scholarly journals Maximal Elements and Equilibria of Generalized Games for Condensing Correspondences

1996 ◽  
Vol 203 (1) ◽  
pp. 13-30 ◽  
Author(s):  
Xian-Zhi Yuan
Keyword(s):  
Maximal Elements ◽  
Generalized Games

scholarly journals Equilibrium points of random generalized games

1998 ◽  
Vol 21 (4) ◽  
pp. 791-800 ◽  
Author(s):  
E. Tarafdar ◽  
Xian-Zhi Yuan
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Lower Semicontinuous ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Generalized Games ◽  
Random Games

In this paper, the concepts of random maximal elements, random equilibria and random generalized games are described. Secondly by measurable selection theorem, some existence theorems of random maximal elements forLc-majorized correspondences are obtained. Then we prove existence theorems of random equilibria for non-compact one-person random games. Finally, a random equilibrium existence theorem for non-compact random generalized games (resp., random abstract economics) in topological vector spaces and a random equilibrium existence theorem of non-compact random games in locally convex topological vector spaces in which the constraint mappings are lower semicontinuous with countable number of players (resp., agents) are given. Our results are stochastic versions of corresponding results in the recent literatures.

scholarly journals Maximal elements and equilibria of generalized games for𝒰-majorized and condensing correspondences

1999 ◽  
Vol 22 (1) ◽  
pp. 179-189 ◽  
Author(s):  
George Xian-Zhi Yuan ◽  
E. Tarafdar
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
New Type ◽  
Generalized Games ◽  
Locally Convex ◽  
Qualitative Games

In this paper, we first give an existence theorem of maximal elements for a new type of preference correspondences which are𝒰-majorized. Then some existence theorems for compact (resp., non-compact) qualitative games and generalized games in which the constraint or preference correspondences are𝒰-majorized (resp.,Ψ-condensing) are obtained in locally convex topological vector spaces.

scholarly journals Non-compact random generalized games and random quasi-variational inequalities

1994 ◽  
Vol 7 (4) ◽  
pp. 467-486 ◽  
Author(s):  
Xian-Zhi Yuan
Keyword(s):  
Variational Inequalities ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Countable Number ◽  
Maximal Elements ◽  
Random Fixed Point ◽  
Generalized Game ◽  
Generalized Games ◽  
Person Game

In this paper, existence theorems of random maximal elements, random equilibria for the random one-person game and random generalized game with a countable number of players are given as applications of random fixed point theorems. By employing existence theorems of random generalized games, we deduce the existence of solutions for non-compact random quasi-variational inequalities. These in turn are used to establish several existence theorems of noncompact generalized random quasi-variational inequalities which are either stochastic versions of known deterministic inequalities or refinements of corresponding results known in the literature.

scholarly journals Fixed Points, Maximal Elements and Equilibria of Generalized Games in Abstract Convex Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Yan-Mei Du
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Recent Literature ◽  
Existence Theorems ◽  
Maximal Elements ◽  
Abstract Convex Space ◽  
Generalized Games ◽  
Set Valued Mappings ◽  
Qualitative Games

We firstly prove some new fixed point theorems for set-valued mappings in noncompact abstract convex space. Next, two existence theorems of maximal elements for class of𝒜C,θmapping and𝒜C,θ-majorized mapping are obtained. As in applications, we establish new equilibria existence theorems for qualitative games and generalized games. Our theorems improve and generalize the most known results in recent literature.

Fixed points, maximal elements and equilibria of generalized games

1997 ◽  
Vol 28 (4) ◽  
pp. 689-699 ◽  
Author(s):  
Ghanshyam Mehta ◽  
Kok-Keong Tan ◽  
Xian-Zhi Yuan
Keyword(s):  
Fixed Points ◽  
Maximal Elements ◽  
Generalized Games
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