Axiomatic Models of Bargaining
The problem to be considered here is the one faced by bargainers who must reach a consensus--i.e., a unanimous decision. Specifically, we will be consid ering n-person games in which there is a set of feasible alternatives, any one of which can be the ou
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Alvin E. Roth
Axiomatic Models of Bargaining
Springer-Verlag Berlin Heidelberg New York 1979
Editorial Boar d H. Albach • A. V. Balakrishnan • M. Beckmann (Managing Editor) P. Dhrymes • J. Green • W. Hildenbrand • W. Krelle H. P. Künzi (Managing Editor) • K. Ritter • R. Sato • H. Schelbert P. Schönfeld
Managing Editors Prof. Dr. M. Beckmann Brown University Providence, RI 02912/USA
Prof. Dr. H. P. Künzi Universität Zürich 8090 Zürich/Schweiz
Author Alvin E. Roth University of Illinois at Urbana-Champaign College of Commerce and Business Administration 350 Commerce Bldg. (West) Urbana, IL 61801/USA
AMS Subject Classifications (1970): 90D10, 90D12, 90D40 ISBN 978-3-540-09540-8 ISBN 978-3-642-51570-5 (eBook) DOI 10.1007/978-3-642-51570-5
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Preface The problem to be considered here is the one faced by bargainers who must reach a consensus--i.e., a unanimous decision.
Specifically, we will be consid
ering n-person games in which there is a set of feasible alternatives, any one of which can be the outcome of bargaining if it is agreed to by all the bargainers. In the event that no unanimous agreement is reached, some pre-specified disagree ment outcome will be the result.
Thus, in games of this type, each player has a
veto over any alternative other than the disagreement outcome. There are several reasons for studying games of this type.
First, many
negotiating situations, particularly those involving only two bargainers (i.e., when n = 2), are conducted under essentially these rules. Also, bargaining games of this type often occur as components of more complex processes.
In addi
tion, the simplicity of bargaining games makes them an excellent vehicle for studying the effect of any assumptions which are made in their analysis.
The
effect of many of the assumptions which are made in the analysis of more complex cooperative games can more easily be discerned in studying bargaining games. The various models of bargaining considered here will be studied axiomatically.
That is, each model will be studied by specifying a set of properties which
serve to characterize it uniquely. Only conventional mathematical notation will be used throughout.
Thus R
n
will
denote n-dimensional Euclidean space, S = {X|B} will mean that S is the set of elements x such that condition Bholds, and a,b e S will denote that a and b are elements of S. For n-tuples x,y e R , x > y means that X >y for each i = 1, ..., n n n; Σ x denotes the
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