Perfect-information games with lower-semicontinuous payoffs

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

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We prove that every multiplayer perfect-information game with bounded and lower-semicontinuous payoffs admits a subgameperfect ε-equilibrium in pure strategies. This result complements Example 3 in Solan and Vieille [Solan, E., N. Vieille. 2003. Deterministic multi-player Dynkin games. J. Math. Econom. 39 911-929], which shows that a subgame-perfect ε-equilibrium in pure strategies need not exist when the payoffs are not lower-semicontinuous. In addition, if the range of payoffs is finite, we characterize in the form of a Folk Theorem the set of all plays and payoffs that are induced by subgame-perfect 0-equilibria in pure strategies.

Original languageEnglish
Pages (from-to)742-755
Number of pages14
JournalMathematics of Operations Research
Issue number4
StatePublished - Nov 2010


  • Lower-semicontinuous payoffs
  • Perfect information
  • Subgame-perfect equilibrium


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