Approximation method and equilibria of abstract economies

Tan, Kok-Keong; Yuan, Xian-Zhi

doi:10.1090/S0002-9939-1994-1211591-2

Approximation method and equilibria of abstract economies
HTML articles powered by AMS MathViewer

by Kok-Keong Tan and Xian-Zhi Yuan PDF

Proc. Amer. Math. Soc. 122 (1994), 503-510 Request permission

Abstract:

By applying an equilibrium existence theorem for a qualitative game due to Ding and Tan and by employing an "approximation" method used by Tulcea, we obtain an equilibrium existence theorem for an abstract economy (generalized game) in which the constraint correspondences are not assumed to have open graphs nor open lower sections (which are generally assumed in the literature). Our result generalizes the corresponding results of Shafer and Sonnenschein (1975), Borglin and Keiding (1976), Yannelis and Prabhakar (1983), Tulcea (1986), and Chang (1990) in several ways.

References

Charalambos D. Aliprantis and Donald J. Brown, Equilibria in markets with a Riesz space of commodities, J. Math. Econom. 11 (1983), no. 2, 189–207. MR 701616, DOI 10.1016/0304-4068(83)90036-8
Anders Borglin and Hans Keiding, Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econom. 3 (1976), no. 3, 313–316. MR 444091, DOI 10.1016/0304-4068(76)90016-1
Shiow-Yu Chang, On the Nash equilibrium, Soochow J. Math. 16 (1990), no. 2, 241–248. MR 1083760
Xie Ping Ding and Kok-Keong Tan, On equilibria of noncompact generalized games, J. Math. Anal. Appl. 177 (1993), no. 1, 226–238. MR 1224816, DOI 10.1006/jmaa.1993.1254

On the role of complete, transitive preferences in equilibrium theory

Ernest Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361–382. MR 77107, DOI 10.2307/1969615
Wayne Shafer and Hugo Sonnenschein, Equilibrium in abstract economies without ordered preferences, J. Math. Econom. 2 (1975), no. 3, 345–348. MR 398464, DOI 10.1016/0304-4068(75)90002-6

On the equilibriums of generalized games

Nicholas C. Yannelis, Equilibria in noncooperative models of competition, J. Econom. Theory 41 (1987), no. 1, 96–111. MR 875986, DOI 10.1016/0022-0531(87)90007-X
Nicholas C. Yannelis and N. D. Prabhakar, Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econom. 12 (1983), no. 3, 233–245. MR 743037, DOI 10.1016/0304-4068(83)90041-1