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Errors can increase cooperation in finite populations

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  • Zhang, Huanren

Abstract

I use an evolutionary game to investigate how the level of noise influences cooperation and efficiency in a dynamic setting. Players choose strategies to play indefinitely repeated prisoner's dilemmas; the strategies are represented by finite automata, and complexity costs are imposed. Players update their strategies based on the successfulness of the strategies. Using both theoretical analysis and computational experiments, I show that the presence of noise dramatically changes the system dynamics. The effect of noise interacts with the benefit of cooperation: noise can increase cooperation, but only when its level is low and the benefit of cooperation is high. In the noise-free environment, I observe constant oscillations between cooperation and defection. In contrast, the presence of noise makes Win-Stay Lose-Shift (WSLS) a successful strategy when the benefit of cooperation is sufficiently high, making cooperation relatively stable and leading to an efficient outcome.

Suggested Citation

  • Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    • Handle: RePEc:eee:gamebe:v:107:y:2018:i:c:p:203-219
    DOI: 10.1016/j.geb.2017.10.023
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    Cited by:

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    2. Zhang, Shuhua & Zhang, Zhipeng & Wu, Yu’e & Yan, Ming & Li, Yu, 2019. "Strategy preference promotes cooperation in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 181-188.
    3. Evans, Alecia & Sesmero, Juan Pablo, 2022. "Noisy Payoffs in an Infinitely Repeated Prisoner’s Dilemma – Experimental Evidence," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322434, Agricultural and Applied Economics Association.
    4. Zeng, Weijun & Ai, Hongfeng & Zhao, Man, 2019. "Asymmetrical expectations of future interaction and cooperation in the iterated prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 148-164.
    5. Peter S. Park & Martin A. Nowak & Christian Hilbe, 2022. "Cooperation in alternating interactions with memory constraints," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
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    7. Dingxuan Huang & Claudio O. Delang & Yongjiao Wu & Shuliang Li, 2021. "An Improved Lotka–Volterra Model Using Quantum Game Theory," Mathematics, MDPI, vol. 9(18), pages 1-17, September.

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    More about this item

    Keywords

    Cooperation; Prisoner's dilemma; Evolutionary game theory; Evolutionary dynamics; Uncertainty; Learning; Bounded rationality;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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