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The Evolution of Conventions under Condition-Dependent Mistakes

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  • Ennio Bilancini
  • Leonardo Boncinelli

    (Dipartimento di Scienze per l'Economia e l'Impresa)

Abstract

In this paper we study the long run convention emerging from stag-hunt interactions when errors converge to zero at a rate that is positively related to the payoff earned in the previous period. We refer to such errors as condition-dependent mistakes. We find that, if interactions are sufficiently stable over time, then the payoff-dominant convention emerges in the long run. Moreover, if interactions are neither too stable nor too volatile, then the risk-dominant convention is selected in the long run. Finally, if interactions are quite volatile, then the maximin convention emerges even if it is not risk-dominant. We introduce the notion of \emph{condition-adjusted-risk-dominance} to characterize the convention emerging in the long run under condition-dependent mistakes. We contrast these results with the results obtained under alternative error models: uniform mistakes, i.e., errors converge to zero at a rate that is constant over states, and payoff-dependent mistakes, i.e., errors converge to zero at a rate that depends on expected losses.

Suggested Citation

  • Ennio Bilancini & Leonardo Boncinelli, 2016. "The Evolution of Conventions under Condition-Dependent Mistakes," Working Papers - Economics wp2016_11.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  • Handle: RePEc:frz:wpaper:wp2016_11.rdf
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    Cited by:

    1. Bilancini, Ennio & Boncinelli, Leonardo & Newton, Jonathan, 2020. "Evolution and Rawlsian social choice in matching," Games and Economic Behavior, Elsevier, vol. 123(C), pages 68-80.
    2. Hwang, Sung-Ha & Rey-Bellet, Luc, 2021. "Positive feedback in coordination games: Stochastic evolutionary dynamics and the logit choice rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 355-373.
    3. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    4. Sawa, Ryoji, 2021. "A stochastic stability analysis with observation errors in normal form games," Games and Economic Behavior, Elsevier, vol. 129(C), pages 570-589.
    5. Bilancini, Ennio & Boncinelli, Leonardo & Nax, Heinrich H., 2021. "What noise matters? Experimental evidence for stochastic deviations in social norms," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 90(C).
    6. Roberto Rozzi, 2021. "Competing Conventions with Costly Information Acquisition," Games, MDPI, vol. 12(3), pages 1-29, June.
    7. 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.
    8. Sawa, Ryoji, 2021. "A prospect theory Nash bargaining solution and its stochastic stability," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 692-711.
    9. Sawa, Ryoji & Wu, Jiabin, 2018. "Reference-dependent preferences, super-dominance and stochastic stability," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 96-104.
    10. Sawa, Ryoji & Wu, Jiabin, 2018. "Prospect dynamics and loss dominance," Games and Economic Behavior, Elsevier, vol. 112(C), pages 98-124.
    11. Nicola Campigotto, 2021. "Pairwise imitation and evolution of the social contract," Journal of Evolutionary Economics, Springer, vol. 31(4), pages 1333-1354, September.

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    More about this item

    Keywords

    risk-dominant; payoff-dominant; maximin; mistakes; stag hunt; stochastic stability.;
    All these keywords.

    JEL classification:

    • 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

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