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Axiomatic models of bargaining
86
Book Reviews
Chapter 9 discusses recent developments in multicriteria linear prograrrming. Chapter 10 suggests possible applications of sensitivity analysis including a parametrization of transportation problems. An extensive list of over 600 references is included along wi~h an annotated bibliography. The book is not an easy one to read. In some parts the notation is complicated and the discussion is lengthy. On the other hand, the book is not intSnded to be used as a textbook. As a reference book, the careful reader will find a detailed and comprehensive treatment. The author has carefully chosen examples that illustrate all important points. For the most part, applications oriented readers will not have to read the abridged mathematical presentations in order to gain useful and accurate insight into the theory. Because of the important role that sensitivity analysis plays in the application of linear programming, this book should be a useful reference to a broad spectrum of readers. Joseph G. ECKER R ensselaer Poly technic lnstitute Troy, New York, U.S.A.
tions and permutation polytopes (H.P. Young); Symmetric blocking and anti-blocking relations for generalized circulations (L.E. Trotter, Jr. and D.B. Weinberger); Elementary vectors and two polyhedral relaxations (R.G. Bland); Support functions, blocking pairs, and anti-blocking pairs (E.L. Johnson); On lattice polyhedra III: Blockers and anti-blockers of lattice clutters (A.J. Hoffman); Adjoints of projective transformations and face-figures of convex polytopes (V. Klee); Some applications of equalized matrices (Z. Baranyai); Multicoloring of a graph (C. Berge). Besides these papers A.J. Hoffman appreciates Ray Fulkerson's contributions to polyhedral combinatorics and L.J. BiUera and W.F. Lucas give a short biography of Delbert Ray Fulkerson's life. The contributions are all of very high quality and together give an excellent survey of ongoing research in polyhedral combinatorics. A ch im BA CHEM University o f Bonn Bonn, Germany, Fed. Rep.
Alvin E. ROTH M.L. BALINSKI and A.J. HOFFMAN (Eds.) Polyhedral Combinatorics: Dedicated to the Memory of D.R. Fulkerson Volume 8 in: Mathematical Programming Studies, North-Holland, Amsterdam, 1978, vii + 234 pages, Dfl. 49.50, paperback In honour of D.R. Fulkerson who died 1976 M.L. Balinski and A.J. Hoffman edited a special issue of "Mathematical Programming Study" devoted to "Polyhedral Combinatorics". a subject to which D.R. Fulkerson was a principal contributor. The papers are concerned with the following topics: Notes on Bland's pivoting rule (D. Avis and V. Chv~ital); An algorithm for finding Hamiltonian circuits in certain graphs (R.E. Bixby and D.-L. Wang); A primal algorithm for optimum matching (W.H. Cunningham and A.B. Marsh, III); An analysis of approximations for maximizing submodular set functions-ll (M.L. Fisher, G.L. Nemhauser and L.A. Wolsey); A practical algorithm for the Monger-type generalization of the independent assignment problem (M. Iri); Colouring criteria for adjacency on 0-1polyhedra (D. Hausmann and B. Korte); On permuta-
Axiomatic Models of Bargaining Volume 170 in: Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1979, v + 121 pages, DM 18.This book appears to be a comprehensive attempt to treat various models of bargaining on a unified, axiomatic basis. A prominent place is given to Nash's model of two-person bargaining problems, in contrast to other solutions by yon Neumann-Morgenstern and Edgeworth. Nash's theory is stretched extensively (Part I), and along this line foundational matters are emphasized e.g. utility theory, individual rationality, symmetric and asymmetric games, models of negotiation la Zeuthen-Harsanyi, strategic risk posture generalizing various concepts of behavior under risk. Many of the research results of ~he author scattered in the technical journal literature have been compiled, elaborated and made accessible to a wider audience. In Part II other than Nash-related models of bargaining are discussed. These essentially involve bargaining situations under incomplete information. The results appear to be strengthened by interpersonal comparison of utility functions, proportional solu-
Book Reviews tions to games and strong rationality assumptions. A summary at the end of the book covers the crucial properties and theorems, and permits for the impatient reader a quick glance at the important technical points. This is a lucid exposition of an increasingly importa:at area of game theory being of immediate interest to equilibrium theory in mathematical economics. Also theoretically minded operations researchers may benefit from it.
H. W. GOTTINGER MEDIS/GSF Miinchen and University of BielefeM Mfinchen, GetTnany, Fed. Rep.
Peter NIJKAMP
Multidimensional Spatial Data and Decision Analysis
87
pies, many of them case studies, conclude each chapter. Despite the large number of technical terms (how about 'a fuzzy multigroup multicriteria analysis') the book reads well and makes out a strong case for the use of multiple objective programming methods in public policy making. In addition, it shows by example how this can be done. Perhap~ it would have added to the human interest side if we had been told whether or not the final decisions were in accordance with the recommended solutions! The votume is well produced and very few misprints were detected. The only one I found of any importance was the omission of the number 8 from the figure on page 1 ~9.
