Efficiency of cooperation incentives in evolutionary population games under payoff-observation errors

Shengxian Wang; Chengyu Yin; Xiaojie Chen; Ming Cao

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arXiv · 2608.30982

Efficiency of cooperation incentives in evolutionary population games under payoff-observation errors

Shengxian Wang·Chengyu Yin·Xiaojie Chen·Ming Cao

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Abstract

Traditional studies on evolutionary dynamics of cooperation have concentrated on an idealized game setup free of payoff-observation errors. However, in real-world scenarios, individuals frequently encounter errors when observing the payoffs of their opponents during game interactions, resulting from unintentional mistakes, such as data misrecording, overlooking critical details, and miscalculations. This gap between idealized error-free game models and the error-prone real-world game interactions leads to the lack of insight into the impact of payoff-observation errors on the evolutionary dynamics of population games, in particular the efficiency of cooperation incentives. In this paper, we construct a research framework for population games with payoff-observation errors, which enables us to investigate the effects of errors on the evolutionary dynamics of cooperation in the evolutionary Prisoner's Dilemma game with combined incentives. To quantify the implementation costs of incentives in the presence of errors, we devise an index function and employ optimal control theory to derive the optimal incentive protocols. Our theoretical and numerical results reveal that payoff-observation errors can lower the costs compared to error-free cases, and we also derive the theoretical conditions for these results. Finally, we formulate an optimization problem to explore the cost difference between the optimal incentive protocols with and without errors, and further design an algorithm to obtain the numerical solution that minimizes this difference.

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Shengxian Wang, Chengyu Yin, Xiaojie Chen, Ming Cao. 2026-08-31. Efficiency of cooperation incentives in evolutionary population games under payoff-observation errors. https://arxiv.org/abs/2608.30982

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