Asymptotic interpretations for equilibria of nonatomic games

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Abstract

We show that a mixed equilibrium of a semi-anonymous nonatomic game can be used to generate pure-strategy profiles for finite games randomly generated from the type distribution of the nonatomic game. As the numbers of players involved in the finite games increase, the generated profiles will be asymptotically equilibrium. The converse of this result is also true, i.e., a mixed-strategy profile that is not an equilibrium for the nonatomic game will not be able to achieve the above asymptotic rationality for large finite games. The combined finding can be specialized to situations where the nonatomic game is anonymous and where the given equilibrium is pure. Besides their practical values, these results offer yet one more justification for the study of nonatomic games. They also suggest that efforts may be better spent on searching for mixed rather than pure equilibria of nonatomic games.

Original languageEnglish (US)
Pages (from-to)491-499
Number of pages9
JournalJournal of Mathematical Economics
Volume47
Issue number4-5
DOIs
StatePublished - Aug 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics
  • Applied Mathematics

Keywords

  • Empirical distribution
  • Law of large numbers
  • Nonatomic games

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