Keith ORD University o f Warwick Warwick, United Kingdom
Wiley, Chichester, 1979, xii + 322 pages, £ 14.75 J. MURDOCH This is an interesting book which covers a broader range than its title might suggest. The author is Professor of Regional Economics at the Free University of Amsterdam and has contributed considerably to the literature on multiple objective programming. The book, then, applies multi-objective methods to regional planning problems and the term 'spatial' is to be understood in this context. rhe first six chapters of the book (Part A) describe a variety of analytical methods, several of which may be new to the reader (such as multi-dimensional scalin~) while others are new in name only (stepwise regressioa becomes interdependence analysis). While these descriptions are sometimes rather terse, adequate references are provided as back-up. The remaining eight chapters (Part B) concentrate upon decision making in the presence of multiple objectives. Several different methods are reviewed, but always with one eye on whether they are operational. In particular, the author favours an interactive approach whereby the requirements for each objective can be steadily raised until the optimal solution is found. He has scant regard for 'uni-dimensional' methods such as cost-benefit analysis which disguise the true nature of the trades-off being made. In later chapters, the ideas are extended to cover stochastic and 'fuzzy' models, the technique of multidimensional scaling being used to construct a metric space from the ordinal inputs of the fuzzy approach. Exam-
Control Charts Macmillan, London, 1979, viii + 150 pages, £ 4.95 This book deals with the use of both Shewhart and Cumulative Sum quality control charts. It is intended as a practical manual for use by professional workers and students of quality control and statistics. A special feature of this book is the attention given to the use of the CuSum system and its role as a diagnostic management technique. John Murdoch, experienced in industry in the application of Statistics and Operatio~al Research to management problems, is now Head of the Statistics and Operational Research Unit at Cranfield Institute of Technology, Bedford. This information is given on the back cover of this paperback edition. The frame of this text-book is logical and straightforward. The introductory Chapters 1-4 deal with Process Variation, Principles of Control, Statistical Theory in Control Chart Design and Process Capability. In Chapters 5--8 the Shewhart and CuSum Control Charts for both variable and attribute measures are explained and comp~,~ed. The Decision Interval Met' a is used for the design of a CuSum Control Chart. Finally ill Chapter 9 the reader is introduced to Sampling Inspection - Single Attribute Schemes. The appendix contains 11 statistical tables and nomograms. Throughout the book numerous exam#es,
Book Reviews
Chapter 9 discusses recent developments in multicriteria linear prograrrming. Chapter 10 suggests possible applications of sensitivity analysis including a parametrization of transportation problems. An extensive list of over 600 references is included along wi~h an annotated bibliography. The book is not an easy one to read. In some parts the notation is complicated and the discussion is lengthy. On the other hand, the book is not intSnded to be used as a textbook. As a reference book, the careful reader will find a detailed and comprehensive treatment. The author has carefully chosen examples that illustrate all important points. For the most part, applications oriented readers will not have to read the abridged mathematical presentations in order to gain useful and accurate insight into the theory. Because of the important role that sensitivity analysis plays in the application of linear programming, this book should be a useful reference to a broad spectrum of readers. Joseph G. ECKER R ensselaer Poly technic lnstitute Troy, New York, U.S.A.
tions and permutation polytopes (H.P. Young); Symmetric blocking and anti-blocking relations for generalized circulations (L.E. Trotter, Jr. and D.B. Weinberger); Elementary vectors and two polyhedral relaxations (R.G. Bland); Support functions, blocking pairs, and anti-blocking pairs (E.L. Johnson); On lattice polyhedra III: Blockers and anti-blockers of lattice clutters (A.J. Hoffman); Adjoints of projective transformations and face-figures of convex polytopes (V. Klee); Some applications of equalized matrices (Z. Baranyai); Multicoloring of a graph (C. Berge). Besides these papers A.J. Hoffman appreciates Ray Fulkerson's contributions to polyhedral combinatorics and L.J. BiUera and W.F. Lucas give a short biography of Delbert Ray Fulkerson's life. The contributions are all of very high quality and together give an excellent survey of ongoing research in polyhedral combinatorics. A ch im BA CHEM University o f Bonn Bonn, Germany, Fed. Rep.
