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

Author

Listed:
  • Bezalel Peleg

    (Department of Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, ISRAEL)

  • 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)

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.

Suggested Citation

  • Bezalel Peleg & Stef Tijs & Jos Potters, 1995. "Minimal of consitent solutions for strategic games,in paticular for potential games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 81-93.
    • Handle: RePEc:spr:joecth:v:7:y:1995:i:1:p:81-93
    Note: Received: February 26, 1994; revised version August 25, 1994
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