Infinite Horizon Noncooperative Differential Games with Non-Smooth Costs

In the present paper, we consider a class of two players infinite horizon differential games, with piecewise smooth costs exponentially discounted in time. Through the analysis of the value functions, we study in which cases it is possible to establish the existence Nash equilibrium solutions in feedback form. We also provide examples of piecewise linear costs whose corresponding games have either infinitely many Nash equilibria or no solutions at all.Comment: 17 pages, 5 figure

Asymptotic analysis of Nash equilibria in nonzero-sum linear-quadratic differential games: The two player case

Game Theory;Nash Equilibrium

Algorithms for Computing Nash Equilibria in Deterministic LQ Games

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.

Linear Quadratic Games:An Overview

In this paper we review some basic results on linear quadratic differential games.We consider both the cooperative and non-cooperative case.For the non-cooperative game we consider the open-loop and (linear) feedback information structure.Furthermore the effect of adding uncertainty is considered.The overview is based on [9].Readers interested in detailed proofs and additional results are referred to this book.

Moving Horizon Control in Dynamic Games

We consider a continuous time system influenced by different agents who adopt moving horizon control. The well known Nash equilibrium concept is used to define two solution concepts fitting in the moving horizon structure. One of them is analyzed in more detail in the class of linear quadratic games. The (dis)advantages of moving horizon control are illustrated by means of a government debt stabilization model.