### 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.

Original language | English |
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Pages (from-to) | 325-354 |

Number of pages | 30 |

Journal | Studia Logica |

Volume | 57 |

Issue number | 2-3 |

Publication status | Published - 1996 |

Externally published | Yes |

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### Keywords

- Common knowledge
- Infinitary predicate kd4
- Nash equilibrium
- Undecidability on playability

### ASJC Scopus subject areas

- Logic

### Cite this

*Studia Logica*,

*57*(2-3), 325-354.