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Evolutionary Stability of Behavioural Rules

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  • Khan, Abhimanyu

Abstract

I develop the notion of evolutionary stability of behavioural rules in a game-theoretic setting. Each individual chooses a strategy, possibly taking into account the game's history, and the manner in which he chooses his strategy is encapsulated by a behavioural rule. 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 another behavioural rule, the fitness of each incumbent behavioural rule exceeds that of the mutant behavioural rule. I show that any population comprised of more than one behavioural rule is not stable, and present necessary and sufficient conditions for stability of a population comprised of a single behavioural rule.

Suggested Citation

  • Khan, Abhimanyu, 2021. "Evolutionary Stability of Behavioural Rules," MPRA Paper 111309, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:111309
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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.
    2. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    3. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1543-1554, August.
    4. LiCalzi Marco, 1995. "Fictitious Play by Cases," Games and Economic Behavior, Elsevier, vol. 11(1), pages 64-89, October.
    5. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
    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. 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.
    2. Oliveira, Fernando S., 2023. "The emergence of social inequality: A Co-Evolutionary analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 215(C), pages 192-206.
    3. Daan Lindeman & Marius I. Ochea, 2024. "Imitation Dynamics in Oligopoly Games with Heterogeneous Players," Games, MDPI, vol. 15(2), pages 1-26, February.

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    More about this item

    Keywords

    behavioural rules; evolutionary stability;

    JEL classification:

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

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