Perfect-Information Games with Lower-Semicontinuous Payoffs

  • Authors:

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

  • Affiliations:

  • Department of Quantitative Economics, Maastricht University, PO Box 616, 6200 MD Maastricht, The Netherlands;Department of Knowledge Engineering, Maastricht University, PO Box 616, 6200 MD Maastricht, The Netherlands;School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel;Department of Knowledge Engineering, Maastricht University, PO Box 616, 6200 MD Maastricht, The Netherlands;School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel;Department of Knowledge Engineering, Maastricht University, PO Box 616, 6200 MD Maastricht, The Netherlands

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 2010

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Abstract

We prove that every multiplayer perfect-information game with bounded and lower-semicontinuous payoffs admits a subgame-perfect 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.