Abstract
In this paper, we study minimax regret equilibria. First, existence theorem of minimax regret equilibria is proved. Further, the generic stability of minimax regret equilibria is studied. We show that the set of minimax regret equilibria for most of problems (in sense of Baire category) is a singleton set.
Similar content being viewed by others
References
Renou L., Schlag K.H.: Minimax regret and strategic uncertainty. J. Econ. Theory 145, 264–286 (2010)
Hayashi T.: Regret aversion and opportunity dependence. J. Econ. Theory. 139, 242–268 (2008)
Stoye J.: Axioms for Minimax Regret Choice Correspondences. New York University, Mimeo (2007)
Stoye J.: Statistical Decisions Under Ambiguity. New York University, Mimeo (2007)
Fort M.K. Jr: Essential and nonessential fixed points. Amer. J. Math. 72, 315–322 (1950)
Kinoshita S.: On essential components of the set of fixed points. Osaka J. Math. 4, 19–22 (1952)
Kohlberg E., Mertens J.F.: The strategy stability of equilibria. Econometrica 54, 1005–1037 (1986)
Yu J., Xiang S.W.: On essential component of the set of Nash equilibrium points. Nonlinear Anal. TMA 38, 259–264 (1999)
Jiang J.H.: Essential component of the set of fixed points of the multi-valued maps and its applications to the theory of games. Sci. Sin. 12, 951–964 (1963)
Kenderov, P.S.: Most of the optimization problems have unique solution. In: Brosowski, B., Deutsch, F. (eds.) Proceedings Oberwolhfach Conference on Parametric Optimization, Birkhauser, Basel, pp. 203–216 (1984)
Wu W.J., Jiang J.H.: Essential equilibrium points of n-person noncooperative game. Sci. Sin. 11, 1307–1322 (1962)
Xiang S.W., Xiang S.H.: Generic stability on weight factor in multiobjective optimization problems. Panam. Math. J. 7, 79–84 (1997)
Yang H., Yu J.: On essential components of the set of weakly Pareto-Nash equilibrium. Appl. Math. Lett. 15, 553–560 (2002)
Yu J.: Essential weak efficient solution in multiobjective optimization problems. J. Math. Anal. Appl. 166, 230–235 (1992)
Yu J.: Essential equilibria in game theory. Acta. Math. Appl. Sci. Sin. 16, 153–157 (1993)
Yu J.: Essential equilibria of n-person noncooperative games. J. Math. Econ. 31, 361–372 (1999)
Yu J., Yang H.: The essential component of the set of equilibrium points of set-value maps. J. Math. Anal. Appl. 300, 334–342 (2004)
Yu J., Yang H., Xiang S.W.: Unified approach to existence and stability of essential components. Nonlinear. Anal. TMA. 63, e2415–e2425 (2005)
Klein E., Thompson A.: Theory of Correspondences. Wiley, New York (1984)
Aubin J.P., Ekeland I.: Applied Nonlinear Analysis. Wiley, New York (1984)
Pardalos P.M., Rassias T.M., Khan A.A.: Nonlinear Analysis and Variational Problem. Springer, Berlin (2010)
Giannessi F., Maugeri A., Pardalos Panos M.: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models, Series: Nonconvex Optimization and Its Applications, Vol 58. Kluwer Academic Publishers, Dordrecht (2002)
Baye M., Morgan J.: Price dispersion in the lab and on the internet: Theory and evidence. RAND J. Econ. 35, 449–466 (2004)
Gilboa I., Schmeidler D.: Maxmin expected utility with non-unique priors. J. Math. Econ. 18, 133–173 (1989)
Milnor, J.: Games against Nature. In: Thrall, R., Coombs, C., Davis , R. (eds.) Decision Processes, pp. 49–60. Wiley, London (1954)
Puppe C., Schlag K.H.: Choice under complete uncertainty when outcome spaces are state dependent. Theory Dec. 66(1), 1–16 (2009)
Bank B., Guddat J., Klatte D., Kummer B., Tammer K.: Nonlinear Parametric Optimization. Basel, Birkhäuser Verlag (1983)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, Z., Pu, Y.J. Existence and stability of minimax regret equilibria. J Glob Optim 54, 17–26 (2012). https://doi.org/10.1007/s10898-011-9738-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-011-9738-6