This work is devoted to the investigation and solution of differential games with a vector-valued pay-off function. Slater-, Pareto- and Geoffrion-optimal strategies are defined for such a game, and their positive and negative properties are examined. A new class of solutions called vector-valued guarantees is proposed and their properties examined. According to the authors, this new approach is superior primarily because it has the properties of equivalence and interchangeability - antagonistic players should be able to achieve guaranteed results simultaneously. The approach is tested in a competition problem, as well as a pursuit game with noise. This book should be useful for students, postgraduates and specialists who are investigating the different fields of applied mathematics, control theory, economics and near-by directions of scientific knowledge.
Author(s): V.I. Zhukovskiy and M.E. Salukvadze (Eds.)
Series: Mathematics in Science and Engineering 193
Publisher: Academic Press
Year: 1994
Language: English
Pages: iii-xvii, 1-404
Content:
Edited by
Page iii
Copyright page
Page iv
Preface
Pages xi-xiii
Vladislav Zhukovskiy, Mindia Salukvadze
Notation
Pages xv-xvi
Abstract
Page xvii
Chapter 1 Quasimotions and Their Properties
Pages 1-48
Chapter 2 Slater Optimality
Pages 49-79
Chapter 3 Pareto Optimality
Pages 81-129
Chapter 4 Geoffrion Optimality
Pages 131-167
Chapter 5 Vector-Valued Saddle Points
Pages 169-236
Chapter 6 Vector-Valued Guarantees
Pages 237-280
Chapter 7 The Competition Problem
Pages 281-333
Chapter 8 A Pursuit Game with Noise
Pages 335-369
Appendix 1: Concepts from Topology
Pages 371-376
Appendix 2: Upper Semicontinuous Multivalent Mappings
Pages 377-378
Appendix 3: Auxiliary Propositions from the Theory of Multicriterial Problems
Pages 379-381
Appendix 4: Vector-Valued Maximins in Static Problems
Pages 383-387
References
Pages 389-395
Author Index
Pages 397-399
Subject Index
Pages 401-404
