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Integrating emotion and expectation improves cooperation

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  • Lu, Wen
  • Liang, Shu

Abstract

Cooperation is a key issue attracting widespread attention across various fields. Emotions and expectations jointly participate in the decision-making process, and are key factors influencing the evolution of cooperation. Therefore, this paper proposes a game evolution model that considers the dual influences of emotions and expectations. In the model, a player’s initial strategy depends on their emotions. Subsequently, expectations influence the decision-making process, altering the player’s initial strategy to the current strategy. Specifically, high expectations lead players to maintain their initial strategy, whereas low expectations prompt them to change strategies. Furthermore, the paper analyzes the evolution of cooperation in the prisoner’s dilemma and the influence of expectations. Simulation results show that under high betrayal temptation, players with loneliness and defection would change their initial strategy to cooperation due to low expectations, while those players who initially gather with cooperation strategies maintain the cooperation strategies due to higher expectations, ultimately increasing the cooperation fraction and payoff of the population. Therefore, expectations effectively enhance the cooperation level and payoff of the population. When the scale of individuals changing their strategies based on expectations (ICSE) is large, the effect of expectations on enhancing cooperation and payoff is more pronounced. Frequent consideration of anticipated initial strategy changes also yields the same effect. Additionally, mechanisms of the influence of emotion on payoff, direct emotion interaction and the influence of strategy on emotion collectively contribute to enhancing the significantly evolutionary advantage of friendly emotions and cooperation strategies. This paper contributes to a deeper understanding of the role of expectations in the evolution of emotions and cooperation, laying the groundwork for enhancing social cooperation through expectation management.

Suggested Citation

  • Lu, Wen & Liang, Shu, 2026. "Integrating emotion and expectation improves cooperation," Applied Mathematics and Computation, Elsevier, vol. 511(C).
    • Handle: RePEc:eee:apmaco:v:511:y:2026:i:c:s0096300325004618
    DOI: 10.1016/j.amc.2025.129736
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    1. Satoshi Uchida & Hitoshi Yamamoto & Isamu Okada & Tatsuya Sasaki, 2019. "Evolution of Cooperation with Peer Punishment under Prospect Theory," Games, MDPI, vol. 10(1), pages 1-13, February.
    2. Han, Zhen & Wu, Wenning & Song, Qun & Zhu, Peican, 2024. "Analysis of payoff expectation in evolutionary game based on Bush–Mosteller model," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Ng, Gary Ting Tat & Au, Wing Tung & Lai, Derek Chun Kiu, 2024. "The role of game riskiness on the expectation-cooperation link in social dilemmas and its relations with fear and greed," Judgment and Decision Making, Cambridge University Press, vol. 19, pages 1-1, January.
    4. Lu, Peng, 2015. "Imitating winner or sympathizing loser? Quadratic effects on cooperative behavior in prisoners’ dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 327-337.
    5. Kölle, Felix & Quercia, Simone, 2021. "The influence of empirical and normative expectations on cooperation," Journal of Economic Behavior & Organization, Elsevier, vol. 190(C), pages 691-703.
    6. Li, Songjie & Bao, Wei & Dai, Yayun & Ye, Ye & Xie, Nenggang, 2022. "Emotional game and the evolution of cooperation considering the effects of reputation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    7. Dorothee Mischkowski & Rebecca Stone & Alexander Stremitzer, 2019. "Promises, Expectations, and Social Cooperation," Journal of Law and Economics, University of Chicago Press, vol. 62(4), pages 687-712.
    8. Ernst Fehr & Simon Gächter, 2002. "Altruistic punishment in humans," Nature, Nature, vol. 415(6868), pages 137-140, January.
    9. Wang, Qiuling & Jia, Danyang, 2019. "Expectation driven by update willingness promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 174-179.
    10. George, Jennifer M. & Dane, Erik, 2016. "Affect, emotion, and decision making," Organizational Behavior and Human Decision Processes, Elsevier, vol. 136(C), pages 47-55.
    11. Xie, Kai & Liu, Xingwen & Chen, Hao & Yang, Jun, 2022. "Preferential selection and expected payoff drive cooperation in spatial voluntary public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    12. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    13. Muramatsu, Roberta & Hanoch, Yaniv, 2005. "Emotions as a mechanism for boundedly rational agents: The fast and frugal way," Journal of Economic Psychology, Elsevier, vol. 26(2), pages 201-221, April.
    14. Wang, Lu & Ye, Shun-Qiang & Cheong, Kang Hao & Bao, Wei & Xie, Neng-gang, 2018. "The role of emotions in spatial prisoner’s dilemma game with voluntary participation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1396-1407.
    15. Fu, Xiao & Liu, Xuesong & Hu, Yuhan & Huang, Shaoxu, 2023. "Emotion-based renewal strategies to promote cooperation in spatial prisoner’s dilemma games," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    16. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
    17. Lu, Wen & Liang, Shu, 2023. "Direct emotional interaction in prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    18. Wang, Yongjie & Chen, Tong & Chen, Qiao & Si, Guangrun, 2017. "Emotional decisions in structured populations for the evolution of public cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 475-481.
    19. Arefin, Md. Rajib & Tanimoto, Jun, 2024. "Coupling injunctive social norms with evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    20. Engel, Christoph & Kube, Sebastian & Kurschilgen, Michael, 2021. "Managing expectations: How selective information affects cooperation and punishment in social dilemma games," Journal of Economic Behavior & Organization, Elsevier, vol. 187(C), pages 111-136.
    21. Nicholas C. Barberis, 2013. "Thirty Years of Prospect Theory in Economics: A Review and Assessment," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 173-196, Winter.
    22. Chen, Wei & Wang, Jianwei & Yu, Fengyuan & He, Jialu & Xu, Wenshu & Wang, Rong, 2021. "Effects of emotion on the evolution of cooperation in a spatial prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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