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Evolutionary Stability of Behavioural Rules

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  • Khan, Abhimanyu

Abstract

I develop a notion of evolutionary stability of behavioural rules when individuals simultaneously interact in a family of strategic games. An individual’s strategy choice is determined by his behavioural rule which may take into account the manner in which the games have been played in the past. The payoffs obtained by individuals following a particular behavioural rule determine that rule’s fitness. A population is stable if, whenever some individuals from an incumbent behavioural rule mutate and follow a mutant behavioural rule, the fitness of each incumbent behavioural rule exceeds that of the mutant behavioural rule. The behavioural rules approach thus conceptualises stability when individuals simultaneously interact in a variety of strategic environments. I first show the lack of stability whenever individuals exhibit heterogeneity in their behavioural rules. Furthermore, when all individuals follow the same behavioural rule, I find that the behavioural rules approach to stability is a refinement of the evolutionary stability of strategies approach in that the necessary condition for stability of behavioural rules is stronger than the corresponding condition for evolutionary stability of strategies. Finally, I present a sufficient condition for stability that is reasonably close to the necessary condition alluded to above.

Suggested Citation

  • Khan, Abhimanyu, 2021. "Evolutionary Stability of Behavioural Rules," MPRA Paper 112920, University Library of Munich, Germany, revised 01 May 2022.
    • Handle: RePEc:pra:mprapa:112920
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    References listed on IDEAS

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    1. , & ,, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
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    5. LiCalzi Marco, 1995. "Fictitious Play by Cases," Games and Economic Behavior, Elsevier, vol. 11(1), pages 64-89, October.
    6. Kaniovski, Yuri M. & Kryazhimskii, Arkadii V. & Young, H. Peyton, 2000. "Adaptive Dynamics in Games Played by Heterogeneous Populations," Games and Economic Behavior, Elsevier, vol. 31(1), pages 50-96, April.
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    Cited by:

    1. Daan Lindeman & Marius I. Ochea, 2024. "Imitation Dynamics in Oligopoly Games with Heterogeneous Players," Games, MDPI, vol. 15(2), pages 1-26, February.
    2. Abhimanyu Khan, 2021. "Evolution of conventions in games between behavioural rules," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 209-224, October.

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    More about this item

    Keywords

    behavioural rules; evolutionary stability; stability; evolutionary stable strategies;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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