Sufficient conditions for Nash equilibrium point in the linear quadratic game for Markov jump positive systems

2017 ◽  
Vol 11 (15) ◽  
pp. 2658-2667 ◽  
Author(s):  
Vasile Dragan ◽  
Ivan G. Ivanov
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Sufficient Conditions ◽  
Positive Systems ◽  
Linear Quadratic ◽  
Markov Jump ◽  
Nash Equilibrium Point

scholarly journals Partially Observed Nonzero-Sum Differential Game of BSDEs with Delay and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qiguang An ◽  
Qingfeng Zhu
Keyword(s):  
Nash Equilibrium ◽  
Maximum Principle ◽  
Equilibrium Point ◽  
Time Delays ◽  
Necessary Condition ◽  
State Variables ◽  
Linear Quadratic ◽  
Nash Equilibrium Point ◽  
The Maximum Principle ◽  
Partially Observed

A class of partially observed nonzero-sum differential games for backward stochastic differential equations with time delays is studied, in which both game system and cost functional involve the time delays of state variables and control variables under each participant with different observation equations. A necessary condition (maximum principle) for the Nash equilibrium point to this kind of partially observed game is established, and a sufficient condition (verification theorem) for the Nash equilibrium point is given. A partially observed linear quadratic game is taken as an example to illustrate the application of the maximum principle.

Nash Equilibrium Points for Generalized Matrix Game Model with Interval Payoffs

2021 ◽  
pp. 2150021
Author(s):  
Ajay Kumar Bhurjee ◽  
Vinay Yadav
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Linear Optimization ◽  
Sufficient Conditions ◽  
Matrix Game ◽  
Game Model ◽  
Data Sets ◽  
Nash Equilibrium Point ◽  
Generalized Matrix

Game theory-based models are widely used to solve multiple competitive problems such as oligopolistic competitions, marketing of new products, promotion of existing products competitions, and election presage. The payoffs of these competitive models have been conventionally considered as deterministic. However, these payoffs have ambiguity due to the uncertainty in the data sets. Interval analysis-based approaches are found to be efficient to tackle such uncertainty in data sets. In these approaches, the payoffs of the game model lie in some closed interval, which are estimated by previous information. The present paper considers a multiple player game model in which payoffs are uncertain and varies in a closed intervals. The necessary and sufficient conditions are explained to discuss the existence of Nash equilibrium point of such game models. Moreover, Nash equilibrium point of the model is obtained by solving a crisp bi-linear optimization problem. The developed methodology is further applied for obtaining the possible optimal strategy to win the parliament election presage problem.

scholarly journals Nonzero Sum Differential Game of Mean-Field BSDEs with Jumps under Partial Information

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xiaolan Chen ◽  
Qingfeng Zhu
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Differential Game ◽  
Partial Information ◽  
Mean Field ◽  
Random Measure ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
Nash Equilibrium Point ◽  
State Process

This paper is concerned with a kind of nonzero sum differential game of mean-field backward stochastic differential equations with jump (MF-BSDEJ), in which the coefficient contains not only the state process but also its marginal distribution. Moreover, the cost functional is also of mean-field type. It is required that the control is adapted to a subfiltration of the filtration generated by the underlying Brownian motion and Poisson random measure. We establish a necessary condition in the form of maximum principle with Pontryagin’s type for open-loop Nash equilibrium point of this type of partial information game and then give a verification theorem which is a sufficient condition for Nash equilibrium point. The theoretical results are applied to study a partial information linear-quadratic (LQ) game.

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 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.

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