On Properness and Protectiveness in Two-Person Multicriteria Games

Journal of Optimization Theory and Applications - Tập 140 - Trang 499-512 - 2008
M. Quant1, P. Borm1, G. Fiestras-Janeiro2, F. van Megen1
1Department of Econometrics & OR and CentER, Tilburg University, Tilburg, Netherlands
2Departemento de Estatística e Investigación Operativa, Universidade de Vigo, Vigo, Spain

Tóm tắt

This paper extends the concepts of proper equilibria, protective behavior and prudent behavior to multicriteria games. Three types of proper equilibria based on different types of domination are introduced. It is shown that protective behavior coincides with prudent behavior. Possible relations and existence are analyzed.

Tài liệu tham khảo

Blackwell, D.: An analog of the minimax theorem for vector payoffs. Pac. J. Math. 6, 1–8 (1956) Shapley, L.: Equilibrium points in games with vector payoffs. Nav. Res. Logist. Q. 1, 57–61 (1959) Nash, J.: Noncooperative games. Ann. Math. 54, 575–625 (1951) Borm, P., van den Aarssen, J., Tijs, S.: Pareto equilibria in multiobjective games. Methods Oper. Res. 60, 303–312 (1988) Zhao, J.: The equilibria of a multiple objective game. Int. J. Game Theory 20, 171–182 (1991) Geoffrion, A.: Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22, 618–630 (1968) Selten, R.: Reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theory 4, 25–55 (1975) Borm, P., van Megen, F., Tijs, S.: A perfectness concept for multicriteria games. Math. Methods Oper. Res. 49, 401–412 (1999) Myerson, R.: Refinements of the Nash equilibrium concept. Int. J. Game Theory 7, 73–80 (1978) Fiestras-Janeiro, G., Borm, P., van Megen, F.: Protective and prudent behavior in games. J. Econ. Theory 78, 167–175 (1998)