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<p>In <i>n</i>-person games with compact strategy spaces and continuous payoff functions, the expected payoff functions of the mixed extension are continuous with respect to the product of the weak* topologies. We provide an elementary proof of this fact. The analysis reveals that the Hausdorff separation axiom, commonly imposed on the topology of players’ strategy spaces, is not needed. We also show that the definition of expected payoffs as an iterated integral does not depend on the ordering of the players.</p>

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A simple proof of the continuity of expected payoffs

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Christian Ewerhart

摘要

In n-person games with compact strategy spaces and continuous payoff functions, the expected payoff functions of the mixed extension are continuous with respect to the product of the weak* topologies. We provide an elementary proof of this fact. The analysis reveals that the Hausdorff separation axiom, commonly imposed on the topology of players’ strategy spaces, is not needed. We also show that the definition of expected payoffs as an iterated integral does not depend on the ordering of the players.