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The study of abstract economies with two constraint correspondences. (English) Zbl 1141.91034
The authors obtain an existence theorem on equilibria for generalized abstract economies with two constraint correspondences in which the strategic space is not compact and the set of players is not countable.
MSC:
91B54Special types of economies
References:
[1]Debreu, G.: A social equilibrium theorem. Proc. Natl. Acad. Sci. USA 38, 386–393 (1952) · Zbl 0047.38804 · doi:10.1073/pnas.38.10.886
[2]Debreu, G.: Theory of Value. Yale University, New Haven (1959)
[3]Gale, D., Mas-Collel, A.: An equilibrium existence for a general model without ordered preferences. J. Math. Econ. 2, 9–15 (1975) · Zbl 0324.90010 · doi:10.1016/0304-4068(75)90009-9
[4]Borglin, A., Keiding, H.: Existence of equilibrium actions of equilibrium: a note on the new existence theorems. J. Math. Econ. 3, 313–316 (1976) · Zbl 0349.90157 · doi:10.1016/0304-4068(76)90016-1
[5]Yannelis, N.C., Prabhakar, N.D.: Existence of maximal elements and equilibria in linear topological spaces. J. Math. Econ. 12, 233–245 (1983) · Zbl 0536.90019 · doi:10.1016/0304-4068(83)90041-1
[6]Tian, G.: Equilibrium in abstract economies with a non-compact infinite dimensional strategy space, an infinite number of agents and without ordered preferences. Econ. Lett. 33, 203–206 (1990) · doi:10.1016/0165-1765(90)90001-H
[7]Tan, K.K., Yuan, X.Z.: Lower semicontinuity of multivalued mappings and equilibrium points. In: Proceedings of the First World Congress of Nonlinear Analysis, Walter de Gruyter, pp. 1849–1960 (1996)
[8]Ding, X.P., Kim, W.K., Tan, K.K.: A selection theorem and its applications. Bull. Aust. Math. Soc. 46, 205–212 (1992) · Zbl 0762.47030 · doi:10.1017/S0004972700011849
[9]Tan, K.K., Yuan, X.Z.: Approximation method and equilibria of abstract economies. Proc. Am. Math. Soc. 122, 503–510 (1994) · doi:10.1090/S0002-9939-1994-1211591-2
[10]Kim, W.K., Tan, K.K.: New existence theorems of equilibria and applications. Nonlinear Anal. 47, 531–542 (2001) · Zbl 1042.47534 · doi:10.1016/S0362-546X(01)00198-5
[11]Wu, X.: A new fixed point theorem and its applications. Proc. Am. Math. Soc. 125, 1779–1783 (1997) · Zbl 0871.47038 · doi:10.1090/S0002-9939-97-03903-8
[12]Himmelberg, C.J.: Fixed points of compact multifunctions. J. Math. Anal. Appl. 38, 205–207 (1972) · Zbl 0225.54049 · doi:10.1016/0022-247X(72)90128-X
[13]Berge, C.: Topological spaces, including a treatment of multivalued functions, vector spaces and convexity. Translated by E.M. Patterson, Oliver and Boyd Ltd (1963)
[14]Tan, N.X.: Quasi-variational inequalities in topological linear locally convex Hausdorff spaces. Math. Nachr. 122, 231–245 (1985) · doi:10.1002/mana.19851220123
[15]Michael, E.: Continuous selections I. Ann. Math. 63, 361–382 (1956) · Zbl 0071.15902 · doi:10.2307/1969615
[16]Michael, E.: A theorem on semicontinuous set-valued functions. Duke Math. J. 26, 647–651 (1959) · Zbl 0151.30805 · doi:10.1215/S0012-7094-59-02662-6
[17]Rim, D.I., Kim, W.K.: A fixed point theorem and existence of equilibrium for abstract economies. Bull. Aust. Math. Soc. 45, 385–394 (1992) · Zbl 0745.90015 · doi:10.1017/S0004972700030288
[18]Mehta, G., Tan, K.K., Yuan, X.Z.: Fixed points, Maximal elements and equilibria of generalized games. Nonlinear Anal. Theory Meth. Appl. 28, 689–699 (1997) · Zbl 0869.90092 · doi:10.1016/0362-546X(95)00183-V
[19]Chang, S.S., Lee, B.S., Wu, X., Chao, Y.J., Lee, G.M.: On the generalized quasi-variational inequality problems. J. Math. Anal. Appl. 203, 686–711 (1996) · Zbl 0867.49008 · doi:10.1006/jmaa.1996.0406
[20]Engelking, R.: General Topology. Heldermann Verlag, Berlin (1989)
[21]Fan, K.: Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. USA 38, 121–126 (1952) · Zbl 0047.35103 · doi:10.1073/pnas.38.2.121
[22]Chang, S.Y.: On the Nash equilibrium. Soochow J. Math. 16, 241–248 (1990)