Academic Press, London and San Diego, 1995
The first part of the book, part I, which comprises Chapters 2 to 4, covers the material that is generally taught in an advanced undergraduate or first-year graduate course on noncooperative game theory. The coverage includes static finite and infinite games of both the zero-sum and nonzero-sum type and in the latter case both Nash and Stackelberg solution concepts are discussed. Furthermore, this part includes an extensive treatment of the class of dynamic games in which the strategy spaces are finite---the so-called multi-act games. Through an extensive tree formulation, the impact of information patterns on the existence, uniqueness and the nature of different types of noncooperative equilibria of multi-act games is thoroughly investigated. Most of the important concepts of static and dynamic game theory are introduced in these three chapters, and they are supplemented by several illustrative examples. Exposition of the material is quite novel, emphasising concepts and techniques of multi-person decision making rather than mathematical details. However, mathematical proofs of most of the results are also provided, but without hindering the flow of main ideas. The major changes in this part over the first edition are the inclusion of additional material on: randomised strategies, finite games with repeated decisions and action-dependent information sets (Chapter 2); various refinements on the Nash equilibrium concept, such as trembling-hand, proper and perfect equilibria (Chapter 3); and in the context of static infinite games, stability of Nash equilibria and its relation with numerical schemes, consistent conjectural variations equilibrium, and some new theorems on existence of Nash equilibria (Chapter 4). Some specific types of zero-sum games on the square (Chapter 4) have been left out.
The second part of the book, part II, which includes Chapters 5 to 8, extends the theory of the first part to infinite dynamic games in both discrete and continuous time (the so-known differential games). Here the emphasis is again on the close interrelation between information patterns and noncooperative equilibria of such multi-person dynamic decision problems. We present a unified treatment of the existing, but scattered, results in the literature on infinite dynamic games as well as some new results on the topic. The treatment is confined to deterministic games and to stochastic games under perfect state information, mainly because inclusion of a complete investigation on stochastic dynamic games under imperfect state information would require presentation of some new techniques and thereby a volume much larger than the present one. Again, some of the major changes in this part over the first edition are the inclusion of new material on: time consistency (Chapters 5-7); viscosity solutions of the Hamilton-Jacobi-Bellman-Isaacs equation (Chapters 5 and 8); affine-quadratic dynamic games and results on infinite-horizon games in discrete and continuous time (Chapters 5 and 6); applications in robust (H-infinity) controller designs (Chapter 8); incentive theory and relationship with Stackelberg solutions (Chapter 7); and Stackelberg equilibrium in the continuous time (Chapter 7). The material on the dolichobrachistochrone which was in Chapter 8 of the first edition, has been left out. Furthermore, the three appendices (A-C) are expanded versions of the earlier ones, and present the necessary background material on vector spaces, matrix algebra, optimisation, probability and stochastic processes, and fixed point theorems.
Each chapter (with the exception of the first) is supplemented with a problem section. Each problem section contains standard exercises on the contents of the chapter, which a reader who has carefully followed the text should have no difficulty in solving, as well as exercises which can be solved by making use of the techniques developed in the text, but which require some elaborate thinking on the part of the reader. Following the problem section in each chapter (except the first) is a notes section, which is devoted to historical remarks and sources for further reading on the topics covered in that particular chapter.
A one-semester course on noncooperative game theory, taught using this book, would involve mainly Part I and also an appropriate blend of some of the topics covered in Part II, this latter choice depending to a great extent on the taste of the instructor and the background of the students. Such a course would be suitable for advanced undergraduate or first-year graduate students in engineering, economics, mathematics, operations research and business administration. In order to follow the main flow of Chapters 2 and 3 the student need not have a strong mathematical background---apart from some elementary analysis, but he should be able to think in mathematical terms. However, proofs of some of the theorems in these two chapters, as well as the contents of Chapter 4, require some basic knowledge of real analysis and probability, which is summarised in the three appendices that are included towards the end of the book.
Part II of the book, on the other hand, is intended more for the researcher in the field, to provide him with the state-of-art in infinite dynamic game theory. However, selected topics from this part could also be used as a part of a graduate course on dynamic optimisation, optimal control theory or mathematical economics.
This edition has been prepared by means of LaTeX. Toward that end the text of the original edition was scanned, the formulas and figures were added separately. Despite the flexibility of LaTeX and an intensive use of electronic mail, the preparation of this new edition has taken us much longer than anticipated, and we are grateful to the publisher for being flexible with respect to deadlines. The preparation would have taken even longer if our secretaries, Francie Bridges and Tatiana Tijanova respectively, with their expertise of LaTeX, had not been around. In the first stage Francie was responsible for the scanning and the retyping of the formulas, and Tatiana for the labelling and the figures, but in later stages they helped wherever necessary, and their assistance in this matter is gratefully acknowledged. The first author would also like to acknowledge his association with the Center for Advanced Study at the University of Illinois during the Fall 1993 semester, which provided him with released time (from teaching) which he spent partly in the writing of the new material in this second edition. The second author would like to thank INRIA Sophia-Antipolis in the person of its director, Pierre Bernhard, for allowing him to work on this revision while he spent a sabbatical there. We both would also like to take this opportunity to thank many of our colleagues and students for their inputs and suggestions for this second edition. Particular recognition goes to Niek Tholen, of Delft University of Technology, who read through most of the manuscript, caught many misprints, and made penetrating comments and suggestions.
We hope that this revised edition may find its way as its predecessor did.
Tamer Basar --------- Geert Jan Olsder
Urbana, March 1994 ----- Delft, March 1994
Chapter 1: Introduction and Motivation ..... (p. 1)
References ........ ..... (p. 489)
List of Corollaries, Definitions, Examples, Lemmas, Propositions Remarks and Theorems (p. 509)
Index ...... ..... (p. 515)