A simple proof of the continuity of expected payoffs

Christian Ewerhart

No 479, ECON - Working Papers from Department of Economics - University of Zurich

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.

Keywords: Compact games; expected payoffs; weak* topology; continuity; Hausdorff separability axiom (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2025-09
New Economics Papers: this item is included in nep-gth and nep-mic
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