1. An undecidable statement regarding zero-sum games.
- Author
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Fey, Mark
- Subjects
- *
ZERO sum games , *ERGODIC theory , *SET theory , *EXPECTED utility , *MATHEMATICS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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