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Register a new userCommon Beliefs and Public Announcements in Strategic Games with Arbitrary Strategy Sets
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Added by
Krzysztof R. Apt
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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We provide an epistemic analysis of arbitrary strategic games based on possibility correspondences. We first establish a generic result that links true common beliefs (and, respectively, common knowledge) of players rationality defined by means of `monotonic properties, with the iterated elimination of strategies that do not satisfy these properties. It allows us to deduce the customary results concerned with true common beliefs of rationality and iterated elimination of strictly dominated strategies as simple corollaries. This approach relies on Tarskis Fixpoint Theorem. We also provide an axiomatic presentation of this generic result. This allows us to clarify the proof-theoretic principles assumed in players reasoning. Finally, we provide an alternative characterization of the iterated elimination of strategies based on the concept of a public announcement. It applies to `global properties. Both classes of properties include the notions of rationalizability and the iterated elimination of strictly dominated strategies.
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It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a player has an incentive to adopt, that would be evolutionary stable or that could learn itself. Rather, a player has an incentive to strategically teach such a learning opponent in order secure at least the Stackelberg leader payoff. The impossibility result remains intact when restricted to the classes of generic games, two-player games, potential games, games with strategic complements or 2x2 games, in which learning is known to be nice. More generally, it also applies to uncoupled learning heuristics leading to correlated equilibria, rationalizable outcomes, iterated admissible outcomes, or minimal curb sets. A possibility result restricted to strategically trivial games fails if some generic games outside this class are considered as well.
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