### Abstract

From the Ex Ante point of view, an axiomatization of decision making in a game with pure strategies is given, while considering its epistemic aspects in propositional game (epistemic) logic. Our axiomatization consists of four base axioms for predicted final decisions. One of them is an epistemic requirement, which together with the others leads to an infinite regress of the knowledge of these axioms. The resulting outcome of this regress is expressed as the common knowledge of the base axioms. We give meta-theoretical evaluations of the derivation of this infinite regress, and consider its implications in solvable and unsolvable games. For a solvable game, it determines predicted decisions to be the common knowledge of a Nash equilibrium, and for an unsolvable game, it is the common knowledge of a subsolution in Nash's sense. The latter result needs the common knowledge of the additional information of which subsolution would be played. We give also meta-theoretical evaluations of these results.

Original language | English |
---|---|

Pages (from-to) | 105-137 |

Number of pages | 33 |

Journal | Mathematical Social Sciences |

Volume | 38 |

Issue number | 2 |

Publication status | Published - 1999 Sep |

Externally published | Yes |

### Fingerprint

### Keywords

- Common knowledge
- Final decisions
- Game Logic
- Infinite regress of knowledge
- Nash equilibrium
- Solvable and unsolvable games

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Economics and Econometrics

### Cite this

*Mathematical Social Sciences*,

*38*(2), 105-137.

**Epistemic considerations of decision making in games.** / Kaneko, Mamoru.

Research output: Contribution to journal › Article

*Mathematical Social Sciences*, vol. 38, no. 2, pp. 105-137.

}

TY - JOUR

T1 - Epistemic considerations of decision making in games

AU - Kaneko, Mamoru

PY - 1999/9

Y1 - 1999/9

N2 - From the Ex Ante point of view, an axiomatization of decision making in a game with pure strategies is given, while considering its epistemic aspects in propositional game (epistemic) logic. Our axiomatization consists of four base axioms for predicted final decisions. One of them is an epistemic requirement, which together with the others leads to an infinite regress of the knowledge of these axioms. The resulting outcome of this regress is expressed as the common knowledge of the base axioms. We give meta-theoretical evaluations of the derivation of this infinite regress, and consider its implications in solvable and unsolvable games. For a solvable game, it determines predicted decisions to be the common knowledge of a Nash equilibrium, and for an unsolvable game, it is the common knowledge of a subsolution in Nash's sense. The latter result needs the common knowledge of the additional information of which subsolution would be played. We give also meta-theoretical evaluations of these results.

AB - From the Ex Ante point of view, an axiomatization of decision making in a game with pure strategies is given, while considering its epistemic aspects in propositional game (epistemic) logic. Our axiomatization consists of four base axioms for predicted final decisions. One of them is an epistemic requirement, which together with the others leads to an infinite regress of the knowledge of these axioms. The resulting outcome of this regress is expressed as the common knowledge of the base axioms. We give meta-theoretical evaluations of the derivation of this infinite regress, and consider its implications in solvable and unsolvable games. For a solvable game, it determines predicted decisions to be the common knowledge of a Nash equilibrium, and for an unsolvable game, it is the common knowledge of a subsolution in Nash's sense. The latter result needs the common knowledge of the additional information of which subsolution would be played. We give also meta-theoretical evaluations of these results.

KW - Common knowledge

KW - Final decisions

KW - Game Logic

KW - Infinite regress of knowledge

KW - Nash equilibrium

KW - Solvable and unsolvable games

UR - http://www.scopus.com/inward/record.url?scp=0012946016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012946016&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0012946016

VL - 38

SP - 105

EP - 137

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

IS - 2

ER -