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Impact of uncertain payoffs on evolution of cooperation in TFT-AllD game based on imitation dynamics

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Listed:
  • Wang, Si-Yi
  • Li, Zi-Xuan
  • Zheng, Xiu-Deng
  • Tao, Yi
  • Li, Cong

Abstract

In order to explore how the evolution of cooperation in TFT-AllD games based on imitation dynamics is affected by the uncertainty of payoffs (or environmental noise), the stochastic evolutionary and convergence stabilities of this system are investigated. We here assume that the uncertainty in payoffs arises from the stochasticity in the number of repeated interactions among individuals. The results show that: (i) the stochastic evolutionary stability is only determined by the properties of the average payoff matrix; (ii) not only the pure strategies TFT (Tit-for-Tat) and AllD (Always Defect) could be both stochastically evolutionarily stable (SES), but also a completely mixed strategy corresponding to the interior equilibrium of the average payoff matrix must be also SES; and (iii) a completely mixed strategy must be not stochastically convergence stable (SCS) even though it is SES. In addition, we show also that for the TFT-AllD games based on imitation dynamics in finite populations, the weak selection can filter the impact of uncertain payoffs on the fixation probability of TFT.

Suggested Citation

  • Wang, Si-Yi & Li, Zi-Xuan & Zheng, Xiu-Deng & Tao, Yi & Li, Cong, 2026. "Impact of uncertain payoffs on evolution of cooperation in TFT-AllD game based on imitation dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 686(C).
    • Handle: RePEc:eee:phsmap:v:686:y:2026:i:c:s0378437126000877
    DOI: 10.1016/j.physa.2026.131351
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