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The Evolution of Conventions under Condition-Dependent Mistakes

Author

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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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    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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