Carnegie Mellon University
Browse
- No file added yet -

Game-theoretic axioms for local rationality and bounded knowledge

Download (920.97 kB)
journal contribution
posted on 1994-01-01, 00:00 authored by Cristina Bicchieri, Gian Aldo. Antonelli
Abstract: "We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like 'rationality at a node' and 'knowledge at a node.' We distinguish between the game theorist's and the players' own 'theory of the game.'The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves.We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferrred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it.Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On thecontrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory."

History

Publisher Statement

All Rights Reserved

Date

1994-01-01

Usage metrics

    Categories

    Keywords

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC