Individual upper semicontinuity and subgame perfect ϵ-equilibria in games with almost perfect information

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Abstract

We study games with almost perfect information and an infinite time horizon. In such games, at each stage, the players simultaneously choose actions from finite action sets, knowing the actions chosen at all previous stages. The payoff of each player is a function of all actions chosen during the game. We define and examine the new condition of individual upper semicontinuity on the payoff functions, which is weaker than upper semicontinuity. We prove that a game with individual upper semicontinuous payoff functions admits a subgame perfect ϵ-equilibrium for every ϵ > 0, in eventually pure strategy profiles.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
Number of pages27
DOIs
Publication statusPublished - 14 Jan 2019

Publication series

SeriesGSBE Research Memoranda
Number002

JEL classifications

  • c62 - Existence and Stability Conditions of Equilibrium
  • c65 - Miscellaneous Mathematical Tools
  • c72 - Noncooperative Games
  • c73 - "Stochastic and Dynamic Games; Evolutionary Games; Repeated Games"

Keywords

  • almost perfect information
  • subgame perfect ϵ-equilibrium
  • individual upper semicontinuity

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