Parameterized games of perfect information

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Abstract

Considered are perfect information games with a borel measurable payoff function that is parameterized by points of a polish space. The existence domain of such a parameterized game is the set of parameters for which the game admits a subgame perfect equilibrium. We show that the existence domain of a parameterized stopping game is a borel set. In general, however, the existence domain of a parameterized game need not be borel, or even an analytic or co-analytic set. We show that the family of existence domains coincides with the family of game projections of borel sets. Consequently, we obtain an upper bound on the set-theoretic complexity of the existence domains, and show that the bound is tight.
Original languageEnglish
Pages (from-to)683-699
Number of pages17
JournalAnnals of Operations Research
Volume287
Issue number2
Early online date28 Oct 2018
DOIs
Publication statusPublished - Apr 2020

Keywords

  • game projection
  • parameterized games
  • perfect information games
  • subgame perfect equilibrium
  • CLASSICAL HIERARCHIES
  • Game projection
  • Parameterized games
  • EQUILIBRIUM
  • Subgame perfect equilibrium
  • MODERN STANDPOINT
  • Perfect information games

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