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The effect of noise and average relatedness between players in iterated games

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  • EL-Seidy, Essam

Abstract

In the real world, repetitive game theory has an influential and effective role, especially in political, economic, biological, social sciences and many other sciences. In this work we are exposed to study the effect of noise on the degree of relatedness between the players with respect to the behavior of strategies and its payoff. Our model in this work is the infinitely repeated prisoner’s dilemma (PD) game. Because our game is infinitely repeated, we consider any strategy of the game represented by a finite states of automaton (two states). By considering the possibility of a small error in implementation of an automaton, we obtained the payoff matrix for all strategies. Consequently we could identify the behavior of some of the strategies.

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  • EL-Seidy, Essam, 2015. "The effect of noise and average relatedness between players in iterated games," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 343-350.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:343-350
    DOI: 10.1016/j.amc.2015.07.053
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    1. Banks, Jeffrey S. & Sundaram, Rangarajan K., 1990. "Repeated games, finite automata, and complexity," Games and Economic Behavior, Elsevier, vol. 2(2), pages 97-117, June.
    2. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    3. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    4. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-279, May.
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    Cited by:

    1. Alam, Muntasir & Nagashima, Keisuke & Tanimoto, Jun, 2018. "Various error settings bring different noise-driven effects on network reciprocity in spatial prisoner's dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 338-346.
    2. Li, Jiaqi & Zhang, Jianlei & Chen, Zengqiang & Liu, Qun, 2023. "Aspiration drives adaptive switching between two different payoff matrices," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    3. Ye, Wenxing & Feng, Weiying & Lü, Chen & Fan, Suohai, 2017. "Memory-based prisoner’s dilemma game with conditional selection on networks," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 31-37.
    4. Li, Jiaqi & Dang, Jianwu & Zhang, Jianlei, 2020. "Length of information-based bidirectional choice in spatial prisoner’s dilemma," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    5. Li, Jiaqi & Zhang, Jianlei & Liu, Qun, 2024. "Spatial game with multiple interaction patterns in constrained interaction environment: A computational method based on opponent’s ability," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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