ISOMORPHISM OF GAMES, AND STRATEGIC EQUIVALENCE,
Abstract
The paper is concerned with the notion of strategic equivalence in the theory of games. The intuitive notion of strategic equivalence is rather vague; but it nevertheless happens to be sufficiently sharp, that a precise mathematical condition A can be specified, which is intuitively recognized to be necessary for strategic equivalence, and a precise mathematical condition B, which is intuitively recognized to be sufficient. It turns out, however, that B is a consequence of A: so, in actuality, it can be said that A (or B) is a necessary and sufficient condition for strategic equivalence. Attention will be devoted mainly to a detailed proof that A implies B. The paper falls into three sections. In the first section the important notions which will be used are introduced, and some arguments of an intuitive sort are given. In the second section, some lemmas of an algebraic or function theoretic nature which are to be used subsequently are established. The last section contains the theorems which establish the desired relation between A and B. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 22, 1948
- Accession Number
- AD0603809
Entities
People
- J. C. C. Mckinsey
Organizations
- RAND Corporation