Skip to main content
Log in

Onn-person noncooperative multicriteria games described in strategic form

  • Section II Game Theoretic Approaches To Multi-Person Decision Making
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper undertakes the problem of multicriteria decision support in conflict situations described as a noncooperative game. Construction of such a decision support requires the development of the noncooperative game theory to be generalized for the multicriteria case. New theoretical results in this case are presented. Features of the multicriteria noncooperative games are shown with use of a duopoly model in case of two goods and two criteria of each player. Concepts of the decision support are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K.J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica 22(1954)265–290.

    Google Scholar 

  2. K.J. Arrow and L. Hurwicz, On the stability of the competitive equilibrium, Econometrica 26(1958)522–552.

    Google Scholar 

  3. J.P. Aubin,Mathematical Methods of Game and Economic Theory (North-Holland, Amsterdam, 1979).

    Google Scholar 

  4. P. Bronisz and L. Kruś, Experiments in calculation of game equilibria using nonsmooth optimization, in:Theory, Software and Test Examples for Decision Support Systems, ed. A. Lewandowski and A.P. Wierzbicki (IIASA, Laxenburg, Austria, 1985) pp. 275–286.

    Google Scholar 

  5. K.C. Kiwiel, A linearization algorithm for constrained nonsmooth minimization, in:System Modelling and Optimization, ed. P. Thoft-Christensen, Lecture Notes in Control and Information Sciences 59 (Springer, Berlin, 1984) pp. 311–320.

    Google Scholar 

  6. L. Kruś and P. Bronisz, Some new results in interactive approach to multicriteria bargaining, in:User Oriented Methodology and Techniques of Decision Analysis and Support, ed. J. Wessels and A.P. Wierzbicki, Lecture Notes in Economics and Mathematical Systems 397 (Springer, 1993) pp. 21–34.

  7. L. Kruś, P. Bronisz and B. Lopuch, MCBARG-enhanced. A system supporting multicriteria bargaining, CP-90-006, International Institute for Applied System Analysis, Laxenburg, Austria (1990).

    Google Scholar 

  8. J. Nash, Equilibrium points inn-person games, Proc. Nat. Acad. Sci. USA 36(1950)48–49.

    Google Scholar 

  9. J. Nash, Non cooperative games, Ann. Math. 54(1951)286–295.

    Google Scholar 

  10. F. Szidarovszky, M.E. Gershon and L. Duckstein,Techniques for Multiobjective Decision Making in Systems Management (Elsevier, Amsterdam, 1986).

    Google Scholar 

  11. S.G. Tzafestas (ed.),Optimization and Control of Dynamic Operations Models (North-Holland, Amsterdam, 1982).

    Google Scholar 

  12. S. Wang, An existence theorem of a Pareto equilibrium, Appl. Math. Lett. 4(1991)61–63.

    Google Scholar 

  13. S. Wang, Existence of Pareto equilibrium, J. Optim. Theory Appl. 79(1993).

  14. A.P. Wierzbicki, A mathematical basis for satisficing decision making, Math. Mod. 3(1982)391–405.

    Google Scholar 

  15. A.P. Wierzbicki, Negotiation and mediation in conflicts I: The role of mathematical approaches and methods, in:Supplemental Ways to Increase International Stability, ed. H. Chestnat et al. (Pergamon Press, Oxford, 1983).

    Google Scholar 

  16. A.P. Wierzbicki, Negotiation and mediation II: Plural rationality and interactive decision processes, in:Plural Rationality and Interactive decision Processes, ed. M. Grauer, M. Thompson and A.P. Wierzbicki, Proc. Sopron 1983 (Springer, Heidelberg, 1985).

    Google Scholar 

  17. A.P. Wierzbicki, Multiple criteria solutions in noncooperative game theory. Part III: Theoretical foundations, Discussion Paper No. 288, Kyoto Institute of Economic Research, Kyoto University, Japan (1990).

    Google Scholar 

  18. A.P. Wierzbicki, Multiple criteria games, theory and applications, WP-92-079, IIASA, Laxenburg, Austria (1992).

    Google Scholar 

  19. V. Chankong and Y.Y. Haimes,Multiobjective Decision Making: Theory and Methodology (North-Holland, New York, 1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kruś, L., Bronisz, P. Onn-person noncooperative multicriteria games described in strategic form. Ann Oper Res 51, 83–97 (1994). https://doi.org/10.1007/BF02032669

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02032669

Keywords

Navigation