Final decisions, the Nash equilibrium and solvability in games with common knowledge of logical abilities

Mamoru Kaneko*, Takashi Nagashima

*この研究の対応する著者

研究成果: Article査読

6 被引用数 (Scopus)

抄録

This paper attempts to explain the Nash equilibrium concept from the viewpoint of its one-shot play interpretation. We consider a final decision to be made by each player before the game is actually played. We formalize this game situation in terms of an infinitary first-order predicate logic. Then we give an axiom for final decisions-in the two-person case, the central requirement for this axiom is: for players i and j, if x is a possible final decision for player i, then (1) player i knows that x is his final decision; (2) there is a final decision y for player j; and (3) for any final decision y for j, x is a best response to y and player i knows that y is j's final decision. The entire axiom takes the form of the common knowledge of the above requirement by its very nature. We assume that the complete logical abilities of the players are common knowledge. Then we prove that for solvable games in Nash's sense, x is a final decision for player i iff it is common knowledge that x is a Nash strategy. A similar result will be obtained for unsolvable games.

本文言語English
ページ(範囲)229-255
ページ数27
ジャーナルMathematical Social Sciences
22
3
DOI
出版ステータスPublished - 1991
外部発表はい

ASJC Scopus subject areas

  • 統計学、確率および不確実性
  • 経済学、計量経済学

フィンガープリント

「Final decisions, the Nash equilibrium and solvability in games with common knowledge of logical abilities」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル