An undecidable statement regarding zero-sum games

Mark Fey

Games and Economic Behavior, 2024, vol. 145, issue C, 19-26

Abstract: In this paper, we give an example of a statement concerning two-player zero-sum games which is undecidable, meaning that it can neither be proven or disproven by the standard axioms of mathematics. Earlier work has shown that there exist “paradoxical” two-player zero-sum games with unbounded payoffs, in which a standard calculation of the two players' expected utilities of a mixed strategy profile yield a positive sum. We show that whether or not a modified version of this paradoxical situation, with bounded payoffs and a weaker measurability requirement, exists is an unanswerable question. Our proof relies on a mixture of techniques from set theory and ergodic theory.

Keywords: Zero-sum game; Undecidable; Herodotus paradox; Set theory (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:145:y:2024:i:c:p:19-26

DOI: 10.1016/j.geb.2024.02.004

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