On the equivalence of mixed and behavior strategies in finitely additive decision problems
| Autor: | János Flesch, Anna Zseleva, Dries Vermeulen |
|---|---|
| Přispěvatelé: | QE Math. Economics & Game Theory, RS: GSBE Theme Conflict & Cooperation, QE Operations research, RS: GSBE Theme Data-Driven Decision-Making |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Discrete mathematics Kuhn's theorem finitely additive probability measure Singleton General Mathematics Existential quantification 05 social sciences equivalent strategy Time horizon KUHNS THEOREM Decision problem Decision maker GAMES Strategy Mixed strategy behavior strategy 0502 economics and business 050207 economics Statistics Probability and Uncertainty Equivalence (measure theory) 050205 econometrics Probability measure Mathematics |
| Zdroj: | Journal of Applied Probability, 56(3), 810-829. Cambridge University Press |
| ISSN: | 0021-9002 |
| DOI: | 10.1017/jpr.2019.47 |
| Popis: | We consider decision problems with arbitrary action spaces, deterministic transitions, and infinite time horizon. In the usual setup when probability measures are countably additive, a general version of Kuhn’s theorem implies under fairly general conditions that for every mixed strategy of the decision maker there exists an equivalent behavior strategy. We examine to what extent this remains valid when probability measures are only assumed to be finitely additive. Under the classical approach of Dubins and Savage (2014), we prove the following statements: (1) If the action space is finite, every mixed strategy has an equivalent behavior strategy. (2) Even if the action space is infinite, at least one optimal mixed strategy has an equivalent behavior strategy. The approach by Dubins and Savage turns out to be essentially maximal: these two statements are no longer valid if we take any extension of their approach that considers all singleton plays. |
| Databáze: | OpenAIRE |
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