Stochastic and Differential Games

by Bardi, Martino; Raghavan, T. E. S.; Parthasarathy, T.

• ISBN13: 9780817640293
• ISBN10: 0817640290
• Format: Hardcover
• Copyright: 1999-04-01
• Publisher: Birkhauser

Summary

This volume presents state-of-the-art surveys, new results, and algorithms that will interest applied mathematicians, control engineers, and operations research specialists. It covers such diverse topics as pursuit-evasion games, viscosity solutions, gambling theory, discounted stochastic games, optimal routing, numerical methods, and others. The volume consists of two parts, with the first dealing with zero-sum differential games and numerical methods, and the second with stochastic and nonzero-sum games, and applications.

Table of Contents

Foreword and Dedication	vii
Tamer Basar
Preface	ix
Contributors	xv
Part I. Zero-Sum Differential Games and Numerical Methods	1	(248)
Constructive Theory of Positional Differential Games and Generalized Solutions to Hamilton-Jacobi Equations	3	(66)
Andrei I. Subbotin
Two-Player, Zero-Sum Differential Games and Viscosity Solutions	69	(36)
Panagiotis E. Souganidis
Numerical Methods for Pursuit-Evasion Games via Viscosity Solutions	105	(72)
Martino Bardi
Maurizio Falcone
Pierpaolo Soravia
Set-Valued Numerical Analysis for Optimal Control and Differential Games	177	(72)
Pierre Cardaliaguet
Marc Quincampoix
Patrick Saint-Pierre
Part II. Stochastic and Nonzero-Sum Games and Applications	249
An Introduction to Gambling Theory and Its Applications to Stochastic Games	251
A. Maitra
W. Sudderth
Discounted Stochastic Games: A Complex Analytic Perspective	271
S.A. Connell
W.W. Szczechla
Jerzy A. Filar
O.J. Vrieze
Nonzero-Sum Stochastic Games	297
Andrzej S. Nowak
Krzysztof Szajowski
The Power of Threats in Stochastic Games	343
Frank Thuijsman
O.J. Vrieze
A Markov Game Approach for Optimal Routing Into a Queuing Network	359
Eitan Altman
On Linear Complementarity and A Discounted Polystochastic Game	377
S.R. Mohan
S.K. Neogy
T. Parthasarathy