Large games and the law of large numbers

Nabil I. Al-Najjar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

This paper introduces discrete large games where the set of players is a countable dense 'grid' with a finitely additive distribution. In these games any function from player names to mixed actions is a legitimate strategy profile. No extraneous continuity or measurability conditions are assumed. Randomness can be modeled explicitly and an exact law of large numbers holds. Equilibria enjoy a strong purification property: every realization of every mixed strategy equilibrium is a pure strategy equilibrium almost surely. Every continuum-player game has a discrete large game representation that preserves the original payoffs, strategy profiles and equilibria. It is argued that strategy profiles in continuum-player games have an ambiguous meaning because measurability requirements force the smoothing out of individual variations. These variations have clear strategic meaning in finite-player games and can be expressed in discrete large games, but not when the set of players is the continuum.

Original languageEnglish (US)
Pages (from-to)1-34
Number of pages34
JournalGames and Economic Behavior
Volume64
Issue number1
DOIs
StatePublished - Sep 1 2008

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

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