Limit knowledge of rationality

Abstract

Epistemic game theory scrutinizes the relationship between knowledge, belief and choice of rational players. Here, the relationship between common knowledge and the limit of higher-order mutual knowledge is studied from a topological point of view. More precisely, the new epistemic operator limit knowledge defined as the topological limit of higher-order mutual knowledge is introduced. We then show that limit knowledge of the specific event rationality can be used for epistemic-topological characterizations of solution concepts in games. As a first step towards this scheme, we construct a game where limit knowledge of rationality appears to be a cogent strict refinement of common knowledge of rationality in terms of solution concepts. More generally, it is shown that for any given game and epistemic model of it satisfying some specific condition, every possible epistemic hypothesis as well as as every solution concept can be characterized by limit knowledge of rationality for some appropriate topology.