Back to Search
Start Over
An undecidable statement regarding zero-sum games.
- Source :
-
Games & Economic Behavior . May2024, Vol. 145, p19-26. 8p. - Publication Year :
- 2024
-
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]
- Subjects :
- *ZERO sum games
*ERGODIC theory
*SET theory
*EXPECTED utility
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 08998256
- Volume :
- 145
- Database :
- Academic Search Index
- Journal :
- Games & Economic Behavior
- Publication Type :
- Academic Journal
- Accession number :
- 177317073
- Full Text :
- https://doi.org/10.1016/j.geb.2024.02.004