scholarly journals Noncompact Equilibrium Points and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Zahra Al-Rumaih ◽  
Souhail Chebbi ◽  
Hong Kun Xu
Keyword(s):  
Nash Equilibrium ◽  
Existence Result ◽  
Equilibrium Points ◽  
Noncooperative Game ◽  
Equilibrium Existence ◽  
Noncompact Domain

We prove an equilibrium existence result for vector functions defined on noncompact domain and we give some applications in optimization and Nash equilibrium in noncooperative game.

EQUILIBRIUM BALKING STRATEGIES IN THE REPAIRABLE M/M/1 G-RETRIAL QUEUE WITH COMPLETE REMOVALS

2019 ◽  
pp. 1-20
Author(s):  
Shan Gao ◽  
Deran Zhang ◽  
Hua Dong ◽  
Xianchao Wang
Keyword(s):  
Nash Equilibrium ◽  
Queueing Theory ◽  
Fundamental Problem ◽  
Pure Strategy ◽  
Retrial Queue ◽  
Noncooperative Game ◽  
Net Benefit ◽  
Negative Customers ◽  
Stable Strategy ◽  
Best Response

We consider an M/M/1 retrial queue subject to negative customers (called as G-retrial queue). The arrival of a negative customer forces all positive customers to leave the system and causes the server to fail. At a failure instant, the server is sent to be repaired immediately. Based on a natural reward-cost structure, all arriving positive customers decide whether to join the orbit or balk when they find the server is busy. All positive customers are selfish and want to maximize their own net benefit. Therefore, this system can be modeled as a symmetric noncooperative game among positive customers and the fundamental problem is to identify the Nash equilibrium balking strategy, which is a stable strategy in the sense that if all positive customers agree to follow it no one can benefit by deviating from it, that is, it is a strategy that is the best response against itself. In this paper, by using queueing theory and game theory, the Nash equilibrium mixed strategy in unobservable case and the Nash equilibrium pure strategy in observable case are considered. We also present some numerical examples to demonstrate the effect of the information together with some parameters on the equilibrium behaviors.

A minimax inequality with applications to existence of equilibrium points

1993 ◽  
Vol 47 (3) ◽  
pp. 483-503 ◽  
Author(s):  
Kok-Keong Tan ◽  
Zian-Zhi Yuan
Keyword(s):  
Existence Theorems ◽  
Equilibrium Points ◽  
Vector Spaces ◽  
Minimax Inequality ◽  
Approximation Technique ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Person Game ◽  
Element Theorem

A new minimax inequality is first proved. As a consequence, five equivalent fixed point theorems are formulated. Next a theorem concerning the existence of maximal elements for an Lc-majorised correspondence is obtained. By the maximal element theorem, existence theorems of equilibrium points for a non-compact one-person game and for a non-compact qualitative game with Lc-majorised correspondences are given. Using the latter result and employing an “approximation” technique used by Tulcea, we deduce equilibrium existence theorems for a non-compact generalised game with LC correspondences in topological vector spaces and in locally convex topological vector spaces. Our results generalise the corresponding results due to Border, Borglin-Keiding, Chang, Ding-Kim-Tan, Ding-Tan, Shafer-Sonnenschein, Shih-Tan, Toussaint, Tulcea and Yannelis-Prabhakar.

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 Nash Equilibrium and the History of Economic Theory

1999 ◽  
Vol 37 (3) ◽  
pp. 1067-1082 ◽  
Author(s):  
Roger B Myerson
Keyword(s):  
Game Theory ◽  
Economic Theory ◽  
Nash Equilibrium ◽  
Social Science ◽  
Historical Context ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
History Of Social Science ◽  
History Of

John Nash's formulation of noncooperative game theory was one of the great breakthroughs in the history of social science. Nash's work in this area is reviewed in its historical context to better understand how the fundamental ideas of noncooperative game theory were developed and how they changed the course of economic theory.

Sign in / Sign up

Export Citation Format

Share Document