ISSN:
1572-8730
Keywords:
infinitary predicate KD4
;
common knowledge
;
Nash equilibrium
;
undecidability on playability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Philosophy
Notes:
Abstract This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00370838
Permalink
