Abstract
A pure-strategy equilibrium existence theorem is extended to include games with non-expected utility players. It is shown that to guarantee the existence of a Nash equilibrium in pure strategies, the linearity of preferences in the probabilities can be replaced by the weaker requirement of quasiconvexity in the probabilities.
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REFERENCES
Camerer, C.F. and Ho, T.H. (1994), Violations of the betweenness axiom and nonlinearity in probability, Journal of Risk and Uncertainty8: 167–196.
Cheng, L.K. and Zhu, M. (1995), Mixed-strategy Nash equilibrium based upon expected utility and quadratic utility, Games and Economic Behavior9: 139–150.
Chew, S.H. (1985), An axiomatization of the rank dependent quasilinear mean generalizing the Gini mean and the quasilinear mean, Manuscript, Johns Hopkins University.
Chew, S.H. (1989), Axiomatic utility theories with the betweenness property, Annals of Operations Research19: 273–298.
Chew, S.H., Karni, E. and Safra, Z. (1987), Risk aversion in the theory of expected utility with rank dependent probabilities, Journal of Economic Theory42: 370–381.
Crawford, V.P. (1990), Equilibrium without independence, Journal of Economic Theory50: 127–154.
Dasgupta, P. and Maskin, E. (1986), The existence of equilibrium in discontinuous economic games, I: Theory, Review of Economic Studies53: 1–26.
Debreu, G. (1952), A social equilibrium existence theorem, Proceedings of the National Academy of Sciences38: 866–893.
Fan, K. (1952), Fixed point and minimax theorems in locally convex topological linear spaces, Proceedings of the National Academy of Sciences38: 121–126.
Glicksberg, I.L. (1952), A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points, Proceedings of the National Academy of Sciences38: 170–174.
Harless, D.W. and Camerer, C.F. (1994), The predictive utility of generalized expected utility theories, Econometrica62: 1251–1289.
Karni, E. and Safra, Z. (1989), Dynamic consistency, revelations in auctions and the structure of preferences, Review of Economic Studies56: 421–433.
Machina, M.J. (1982), ‘Expected utility’ analysis without the independence axiom, Econometrica50: 277–323.
Machina, M.J. (1987), Choice under uncertainty: problems solved and unsolved, Journal of Economic Perspectives1: 121–154.
Neilson, W.S. (1994), Second price auctions without expected utility, Journal of Economic Theory62: 136–151.
Quiggin, J. (1993), Generalized Expected Utility Theory: The rank-dependent model, Dordrecht: Kluwer Academic Publishers.
Ritzberger, K. (1996), On games under expected utility with rank dependent probabilities, Theory and Decision40: 1–27.
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Chen, HC., Neilson, W.S. Pure-strategy Equilibria with Non-expected Utility Players. Theory and Decision 46, 201–212 (1999). https://doi.org/10.1023/A:1005099306184
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DOI: https://doi.org/10.1023/A:1005099306184