Parameterized games of perfect information
János Flesch () and
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János Flesch: Maastricht University
Annals of Operations Research, 2020, vol. 287, issue 2, No 7, 683-699
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.
Keywords: Perfect information games; Subgame perfect equilibrium; Parameterized games; Game projection (search for similar items in EconPapers)
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