scholarly journals Game Theory: The Nash Equilibrium Point Identification In Bi-Matrix Games Of Economic And Social Indicators

2015 ◽  
Vol 7 (2) ◽  
pp. 21-42
Author(s):  
Fernanda Kreuzberg ◽  
Nelson Hein ◽  
Moacir Manoel Rodrigues Junior
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Social Indicators ◽  
Matrix Games ◽  
Nash Equilibrium Point ◽  
Economic And Social Indicators

scholarly journals New Approach of Game Theory for Seller’s Price Selecting Strategies in Bi-Level Programming

2016 ◽  
Vol 10 (4) ◽  
pp. 76
Author(s):  
Kamran Shahanaghi ◽  
Maryam Keyvani Rad
Keyword(s):  
Game Theory ◽  
Supply Chain ◽  
Nash Equilibrium ◽  
Equilibrium Point ◽  
The Other ◽  
Main Question ◽  
Nash Equilibrium Point ◽  
New Approach ◽  
General Algebraic Modeling System ◽  
Optimum Decision

<p>The relationships between the members of supply chain were modeled in many researches, such as cooperative and non-cooperative situation. In our paper, the main question is how much and for which price should each seller offer her product to maximize the profit. In the proposed methodology, Bi-level programming is used for modeling and then GAMS (general algebraic modeling system) language for solving the problem. In the presented model, the first level, called upper sub-problem and supposed as leader is trying to maximize each seller profits by obtaining the optimal offered quantity of individual seller. The objective of follower (buyer) is at second level. The lower sub-problem uses the results of the seller’s model and then maximizes its profit. These optimizations are obtained with regard to the some other constraints. Similar the other game theories problems, the Nash equilibrium point(s) is (are) the optimum decision of this seller-buyer supply chain. A numerical example is employed to illustrate the application of the proposed method.</p>

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

scholarly journals Application of the Game Theory with Perfect Information to an agricultural company

2013 ◽  
Vol 59 (No. 1) ◽  
pp. 1-7 ◽  
Author(s):  
S. Cabrera García ◽  
J.E. Imbert Tamayo ◽  
J. Carbonell-Olivares ◽  
Y. Pacheco Cabrera
Keyword(s):  
Game Theory ◽  
Linear Programming ◽  
Equilibrium Point ◽  
Perfect Information ◽  
Agricultural Economics ◽  
Nash Equilibrium Point ◽  
The Game Theory ◽  
The Hierarchical Structure ◽  
Linear Programming Problems ◽  
The One

This paper deals with the application of Game Theory with Perfect Information to an agricultural economics problem. The goal of this analysis is demonstrating the possibility of obtaining an equilibrium point, as proposed by Nash, in the case of an agricultural company that is considered together with its three sub-units in developing a game with perfect information. Production results in terms of several crops will be considered in this game, together with the necessary parameters to implement different linear programming problems. In the game with perfect information with the hierarchical structure established between the four considered players (a management center and three production units), a Nash equilibrium point is reached, since once the strategies of the rest of the players are known, if any of them would use a strategy different to the one proposed, their earnings would be less than the ones obtained by using the proposed strategies. When the four linear programming problems are solved, a particular case of equilibrium point is reached.

scholarly journals Dynamic Cournot Duopoly Game with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Local Stability ◽  
Stability Region ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Delayed System

The delay Cournot duopoly game is studied. Dynamical behaviors of the game are studied. Equilibrium points and their stability are studied. The results show that the delayed system has the same Nash equilibrium point and the delay can increase the local stability region.

COMPLEXITY OF A REAL ESTATE GAME MODEL WITH A NONLINEAR DEMAND FUNCTION

2011 ◽  
Vol 21 (11) ◽  
pp. 3171-3179 ◽  
Author(s):  
LINGLING MU ◽  
PING LIU ◽  
YANYAN LI ◽  
JINZHU ZHANG
Keyword(s):  
Nash Equilibrium ◽  
Real Estate ◽  
Equilibrium Point ◽  
Demand Function ◽  
Control Method ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Game Model ◽  
Nonlinear Feedback ◽  
Nash Equilibrium Point

In this paper, a real estate game model with nonlinear demand function is proposed. And an analysis of the game's local stability is carried out. It is shown that the stability of Nash equilibrium point is lost through period-doubling bifurcation as some parameters are varied. With numerical simulations method, the results of bifurcation diagrams, maximal Lyapunov exponents and strange attractors are presented. It is found that the chaotic behavior of the model has been stabilized on the Nash equilibrium point by using of nonlinear feedback control method.

Determining Optimal Strategy of a Micro-Grid through Hybrid Method of Nash Equilibrium –Genetic Algorithm

2019 ◽  
Vol 20 (3) ◽  
Author(s):  
Ehsan Jafari
Keyword(s):  
Genetic Algorithm ◽  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Hybrid Method ◽  
Optimal Strategy ◽  
Energy Resource ◽  
Energy Resources ◽  
Optimal Planning ◽  
Nash Equilibrium Point ◽  
Micro Grid

Abstract Increasing the fossil fuels consumption, pollution and rising prices of these fuels have led to the expansion of renewable resources and their replacement with conventional sources. In this paper, a robust algorithm for a micro-grid (MG) planning with the goal of maximizing profits is presented in day-ahead market. The energy resources in MG are wind farms (WFs), photovoltaic (PV), fuel cell (FC), combined heat and power(CHP) units, tidal steam turbine (TST) and energy storage devices (ESDs). This algorithm is divided into two main parts: (1) Optimal planning of each energy resource; (2) Using the Nash equilibrium –genetic algorithm (NE-GA) hybrid method to determine the optimal MG strategy. In energy resources optimal planning, using a stochastic formulation, the generation bids of each energy resource is determined in such a way that the profit of each one is maximized. Also, the constraints of renewable and load demands and selection the best method of demand response (DR) program are investigated. Then the Nash equilibrium point is determined using the primary population produced in the previous step using the NE-GA hybrid method to determine the optimal MG strategy. Thus, using the ability of the genetic algorithm method, the Nash equilibrium point of the generation units is obtained at an acceptable time, and This means that none of the units are willing to change their strategy and that the optimal strategy is extracted. Comparison of results with previous studies shows that the expected profit in the proposed method is more than other method.

HADAMARD AND TYKHONOV WELL-POSEDNESS IN TWO PLAYER GAMES

2003 ◽  
Vol 05 (04) ◽  
pp. 375-384 ◽  
Author(s):  
GRAZIANO PIERI ◽  
ANNA TORRE
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Nash Equilibria ◽  
Well Posedness ◽  
Nash Equilibrium Point ◽  
Suitable Definition ◽  
Payoff Functions ◽  
The Stability ◽  
Definition Of ◽  
Zero Sum

We give a suitable definition of Hadamard well-posedness for Nash equilibria of a game, that is, the stability of Nash equilibrium point with respect to perturbations of payoff functions. Our definition generalizes the analogous notion for minimum problems. For a game with continuous payoff functions, we restrict ourselves to Hadamard well-posedness with respect to uniform convergence and compare this notion with Tykhonov well-posedness of the same game. The main results are: Hadamard implies Tykhonov well-posedness and the converse is true if the payoff functions are bounded. For a zero-sum game the two notions are equivalent.

Sign in / Sign up

Export Citation Format

Share Document