Tian, Guoqiang and Zhou, Jianxin (1991): QuasiVariational Inequalities without Concavity Assumptions. Published in: Journal of Mathematical Analysis and Applications , Vol. 172, (1993): pp. 289299.

PDF
MPRA_paper_41222.pdf Download (429kB)  Preview 
Abstract
This paper generalizes a foundational quasivariationalinequality by relaxing the (0diagonal) concavity condition. The approach adopted in this paper is based on continuous selectiontype arguments and hence it is quite different from the approach used in the literature. Thus it enables us to prose the existence of equilibrium of the constrained noncooperative games without assuming the (quasi) convexity of loss functions.
Item Type:  MPRA Paper 

Original Title:  QuasiVariational Inequalities without Concavity Assumptions 
Language:  English 
Keywords:  QuasiVariational; Inequalities; Concavity 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement 
Item ID:  41222 
Depositing User:  Guoqiang Tian 
Date Deposited:  19. Sep 2012 11:40 
Last Modified:  11. Feb 2013 12:54 
References:  G. Allen, Variational inequalities, complementarity problems, and duality theorems, J. Math. Anal. Appl. 58 (1977), 110. K. Arrow and G. Debreu, Existence of equilibrium for a competitive economy, Econometrica 22 (1954), 265290. J.P. Aubin, “Mathematical Methods of Game and Economic Theory,” NorthHolland, Amsterdam, 1979. J.P. Aubin and I. Ekeland, “Applied Nonlinear Analysis,” Wiley, New York, 1984. T. C. Bergstrom. R. P. Parks and T. Pader. Pereference which have open graphs, j. Math. Econom. 3 (1976), 265268 G. Debreu, A social equilibrium existence theorem, Proc. Natl. Acad. Sci. U.S.A. 38 (1952). K. Fan, A minimax inequality and applications, in “inequalities” (O. Shisha, Ed.), Vol.3, pp. 103113, Academic Press, New York, 1972. K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519537. U. Mosco, Implicit variational problems and quasivariational inequalities, in “Lecture Notes in Math.,” Vol. 543, pp. 83156, SpringerVerlag, New York/Berlin, 1976. J. Nash, Equilibrium points in Nperson games, Proc. Natl. Acad. Sci. U.S.A. 36 (1950), 4849. W. Shafer and H. Sonnenschein, Equilibrium in abstract economies without ordered preferences, J. Math. Econom. 2 (1975), 345348. M. H. Shin and K. K. Tan, Generalized quasivariational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl. 108 (1985), 333343. W. Takahshi, Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan 28 (1976), 477481. E. Tarafdar, A fix point theorem equivalent to the FanKnasterKuratowskiMazurkiewicz theorem, J. Math. Anal. Appl. 128 (1987), 475479. G. Tian, Minimax inequalities equivalent to the FanKnasterKuratowskiMazurkiewicz theorems, to appear. G. Tian, Equilibrium in abstract economies with a noncompact infinite dimensional strategy space, an infinite number of agents and without ordered preferences, Econom. Lett., in press. G. Tian, Fixed points theorems for mappings with noncompact and nonconvex domains, J. Math. Anal. Appl., in press. J.X. Zhou and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasivariational inequalities, J. Math. Anal. Appl. 132 (1988), 213225. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/41222 