Non-existence of subgame-perfect ε-equilibrium in perfect information games with infinite horizon

János Flesch, Jeroen Kuipers, Ayala Mashiah-Yaakovi, Gijs Schoenmakers, Eran Shmaya, Eilon Solan*, Koos Vrieze

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

Every finite extensive-form game with perfect information has a subgame-perfect equilibrium. In this note we settle to the negative an open problem regarding the existence of a subgame-perfect ε-equilibrium in perfect information games with infinite horizon and Borel measurable payoffs, by providing a counter-example. We also consider a refinement called strong subgame-perfect ε-equilibrium, and show by means of another counter-example, with a simpler structure than the previous one, that a game may have no strong subgame-perfect ε-equilibrium for sufficiently smallε>0, even though it admits a subgame-perfect ε-equilibrium for every ε>0.

Original languageEnglish (US)
Pages (from-to)945-951
Number of pages7
JournalInternational Journal of Game Theory
Volume43
Issue number4
DOIs
StatePublished - Jan 1 2014

Keywords

  • Infinite horizon
  • Non-existence
  • Perfect-information games
  • Subgame-perfect equilibrium

ASJC Scopus subject areas

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

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