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

Janos Flesch, P. Jean-Jacques Herings*, Jasmine Maes, Arkadi Predtetchinski

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 \(\epsilon \)-equilibrium for every \(\epsilon >0\), in eventually pure strategy profiles.
Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalEconomic Theory
Publication statusE-pub ahead of print - 29 May 2019


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

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