Solution concepts in continuous-kernel multicriteria games

  • D. Ghose
  • U. R. Prasad
Contributed Papers
  • 75 Downloads

Abstract

This paper considers nonzero-sum multicriteria games with continuous kernels. Solution concepts based on the notions of Pareto optimality, equilibrium, and security are extended to these games. Separate necessary and sufficient conditions and existence results are presented for equilibrium, Pareto-optimal response, and Pareto-optimal security strategies of the players.

Key Words

Game theory multicriteria games nonzero-sum games vector criteria games continuous-kernel games 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Basar, T., andOlsder, G. J.,Dynamic Noncooperative Game Theory, Academic Press, New York, New York, 1982.Google Scholar
  2. 2.
    Blackwell, D.,An Analog of the Minimax Theorem for Vector Payoffs, Pacific Journal of Mathematics, Vol. 6, No. 1, pp. 1–8, 1956.Google Scholar
  3. 3.
    Shapley, L. S.,Equilibrium Points in Games with Vector Payoffs, Naval Research Logistics Quarterly, Vol. 6, No. 1, pp. 57–61, 1959.Google Scholar
  4. 4.
    Corley, H. W.,Games with Vector Payoffs, Journal of Optimization Theory and Applications, Vol. 47, No. 4, pp. 491–498, 1985.Google Scholar
  5. 5.
    Nieuwenhuis, J. W.,Some Minimax Theorems in Vector-Valued Functions, Journal of Optimization Theory and Applications, Vol. 40, No. 3, pp. 463–475, 1983.Google Scholar
  6. 6.
    Ghose, D., andPrasad, U. R.,Solution Concepts in Two-Person Multicriteria Games. Journal of Optimization Theory and Applications, Vol. 63, No. 2, pp. 167–189, 1989.Google Scholar
  7. 7.
    Ghose, D.,A Necessary and Sufficient Condition for Pareto-Optimal Security Strategies in Multicriteria Matrix Games, Journal of Optimization Theory and Applications, Vol. 68, No. 3, pp. 463–481, 1991.Google Scholar
  8. 8.
    Lin, J. G.,Maximal Vectors and Multi-Objective Optimization, Journal of Optimization Theory and Applications, Vol. 18, No. 1, pp. 41–64, 1976.Google Scholar
  9. 9.
    Karlin, S.,Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 1, Addison-Wesley Publishing Company, Reading, Massachusetts, 1959.Google Scholar
  10. 10.
    Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, No. 4, pp. 509–529, 1979.Google Scholar
  11. 11.
    Jahn, J.,Scalarization in Vector Optimization, Mathematical Programming, Vol. 29, No. 2, pp. 203–218, 1984.Google Scholar
  12. 12.
    Arrow, K. J., Barankin, E. W., andBlackwell, D.,Admissible Points of Convex Sets, Contributions to the Theory of Games, II, Edited by H. W. Kuhn and A. W. Tucker, Princeton University Press, Princeton, New Jersey, 1953.Google Scholar
  13. 13.
    Hartley, R.,On Cone-Efficiency, Cone-Convexity and Cone-Compactness, SIAM Journal on Applied Mathematics, Vol. 34, No. 2, pp. 211–222, 1978.Google Scholar
  14. 14.
    Yu, P. L.,Multiple-Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York, New York, 1985.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • D. Ghose
    • 1
  • U. R. Prasad
    • 2
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

Personalised recommendations