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On definitive solutions of strategic gamesстатья
Информация о цитировании статьи получена из
Web of Science
Дата последнего поиска статьи во внешних источниках: 26 декабря 2015 г.
- Автор: Artemov Sergei
- Сборник: Johan van Benthem on Logic and Information Dynamics
- Серия: Outstanding Contributions to Logic
- Том: 5
- Глава в коллективной монографии
- Год издания: 2014
- Издательство: SPRINGER
- Местоположение издательства: VAN GODEWIJCKSTRAAT 30, DORDRECHT, NETHERLANDS, 3311GZ
- Первая страница: 487
- Последняя страница: 507
- DOI: 10.1007/978-3-319-06025-5_17
- Аннотация: In his dissertation of 1950, Nash based his concept of the solution to a game on the assumption that "a rational prediction should be unique, that the players should be able to deduce and make use of it". We study when such definitive solutions exist for strategic games with ordinal payoffs. We offer a new, syntactic approach: instead of reasoning about the specific model of a game, we deduce properties of interest directly from the description of the game itself. This captures Nash's deductive assumptions and helps to bridge a well-known gap between syntactic game descriptions and specific models which could require unwarranted additional epistemic assumptions, e.g., common knowledge of a model. We show that games without Nash equilibria do not have definitive solutions under any notion of rationality, but each Nash equilibrium can be a definitive solution for an appropriate refinement of Aumann rationality. With respect to Aumann rationality itself, games with multiple Nash equilibria cannot have definitive solutions. Some games with a unique Nash equilibrium have definitive solutions, others don't, and the criterion for a definitive solution is provided by the iterated deletion of strictly dominated strategies.
- Добавил в систему: Артемов Сергей Николаевич