On equilibrium refinements in supermodular games

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Abstract

We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategy equilibria. We illustrate that in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games satisfying sequential better-reply security, perfect equilibria may involve play of actions in the interior of the set of weakly dominated actions. We show that supermodular games satisfying sequential better-reply security possess pure strategy perfect equilibria outside the interior of the set of weakly dominated action profiles.

Original languageEnglish (US)
Pages (from-to)869-890
Number of pages22
JournalInternational Journal of Game Theory
Volume44
Issue number4
DOIs
StatePublished - Nov 1 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Keywords

  • Perfect equilibrium
  • Strategically stable set
  • Supermodular game
  • Weakly dominated strategy

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