Alvin E. ROTH M.L. BALINSKI and A.J. HOFFMAN (Eds.) Polyhedral Combinatorics: Dedicated to the Memory of D.R. Fulkerson Volume 8 in: Mathematical Programming Studies, North-Holland, Amsterdam, 1978, vii + 234 pages, Dfl. 49.50, paperback In honour of D.R. Fulkerson who died 1976 M.L. Balinski and A.J. Hoffman edited a special issue of "Mathematical Programming Study" devoted to "Polyhedral Combinatorics". a subject to which D.R. Fulkerson was a principal contributor. The papers are concerned with the following topics: Notes on Bland's pivoting rule (D. Avis and V. Chv~ital); An algorithm for finding Hamiltonian circuits in certain graphs (R.E. Bixby and D.-L. Wang); A primal algorithm for optimum matching (W.H. Cunningham and A.B. Marsh, III); An analysis of approximations for maximizing submodular set functions-ll (M.L. Fisher, G.L. Nemhauser and L.A. Wolsey); A practical algorithm for the Monger-type generalization of the independent assignment problem (M. Iri); Colouring criteria for adjacency on 0-1polyhedra (D. Hausmann and B. Korte); On permuta-
Axiomatic Models of Bargaining Volume 170 in: Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1979, v + 121 pages, DM 18.This book appears to be a comprehensive attempt to treat various models of bargaining on a unified, axiomatic basis. A prominent place is given to Nash's model of two-person bargaining problems, in contrast to other solutions by yon Neumann-Morgenstern and Edgeworth. Nash's theory is stretched extensively (Part I), and along this line foundational matters are emphasized e.g. utility theory, individual rationality, symmetric and asymmetric games, models of negotiation la Zeuthen-Harsanyi, strategic risk posture generalizing various concepts of behavior under risk. Many of the research results of ~he author scattered in the technical journal literature have been compiled, elaborated and made accessible to a wider audience. In Part II other than Nash-related models of bargaining are discussed. These essentially involve bargaining situations under incomplete information. The results appear to be strengthened by interpersonal comparison of utility functions, proportional solu-
Book Reviews tions to games and strong rationality assumptions. A summary at the end of the book covers the crucial properties and theorems, and permits for the impatient reader a quick glance at the important technical points. This is a lucid exposition of an increasingly importa:at area of game theory being of immediate interest to equilibrium theory in mathematical economics. Also theoretically minded operations researchers may benefit from it.
H. W. GOTTINGER MEDIS/GSF Miinchen and University of BielefeM Mfinchen, GetTnany, Fed. Rep.
Peter NIJKAMP
Multidimensional Spatial Data and Decision Analysis
87
pies, many of them case studies, conclude each chapter. Despite the large number of technical terms (how about 'a fuzzy multigroup multicriteria analysis') the book reads well and makes out a strong case for the use of multiple objective programming methods in public policy making. In addition, it shows by example how this can be done. Perhap~ it would have added to the human interest side if we had been told whether or not the final decisions were in accordance with the recommended solutions! The votume is well produced and very few misprints were detected. The only one I found of any importance was the omission of the number 8 from the figure on page 1 ~9.
Keith ORD University o f Warwick Warwick, United Kingdom
Wiley, Chichester, 1979, xii + 322 pages, £ 14.75 J. MURDOCH This is an interesting book which covers a broader range than its title might suggest. The author is Professor of Regional Economics at the Free University of Amsterdam and has contributed considerably to the literature on multiple objective programming. The book, then, applies multi-objective methods to regional planning problems and the term 'spatial' is to be understood in this context. rhe first six chapters of the book (Part A) describe a variety of analytical methods, several of which may be new to the reader (such as multi-dimensional scalin~) while others are new in name only (stepwise regressioa becomes interdependence analysis). While these descriptions are sometimes rather terse, adequate references are provided as back-up. The remaining eight chapters (Part B) concentrate upon decision making in the presence of multiple objectives. Several different methods are reviewed, but always with one eye on whether they are operational. In particular, the author favours an interactive approach whereby the requirements for each objective can be steadily raised until the optimal solution is found. He has scant regard for 'uni-dimensional' methods such as cost-benefit analysis which disguise the true nature of the trades-off being made. In later chapters, the ideas are extended to cover stochastic and 'fuzzy' models, the technique of multidimensional scaling being used to construct a metric space from the ordinal inputs of the fuzzy approach. Exam-
Control Charts Macmillan, London, 1979, viii + 150 pages, £ 4.95 This book deals with the use of both Shewhart and Cumulative Sum quality control charts. It is intended as a practical manual for use by professional workers and students of quality control and statistics. A special feature of this book is the attention given to the use of the CuSum system and its role as a diagnostic management technique. John Murdoch, experienced in industry in the application of Statistics and Operatio~al Research to management problems, is now Head of the Statistics and Operational Research Unit at Cranfield Institute of Technology, Bedford. This information is given on the back cover of this paperback edition. The frame of this text-book is logical and straightforward. The introductory Chapters 1-4 deal with Process Variation, Principles of Control, Statistical Theory in Control Chart Design and Process Capability. In Chapters 5--8 the Shewhart and CuSum Control Charts for both variable and attribute measures are explained and comp~,~ed. The Decision Interval Met' a is used for the design of a CuSum Control Chart. Finally ill Chapter 9 the reader is introduced to Sampling Inspection - Single Attribute Schemes. The appendix contains 11 statistical tables and nomograms. Throughout the book numerous exam#es,