Estimating the Common Cost of a Good When the Local Costs are Known in the Countries of a Community
In an economic community among many countries, the estimate of the common cost of any good, when the local costs in the countries are known, is of substantial interest also for pure theory. In fact, the classical point of view of the compared costs solves
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AND
LECTURES
- No.
211
MULTICRITERIA DECISION
MAKING
EDITED BY
G. LEITMANN UNIVERSITY OF C.\LlfORNIA ,BERKELEY
A. MARZOLLO UNIVERSITY OF TRIESTE
SPRINGER-VERLAG WIEN GMBH
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
©
1975 by Springer-VerlagWien
Originally published by Springer-Verlag Wien·New York in 1975
ISBN 978-3-211-81340-9 DOI 10.1007/978-3-7091-2438-3
ISBN 978-3-7091-2438-3 (eBook)
LIST OF CONTRIBUTORS
A. Blaquiere
Laboratoire d'Automatique Theorique, Universite de Paris VI, Paris, France
G. Castellani
Department of Mathematics, Ca' Foscari University, Venice, Italy
G. Leitmann
Mechanical Engineering Department, University of California at Berkeley, California, USA
Y. Medanic
Mihailo Pupin Institute, Belgrade, Yugoslavia
A. Marzollo
Electrical Engineering Department, University of Trieste and International Centre for Mechanical Sciences, Udine, Italy
W. Stadler
Mechanical Engineering Department, University of California at Berkeley, California, USA
W. Ukovich
Electrical Engineering Department, University of Trieste, Italy
M. Volpato
Department of Mathematics, Ca' Foscari University, Venice, Italy
P.L. Yu
Graduate School of Business, University of Texas, Austin, Texas, USA.
CONTENTS List of Contributors .
1
Preface. . . . . .
5
Cooperative and Non-cooperative Differential Games, G. Leitmann. . . . . . . . . . . . .
7
Vector Valued Optimization in Multi-player Quantitative Games, A. Blaqui~re. . . . . . . . . . . . . . . . .
33
Minimax Pareto Optimal Solutions with Application to Linear Quadratic Problems, J. Medanic. . . . . . . . . . . . . . . . . . . . . . . 55 Preference Optimality and Applications of Pareto Optimality, W. Stadler. . . . . . . . . . . . . .
125
Domination Structures and Non-dominated Solutions, P.L. Yu. . . . . . . . . . . . . . .
227
On Some Broad Classes of Vector Optimal Decisions and their Characterization A. Marzollo, W. Ukovich.. . . . . . . . . . . . . . . . . 281 Estimating the Common Cost of a Good When the Local Costs are Known in the Countries of a Community, M. Volpato. . . . . . . . . . . . . . . . . . . . . . . 325 Explicit Solution for a Class of Allocation Problems, G. Castellani.
351
Erratum of W. Stadler..
3R7
PREFACE
A considerable amount of research has been devoted recently to Multicriteria Decision Making, stimulated by the vast number of real problems, for example in industrial, urban and agricultural economics, in the social sciences, and in the design of complex engineering systems, where many decision makers are present or many, possibly conflicting objectives should be taken into account in order to reach some form of optimality. A rough division into two classes may be made among the approaches to Multicriteria Decision Making problems. The first one deals mainly with the e
