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Journal of Optimization Theory and Applications

, Volume 38, Issue 4, pp 565–579 | Cite as

A solution for noncooperative games

  • P. P. Shenoy
Contributed Papers
  • 53 Downloads

Abstract

In this paper, we study solutions of strict noncooperative games that are played just once. The players are not allowed to communicate with each other. The main ingredient of our theory is the concept of rationalizing a set of strategies for each player of a game. We state an axiom based on this concept that every solution of a noncooperative game is required to satisfy. Strong Nash solvability is shown to be a sufficient condition for the rationalizing set to exist, but it is not necessary. Also, Nash solvability is neither necessary nor sufficient for the existence of the rationalizing set of a game. For a game with no solution (in our sense), a player is assumed to recourse to a standard of behavior. Some standards of behavior are examined and discussed.

Key Words

Noncooperative games Nash equilibrium rationalizable set game theory 

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References

  1. 1.
    Luce, R. D., andRaiffa, H.,Games and Decisions, John Wiley and Sons, New York, New York, 1957.Google Scholar
  2. 2.
    Nash, J. F.,Noncooperative Games, Annals of Mathematics, Vol. 54, pp. 286–295, 1951.Google Scholar
  3. 3.
    Neumann, J. V., andMorgenstern, O.,Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1953.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • P. P. Shenoy
    • 1
  1. 1.School of BusinessUniversity of KansasLawrence

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