Game-Theoretic Axioms for Local Rationality and Bounded Knowledge

Authors: 
Cristina Bicchieri & Gian Aldo Antonelli
Abstract: 

We present an axiomatic approach for a class of finite, extensive form games of perfect iformation that makes use of notions like "rationality at a node" and "knowledge at a node". We show that, in general, a theory that is sufficient to infer an equilibrium must be modular: for each subgame G' of a game G the theory of game G must contain just enough information about the subgame G' to infer an equilibrium for G'. This means, in general, that the level of knowledge relative to any subgame of G must not be the same as the level of knowledge relative to the original game G. We show that whenever the theory of the game is the same at each node, a deviation from equilibrium play forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not cause any revision of the theory of the game.

Date: 
September, 1993
Published in: 
Journal of Logic, Language and Information 4 (1995), 1-23
Number: 
31