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Borel Games with Lower-Semi-Continuous Payoffs

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

    (METEOR)

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    Abstract

    We prove that every multi-player Borel game with bounded and lower-semi-continuous payoffs admits a subgame-perfect epsilon-equilibrium in pure strategies. This result complements Example 3 in Solan and Vieille (2003), which shows that a subgame-perfect epsilon-equilibrium in pure strategies need not exist when the payoffs are not lower-semi-continuous. 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.

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    Bibliographic Info

    Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 040.

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    Date of creation: 2010
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    Handle: RePEc:unm:umamet:2010040

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    Keywords: mathematical economics;

    References

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    1. Kuipers, Jeroen & Flesch, Janos & Schoenmakers, Gijs & Vrieze, Koos, 2008. "Pure Subgame-Perfect Equilibria in Free Transition Games," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    3. Eilon Solan & Nicolas Vielle, 2002. "Deterministic Multi-Player Dynkin Games," Discussion Papers 1355, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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