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

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  • Christian Ewerhart

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.

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  • Christian Ewerhart, 2025. "Games with (dis-)continuous payoff functions and the problem of measurability," ECON - Working Papers 467, Department of Economics - University of Zurich, revised Sep 2025.
    • Handle: RePEc:zur:econwp:467
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    References listed on IDEAS

    as
    1. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    2. Aliprantis, Charalambos D. & Glycopantis, Dionysius & Puzzello, Daniela, 2006. "The joint continuity of the expected payoff functions," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 121-130, April.
    3. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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