Existence and uniqueness of open-loop nash equilibria in linear-quadratic discrete time games

2003 ◽  
Vol 48 (2) ◽  
pp. 267-271 ◽  
Author(s):  
G. Jank ◽  
H. Abou-Kandil
Keyword(s):  
Discrete Time ◽  
Existence And Uniqueness ◽  
Nash Equilibria ◽  
Open Loop ◽  
Linear Quadratic

Slow and Steady Wins the Race: Approximating Nash Equilibria in Nonlinear Quadratic Tracking Games Steter Tropfen höhlt den Stein: Approximation von Nash Gleichgewichten in Nicht-linearen Dynamischen Spielen

2018 ◽  
Vol 238 (6) ◽  
pp. 541-569
Author(s):  
Ivan Savin ◽  
Dmitri Blueschke ◽  
Viktoria Blueschke-Nikolaeva
Keyword(s):  
Objective Function ◽  
Nash Equilibria ◽  
Control Variable ◽  
Dynamic Game ◽  
Inequality Constraint ◽  
Open Loop ◽  
Linear Quadratic ◽  
Traditional Methods ◽  
Dynamic Tracking ◽  
Quadratic Tracking

Abstract We propose a new method for solving nonlinear dynamic tracking games using a meta-heuristic approach. In contrast to ‘traditional’ methods based on linear-quadratic (LQ) techniques, this derivative-free method is very flexible with regard to the objective function specification. The proposed method is applied to a three-player dynamic game and tested versus a derivative-dependent method in approximating solutions of different game specifications. In particular, we consider a dynamic game between fiscal (played by national governments) and monetary policy (played by a central bank) in a monetary union. Apart from replicating results of the LQ-based techniques in a standard setting, we solve two ‘non-standard’ extensions of this game (dealing with an inequality constraint in a control variable and introducing asymmetry in penalties of the objective function), identifying both a cooperative Pareto and a non-cooperative open-loop Nash equilibria, where the traditional methods are not applicable. We, thus, demonstrate that the proposed method allows one to study more realistic problems and gain better insights for economic policy.

One-Player Dynamic Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Dynamic Programming ◽  
Discrete Time ◽  
Information Structure ◽  
Dynamic Games ◽  
Open Loop ◽  
Linear Quadratic ◽  
Time Dynamic ◽  
Discrete Time Dynamical System ◽  
Solution Methods ◽  
The Cost

This chapter focuses on one-player discrete time dynamic games, that is, the optimal control of a discrete time dynamical system. It first considers solution methods for one-player dynamic games, which are simple optimizations, before discussing discrete time cost-to-go. It shows that, regardless of the information structure (open loop, state feedback or other), it is not possible to obtain a cost lower than the cost-to-go. A computationally efficient recursive technique that can be used to compute the cost-to-go is dynamic programming. After providing an overview of discrete time dynamic programming, the chapter explores the complexity of computing the cost-to-go at all stages, the use of MATLAB to solve finite one-player games, and linear quadratic dynamic games. It concludes with a practice exercise and the corresponding solution, along with an additional exercise.

Titik Setimbang Nash pada Permainan Linear Kuadratik Non-kooperatif dengan Asumsi Keseluruhan Pemain dapat Menstabilkan Sistem

2017 ◽  
Vol 1 (2) ◽  
pp. 211-224
Author(s):  
Ezhari Asfa’ani
Keyword(s):  
Quadratic Differential ◽  
Information Structure ◽  
Nash Equilibria ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Open Loop ◽  
Linear Quadratic ◽  
Linear Quadratic Differential Games ◽  
Necessary And Sufficient ◽  
Infinite Planning Horizon

We discuss about Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.      Keywords: linear quadratic differential games, open-loop information structure

scholarly journals Existence and uniqueness of constrained globally optimal feedback controls in a linear-quadratic framework

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
Yashan Xu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Closed Loop ◽  
Synthesis Method ◽  
Open Loop ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Loop Control

A constrained closed-loop optimal control problem is considered in a linear-quadratic framework. To solve the problem, a special type open-loop optimal control problem and a standard open-loop optimal control problem are introduced and carefully studied, via which the existence and uniqueness of the globally optimal closed-loop control is established by a synthesis method.

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