Pure-strategy Nash equilibria in large games: characterization and existence

Haifeng Fu*, Ying Xu, Luyi Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we first characterize pure-strategy Nash equilibria in large games restricted with countable actions or countable payoffs. Then, we provide a counterexample to show that there is no such characterization when the agent space is an arbitrary atomless probability space (in particular, Lebesgue unit interval) and both actions and payoffs are uncountable. Nevertheless, if the agent space is a saturated probability space, the characterization result is still valid. Next, we show that the characterizing distributions for the equilibria exist in a quite general framework. This leads to the existence of pure-strategy Nash equilibria in three different settings of large games. Finally, we notice that our characterization result can also be used to characterize saturated probability spaces.

Original languageEnglish
Pages (from-to)685-697
Number of pages13
JournalInternational Journal of Game Theory
Issue number3
Publication statusPublished - 1 Aug 2016


  • Atomless probability space
  • Characterization
  • Large games
  • Pure-strategy Nash equilibrium
  • Saturated probability space


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