Existence and uniqueness of maximal reductions under iterated strict dominance

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well-defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better-reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator.

Original languageEnglish (US)
Pages (from-to)2007-2023
Number of pages17
JournalEconometrica
Volume70
Issue number5
DOIs
StatePublished - Jan 1 2002
Externally publishedYes

Keywords

  • Existence
  • Game theory
  • Iterated elimination
  • Maximal reduction
  • Order independence
  • Strict dominance

ASJC Scopus subject areas

  • Economics and Econometrics

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