Equilibria with vector-valued utilities and preference information. The analysis of a mixed duopoly

Springer Science and Business Media LLC - Tập 83 - Trang 365-383 - 2017
Amparo M. Mármol1, Luisa Monroy1, M. Ángeles Caraballo2, Asunción Zapata3
1Dpto. de Economía Aplicada III and IMUS, Universidad de Sevilla, Sevilla, Spain
2Dpto. de Economía e Historia Económica, Universidad de Sevilla, Sevilla, Spain
3Dpto. de Economía Aplicada III, Universidad de Sevilla, Sevilla, Spain

Tóm tắt

This paper deals with the equilibria of games when the agents have multiple objectives and, therefore, their utilities cannot be represented by a single value, but by a vector containing the various dimensions of the utility. Our approach allows the incorporation of partial information about the preferences of the agents into the model, and permits the identification of the set of equilibria in accordance with this information. We also propose an additional conservative criterion which can be applied in this framework in order to predict the results of interaction. The potential application of the theoretical results is shown with an analysis of a mixed oligopoly in which the agents value additional objectives other than their own benefit. These objectives are related to social welfare and to the profit of the industry. The flexibility of our approach provides a general theoretical framework for the analysis of a wide range of strategic economic models.

Tài liệu tham khảo

Aumann, R. (1962). Utility theory without the completeness axiom. Econometrica, 30, 445–462. Bade, S. (2005). Nash equilibrium in games with incomplete preferences. Economic Theory, 26, 309–332. Bewley, T. (1986). Knightian utility theory: Part 1. Cowles Foundation Discussion Paper 807. Blackwell, D. (1956). An analog of the minimax theorem for vector payoffs. Pacific Journal of Mathematics, 6, 1–8. Borm, P. E. M., Tijs, S. H., & Van Den Aarssen, J. C. M. (1988). Pareto equilibria in multiobjective games. Methods of Operations Research, 60, 303–312. Corley, H. W. (1985). Games with vector payoffs. Journal of Optimization Theory and Applications, 47, 491–498. De Fraja, G., & Del Bono, F. (1989). Alternative strategies of a public enterprise in oligopoly. Oxford Economic Papers, 41, 302–331. De Fraja, G., & Del Bono, F. (1990). Game theoretic models of mixed oligopoly. Journal of Economic Surveys, 4, 1–7. Dubra, J., Maccheroni, F., & Ok, E. (2004). Expected utility theory without the completeness axiom. Journal of Economic Theory, 115, 118–133. Gilboa, I., & Schmeidler, D. (1989). Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18, 141–153. Keeney, R. L., & Raiffa, H. (1976). Decisions with multiple objectives: Preferences and value tradeoffs. New York: Wiley. Kozhan, R., & Salmon, M. (2009). Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation. Journal of Economic Dynamics & Control, 33, 1106–1122. Kreps, D. M., & Scheinkman, J. A. (1983). Quantity precommitment and Bertrand competition yield Cournot outcomes. The Bell Journal of Economics, 14, 326–337. Merrill, W., & Schneider, N. (1966). Government firms in oligopoly industries: A short run analysis. Quarterly Journal of Economics, 80, 400–12. Nash, J. (1951). Non-cooperative games. Annals of Mathematics, 54(2), 286–295. Ok, E. A. (2002). Utility representation of an incomplete preference relation. Journal of Economic Theory, 104, 429–449. Park, J. (2015). Potential games with incomplete preferences. Journal of Mathematical Economics, 61, 58–66. Patriche, M. (2014). Existence of equilibrium for multiobjective games in abstract convex spaces. Mathematical Reports, 16, 243–252. Sagi, J. S. (2006). Anchored preference relations. Journal of Economic Theory, 13(1), 283–295. Shafer, W., & Sonnenschein, H. (1975). Equilibrium in abstract economies without ordered preferences. Journal of Mathematical Economics, 2, 345–348. Shapley, L. S. (1959). Equilibrium points in games with vector payoffs. Naval Research Logistics Quarterly, 6(1), 57–61. Voorneveld, M., Vermeulen, D., & Borm, P. (1999). Axiomatizations of Pareto equilibria in multicriteria games. Games and Economic Behavior, 28, 146–154. Wakker, P. (2001). Testing and characterizing properties of nonadditive measures through violations of the sure-thing principle. Econometrica, 69(4), 1039–1059. Wald, A. (1950). Statistical decision functions. New York: Wiley. Wang, S. Y. (1993). Existence of Pareto equilibrium. Journal of Optimization Theory and Applications, 79, 373–384. Zeleny, M. (1975). Games with multiple payoff. International Journal of Game Theory, 4(4), 179–191. Zhao, J. (1991). The equilibria of multiple objective games. The International Journal of Game Theory, 20, 171–182.