406 Book Reviews

ments of the reference point approach in "Some improvements to the reference point approach for dynamic MCLP".

Through a game-theoretic approach, V.S. Molostvov studies equilibria in "Multiple-criteria optimization under uncertainty: concepts of opti- mality and sufficient conditions".

In "SIMS, an interactive multi-criteria search system", O.A. Shestakov tries to solve decision making problems in which the objects of choice are characterized in terms of two sets of indica- tors: parameters and criteria.

A. TOrn emphasizes the combined use of search techniques and clustering techniques in order to gain efficiency and to display a global view of the problem analysed in "A sampling-search-cluster- ing approach for solving scalar (local, global) and vector optimizing problems".

The interactive systems DISlOR, DISIOR-RE- SOURCE and DISIOR-SPEKTR are described and il- lustrated in "Interactive systems resulting from a descriptive approach to the solution of complex ill-structured problems" by S.V. Khyanish and A.G. Vlasov.

"Multicriteria problems in pooling resources" by E.E. Dudnikov and V.S. Molostvov ends the collection in considering the allocation of various resources for joint activities by sex eral interested groups.

The major interest of the book lies in the con- frontation with the quite different, more cybernet- ic-oriented, approach by which scientists of East- ern Europe deal with multiple criteria decision making. In their contributions, iil-structuredness is emphasized and mathematical-cybernetic models are constructed to try to tackle it.

The strong interrelationship between operations research and cybernetics is the reason why some of the contributions could only be well appreciated after a decision making session " in practice". It is a pity that some concise explanations about algo- rithms used could not be explained completely, probably in order to reduce the length of the papers.

The book is clearly intended for specialists in the fields of multiple criteria decision making and fuzzy decision making. Rather than finding ready answers to concrete decision problems, they will appreciate it for suggesting a methodological framework for research following less usual direc- tions to the Western readership.

Whether these methods will indeed help " to realize mankind's everlasting dream of happiness and perfection", as Dimitrov's paper concludes, is an open question. Let us hope. . .

Marc D E S P O N T I N Centre for Statistics and

Operations Research Vrije Universiteit, Brussels

L.C. THOMAS

Games, Theory and Applications

Ellis Horwood, Chichester, 279 pages, £26.00

This is one of the Statistic and Operational Research books in the Ellis Horwood series in mathematics and its applications. It is the fourth one I have read and, like the others, it is very pleasing. Brian Conolly, who is the editor of this sub-series should be proud of his authors.

At first, I wondered why Dr. A.J. Jones' Game Theory needed a rival in the same series. But, although a lot of the material is basically the same, the aim is different. This new book is planned for a wider and less mathematical audience: There is no stress on linear programming techniques for solutions, nor on the more esoteric treatments of probability. The applications span a wide field rather than being oriented towards economics.

After the essential background of two-person zero-sum and non-zero sum games, it treats N-per- son games, market games and oligopoly, meta- games, multi-stage games, evolutionary games, and bidding and auctions. It ends with a brief and very clear summary of what gaming is about, relying on references to the literature rather than attempting to put any detailed structure on this still very incoherent area of research and application. 1 ap- preciated the author's interpretation of my dif- ference of opinion with Richard Duke.

It is a book which it very attractive to look at, and I give particularly high marks for the way in which figures, tables and matrices are presented. The style of writing makes is enjoyable to read and the order of presentation makes for a nice logical flow of ideas. The student has lots of examples to clarify the text even further, and there are fascinat- ing problems to solve, with solutions given at the end of the book. Because I do not teach this

Book Reviews 407

subject, I sought the views of a colleague who does: The response was that the book is "ideally suited as an undergraduate text book" and "can be enjoyed by science students who are not doing mathematics". I see no reason to doubt this judg- ment.

Lest anyone think that everything is perfect, I will complain about page 146. In the account of hypergames, Peter Bennett's surname is only once spelt correctly, and the references and name index spellings are also wrong. Soccer holliganism may puzzle those who do not do the football polls or who do not perceive spectator sports as games. More seriously, " the disadvantage that any mis- perception that you perceive cannot then be a misperception" might well be true if hypergames are seen as an absolute prescriptive tool. It will not be true if they are properly used as a tool for inquiry into what might happen " i f . . .?" , leading to human judgment on what might be a wise and safe approach in a conflict situation riddled with potential misperceptions: An individual may of course be aware of a possible misperception and still misperceive. These and other difficulties are examined in P.G. Bennett, "Hypergames: Devel- oping a model of conflict," Futures, December 1980, 489-507, a reference which is not given in this book. I did notice minor typographical slips elsewhere, such as the positioning of limits in definite integrals, but it would be churlish to com- plain further.

Anyone who studies, teaches or uses games should read this book. Even if you are not a beginner, it offers an excellent source for revision: the sections on further reading are an added bonus.

Ken BO WEN Royal Hollowav College

University of London United Kingdom

E. van DAMME

Refinements of the Nash Equilibrium Concept

Volume 219 in: Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1983. vi + 151 pages, DM30.00

This game theory book is an outgrowth of a Ph.D. dissertation, written by the author under the

supervision of Jaap Wessels and Reinhard Selten. Attention is given to noncooperative games in normal form and in extensive form, where binding agreements are not possible. For such games the Nash equilibrium concept is the natural solution concept. Unfortunately, for such games there may be many inequivalent equilibria. One way to escape this difficulty is to try to develop a reasonable selection procedure, which assigns to each game precisely one equilibrium point. One such a selec- tion procedure was developed recently by Harsanyi and Selten. Another way, not to escape but to reduce the equilibrium problem, is to refine the Nash equilibrium concept, i.e. to put extra condi- tions on equilibria in the hope that at least one and not too many equilibria remain. This is done in this monograph, where all kind of refinements are discussed.

Chapter 1 is introductory. Many nice examples of games in normal form and games in extensive form show the need for refinement.

In Chapter 2 for n-person normal form games various refinements where robustness conditions play a role are studied. We mention perfect, proper, essential and regular equilibria. Various mathe- matical relations between the different types of equilibria are described. Furthermore, it is shown that gene~'ically all Nash equilibria are regular.

Chapter 3 restricts to finite two-person games. For bimatrix games characterizations of perfect and regular equilibria are derived and for matrix games proper equilibria are characterized in terms of best strategies/a la Dresher.

Chapter 4 is devoted to games with control costs, i.e. costs which arise if players choose to control their actions. An ordinary normal form game is then a limiting case of games with control costs and it is examined which equilibria are still viable when infinitesimal control costs are in- corporated.

Chapter 5 deals with disturbed games, where one has not precise information about the payoff functions of the opponents. Properties of those equilibria of undisturbed games, which are limits of equilibria of disturbed games, are derived for all kinds of disturbances.

In Chapter 6 for games in extensive form sub- game perfect equilibria, sequential, perfect and proper equilibria are treated. Also the relation between games in extensive form and the corre- sponding games in normal form is discussed.