Games with (dis-)continuous payoff functions and the problem of measurability

Christian Ewerhart

No 467, ECON - Working Papers from Department of Economics - University of Zurich

Abstract: In noncooperative game theory, it is often taken for granted that expected payoffs are well-defined and independent of the integral representation. However, this need not be the case even if strategy spaces are compact and payoffs are bounded. In this paper, we establish general conditions under which the measurability requirements for working with expected payoffs are automatically met. We use our findings to enhance Glicksberg’s equilibrium existence theorem and to rigorously construct the mixed extension of discontinuous games such as contests and auctions.

Keywords: Compact games; expected payoffs; measurability; Baire functions; Glicksberg’s theorem; discontinuous games; u.s.c.-l.s.c. minimax theorem (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2025-03, Revised 2025-09
New Economics Papers: this item is included in nep-gth and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:zur:econwp:467

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