Summary
Multicriteria games or games with vector payoffs are used to model multi-person decision situations in which some decision makers take multiple objectives into account. Although the one-person decision theoretic literature on multiobjective programming is rather well developed (Cohon (1978), Chankong and Haimes (1983), French et al. (1983)), the game theoretic counterpart has attracted relatively little attention. Shapley (1959) was the first to consider Pareto equilibria for games with vector payoffs and this concept is elaborated in Ghose, Prasad (1988) and Borm, Tijs and van den Aarssen (1988). Wang (1991) provides a general existence theorem for Pareto equilibria. In this paper we introduce a refinement of Pareto equilibria based on the perfectness concept of Selten (1975). Existence of perfect Pareto equilibria is shown (Th.3) and alternative characterizations in the spirit of van Damme (1991) for perfect Nash equilibria are provided (Th.4). These results are driven by a characterization of Pareto equilibria in terms of carriers and efficient best reply sets (Th.1 & Th.2).
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References
Borm, P.E.M., Tijs, S.H. and van den Aarssen, J. (1988), Pareto equilibria in multiobjective games, Methods of Operations Research, 6, 1–8.
Chankong, V. and Haimes, Y. (1983), Multiobjective decision making, North-Holland, Amsterdam.
Cohon, J.L. (1978), Multiobjective programming and planning, Academic Press, New York.
Van Damme, E.E.C. (1987), Stability and perfection of Nash equilibria, Springer Verlag, Berlin.
French, S., Hartley, R.,Thomas, L.C. and White, D.J. (editors) (1983), Multi-objective decision making, Academic Press, London.
Ghose, D. and Prasad, U.R. (1989), Solution concepts in two-person multicriteria games, Journal of Optimization Theory and Applications, 59, 1–24.
Selten, R. (1975), Reexamination of the perfectness concept for equilibrium points in extensive games, International Journal of Game Theory, 4, 25–55.
Shapley, L.S. (1959), Equilibrium points in games with vector payoffs, Naval Research Logistics Quarterly, 6, 57–61.
Wang, S. (1991), An existence theorem of a Pareto equilibrium, Applied Mathematical Letters, 3, 61–63.
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© 1995 Springer-Verlag Berlin Heidelberg
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van Megen, F., Borm, P., Tijs, S. (1995). A perfectness concept for multicriteria games. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_48
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DOI: https://doi.org/10.1007/978-3-642-79459-9_48
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