Summary
In this paper we study the existence of Paréto equilibria of a multicriteria metagame. A theorem on existence of a Paréto equilibrium and a theorem on existence of a Nash equilibrium with weights are presented, which improve and extend some known results in the theory of games with multiple payoffs. Also relations between a Paréto equilibrium and other solution concepts of an optimization problem with multiple criteria are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aubin, J.P. and J. Ekeland (1984). Applied Nonlinear Analysis, John Wiley & Sons, New York.
Bergstresser, K. and P.L. Yu (1977).Domination structures and multicriteria problem in N-person games, Theory and Decision,8, 5.
Borm, P.E.M., S.H. Tijs and J.M.C. van den Aarssen (1990).Paréto equilibrium in multiobjective games. Methods of Operations Research60, 302–312.
Corley, H.W. (1985).Games with vector payoffs, Journal of Optimization Theory and Applications47, 491–498.
Ferro, F. (1982).Minimax type theorems for vector-valued functions, Annali di Matematica Pura ed Applicata32, 113–130.
Ghose, D. and U.R. Prasad (1989).Solution concepts in two-person multicriteria games, Journal of Optimization Theory and Applications63, 167–189.
Kruś, L. and P. Bronisz.On n-person noncooperative, multicriteria games described in strategic form, to appear in Annals of Operations Research.
Luc, D.T. (1987).Connectedness of the efficient point sets in quasiconcave vector maximization, Journal of Optimization Theory and Applications122, 346–354.
Szidarovszky, F., M.E. Gershou and L. Duckstein (1986). Techniques for Multiobjective Decision Making in Systems Management, Elsevier, Amsterdam.
Tanaka, T. (1990).Cone-convexity of vector-valued functions, The Science Reports of the Hirosaka University37, 170–177.
Tanaka, T.Generalized quasiconvexities, cone saddle points, and a minimax theorem for vector-valued functions, to appear.
Tzafestas, S.G. (ed.) (1982) Optimization and Control of Dynamical Operations Models, North-Holland, Amsterdam.
Wang, S. (1991).An existence theorem of Paréto equilibrium, Applied Mathematics Letters4, 61–63.
Wang, S. and Z. Li (1992).Scalarization and Lagrange duality in multiobjective optimization, Optimization26, 315–324.
Wang, S. (1993).Existence of a Paréto equilibrium, to appear in Journal of Optimization Theory and Applications79, 373–384.
Yu, P.L. (1979).Second-order game problems: decision dynamics in gaming phenomena, Journal of Optimization Theory and Applications27, 147–166.
Zeleny, M. (1976).Games with multiple payoffs, International Journal of Game Theory4, 179–191.
Author information
Authors and Affiliations
Additional information
Partially supported by NSFC, NSFIMTF and MADIS. The authors are grateful to the referee's valuable comments and suggestions.
Rights and permissions
About this article
Cite this article
Wang, S., Li, Z. Paréto equilibria in multicriteria metagames. Top 3, 247–263 (1995). https://doi.org/10.1007/BF02568588
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02568588