A link between sequential semi-anonymous nonatomic games and their large finite counterparts

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Abstract

We show that obtainable equilibria of a multi-period nonatomic game can be used by players in its large finite counterparts to achieve near-equilibrium payoffs. Such equilibria in the form of random state-to-action rules are parsimonious in form and easy to execute, as they are both oblivious of past history and blind to other players’ present states. Our transient results can be extended to a stationary case, where the finite multi-period games are special discounted stochastic games. In both nonatomic and finite games, players’ states influence their payoffs along with actions they take; also, the random evolution of one particular player’s state is driven by all players’ states as well as actions. The finite games can model diverse situations such as dynamic price competition. But they are notoriously difficult to analyze. Our results thus suggest ways to tackle these problems approximately.

Original languageEnglish (US)
Pages (from-to)383-433
Number of pages51
JournalInternational Journal of Game Theory
Volume46
Issue number2
DOIs
StatePublished - May 1 2017

All Science Journal Classification (ASJC) codes

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

Keywords

  • Convergence in probability
  • Nonatomic game
  • ϵ-Equilibrium

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