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A simple proof of the continuity of expected payoffs

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  • Christian Ewerhart

Abstract

In games with compact pure strategy spaces, the continuity of the payoff functions is preserved in the expected payoff functions of the mixed extension. This note provides an elementary proof of this fact, showing that the commonly assumed Hausdorff property is, in fact, not needed.

Suggested Citation

  • Christian Ewerhart, 2025. "A simple proof of the continuity of expected payoffs," ECON - Working Papers 479, Department of Economics - University of Zurich.
    • Handle: RePEc:zur:econwp:479
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    JEL classification:

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

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