Minimal of consitent solutions for strategic games,in paticular for potential games

Bezalel Peleg, Stef Tijs and Jos Potters
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Stef Tijs: Department of Econometrics, Tilburg University, 5000 LE Tilburg, THE NETHERLANDS
Jos Potters: Department of Mathematics, University of Nijmegen, 6525 ED Nijmegen, THE NETHERLANDS

Economic Theory, 1995, vol. 7, issue 1, 93 pages

Abstract: Solutions defined on classes of strategic games, satisfying One-Person Rationality (OPR), Non-emptiness (NEM) and Consistency (CONS) are considered. The main question to be answered is whether these conditions characterize the Nash Equilibrium solution NE for the given class of games. Depending on the structure of the class of games positive as well as negative answers are obtained. A graph-theoretical framework will be developed to express sufficient conditions for a positive or a negative answer. For the class of (finite) strategic games with at least one Nash equilibrium the answer is positive. For several classes of potential games the answer is negative.

Date: 1997-11-09
Note: Received: February 26, 1994; revised version August 25, 1994
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