract: Stochastic games provide an efficient incentive mechanism for the emergence of cooperation by modeling the feedback between environmental states and individual behaviors, where players usually make decisions through memory strategies. In this paper, a mixed memory-one strategy called the reactive partner strategy (REPA) is introduced into stochastic games, which tends to deterministically cooperate with the cooperative co-player and forgive an opponent’s defection with a probability. By analyzing the payoff relationships between pure memory-one strategies and REPA, it is shown that REPA is always a Nash equilibrium strategy that can resist invasion by defective strategies, and the proper forgiving probability of REPA can promote cooperation under low benefit conditions in stochastic games where the famous pure memory-one strategy of win-stay, lose-shift (WSLS) fails to oppose invasion by defectors. For high benefit values, REPA can act as an evolutionary bridge that connects always defect (AllD), Grim and WSLS strategies, which may offer valuable insights into understanding and promoting both cooperation and strategic evolution in stochastic games.

Keywords: Stochastic game; Evolutionary dynamics; Memory strategies (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:208:y:2026:i:p1:s0960077926002729

DOI: 10.1016/j.chaos.2026.118131

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