scholarly journals Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly

2014 ◽  
Vol 165 (3) ◽  
pp. 1050-1070 ◽  
Author(s):  
B. Jadamba ◽  
F. Raciti
Keyword(s):  
Variational Inequality ◽  
Nash Equilibrium ◽  
Equilibrium Problems ◽  
Cournot Oligopoly ◽  
Stochastic Nash Equilibrium

VARIATIONAL INEQUALITIES IN COURNOT OLIGOPOLY

2007 ◽  
Vol 09 (04) ◽  
pp. 583-598
Author(s):  
C. A. PENSAVALLE ◽  
G. PIERI
Keyword(s):  
Variational Inequality ◽  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Production Function ◽  
Existence And Uniqueness ◽  
Market Price ◽  
Cournot Oligopoly ◽  
Related Variable ◽  
Nash Equilibrium Point ◽  
The Cost

Consider G = (X1,…,XM,g1,…,gM) an M-player game in strategic form, where the set Xi is an interval of real numbers and the payoff functions gi are differentiable with respect to the related variable xi ∈ Xi. If they are also concave, with respect to the related variable, then it is possible to associate to the game G a variational inequality which characterizes its Nash equilibrium points. In this paper it is considered the variational inequality for two sets of Cournot oligopoly games. In the first case, for any i = 1,…,M, we have Xi = [0,+∞); the market price function is in C1 and convex; the cost production function of the player i is linear and the function xi → gi(…,xi,…) is strictly concave. We prove the existence and uniqueness of the Nash equilibrium point and illustrate, with an example, an algorithm which calculates its components. In the second case, for any i = 1,…,M, we have Xi = [0,+∞); the market price function is in C2 and concave and the cost production function of the i-player is in C2 and convex. In these circumstances, as a consequence of well known facts, the existence and uniqueness of the Nash equilibrium point are guaranteed and also the Tykhonov and Hadamard well-posedness of the game. We prove that the game G is well posed with respect to its variational inequality.

scholarly journals An iterative algorithm for the system of split mixed equilibrium problem

2020 ◽  
Vol 53 (1) ◽  
pp. 309-324
Author(s):  
Ibrahim Karahan ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Equilibrium System ◽  
Convergence Conditions ◽  
Mixed Equilibrium Problems ◽  
Split Variational Inequality ◽  
Mixed Equilibrium ◽  
Split Mixed Equilibrium Problem

AbstractIn this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

An optimization method for Nash equilibrium problems

2017 ◽  
Vol 20 (6-7) ◽  
pp. 1465-1469
Author(s):  
Jian Hou ◽  
Qing Chang ◽  
Zong-Chuan Wen
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Problems ◽  
Optimization Method

scholarly journals A note on supervised classification and Nash-equilibrium problems

2017 ◽  
Vol 51 (2) ◽  
pp. 329-341
Author(s):  
Nicolas Couellan
Keyword(s):  
Nash Equilibrium ◽  
Support Vector Machines ◽  
Supervised Classification ◽  
Dual Space ◽  
Equilibrium Problems ◽  
Support Vector ◽  
Generalized Nash Equilibrium ◽  
Class Separation ◽  
Vector Machines ◽  
Generalized Nash Equilibrium Problems

In this note, we investigate connections between supervised classification and (Generalized) Nash equilibrium problems (NEP & GNEP). For the specific case of support vector machines (SVM), we exploit the geometric properties of class separation in the dual space to formulate a non-cooperative game. NEP and Generalized NEP formulations are proposed for both binary and multi-class SVM problems.

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