Axiomatic Bargaining Game Theory

By: H.J. Peters

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Hardcover | 31 July 1992

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Many social or economic conflict situations can be modeled by specifying the alternatives on which the involved parties may agree, and a special alternative which summarizes what happens in the event that no agreement is reached. Such a model is called a bargaining game, and a prescription assigning an alternative to each bargaining game is called a bargaining solution. In the cooperative game-theoretical approach, bargaining solutions are mathematically characterized by desirable properties, usually called axioms. In the noncooperative approach, solutions are derived as equilibria of strategic models describing an underlying bargaining procedure.
Axiomatic Bargaining Game Theory provides the reader with an up-to-date survey of cooperative, axiomatic models of bargaining, starting with Nash's seminal paper, The Bargaining Problem. It presents an overview of the main results in this area during the past four decades. Axiomatic Bargaining Game Theory provides a chapter on noncooperative models of bargaining, in particular on those models leading to bargaining solutions that also result from the axiomatic approach.
The main existing axiomatizations of solutions for coalitional bargaining games are included, as well as an auxiliary chapter on the relevant demands from utility theory.

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Non-Fiction Mathematics Mathematical Foundation Set Theory Optimisation Game Theory Business & Management Business Negotiation Management & Management Techniques Management Decision Making Operational Research Economics

Economic Theory & Philosophy

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Published: 5th December 2010

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Preface
Preliminaries	p. 1
Introduction	p. 1
Basic definitions and concepts	p. 2
Examples	p. 3
Outline of this book	p. 9
Nash bargaining solutions	p. 13
Introduction	p. 13
The bargaining problem	p. 14
Nonsymmetric Nash solutions	p. 17
Alternative characterizations of nonsymmetric Nash solutions	p. 26
Disagreement point axioms	p. 37
Nash bargaining solutions: further results	p. 45
Independence of irrelevant alternatives and revealed preferences	p. 47
Introduction	p. 47
The role of IIA	p. 48
(A)cyclicity of revealed preference without continuity	p. 50
(A)cyclicity of revealed preference with continuity	p. 53
Representation of revealed preference	p. 56
Concluding remarks and related literature	p. 59
Violation of SARP for n ] 2	p. 59
Monotonicity properties	p. 63
Introduction	p. 63
Individual Monotonicity	p. 64
Replication invariance of bargaining solutions	p. 70
Global individual monotonicity	p. 73
Proportional solutions	p. 76
The equal-loss solution	p. 82
The lexicographic egalitarian solution	p. 84
The lexicographic equal-loss solution	p. 88
Further literature	p. 92
Additivity properties	p. 93
Introduction	p. 93
The super-additive solution of Perles and Maschler	p. 94
Simultaneity of issues and additivity in bargaining	p. 96
Partial super-additivity and proportional solutions	p. 98
Restricted additivity and nonsymmetric Nash solutions	p. 101
Risk properties	p. 107
Introduction	p. 107
Risk properties of bargaining solutions	p. 107
Risk properties, independence of irrelevant alternatives, individual monotonicity	p. 112
Risk behavior in "risky" situations	p. 115
Improvement sensitivity of bargaining solutions	p. 116
Risk sensitivity, twist sensitivity, and the slice property	p. 118
Bargaining with a variable number of players	p. 125
Introduction	p. 125
The variable population bargaining model	p. 126
Population monotonicity and the Raiffa-Kalai-Smorodinsky solution	p. 127
Stability and the Nash solution	p. 129
The egalitarian solution, weak stability and population monotonicity	p. 133
Alternative models and solution concepts	p. 135
Introduction	p. 135
Multivalued solutions	p. 135
Probabilistic solutions	p. 142
Nonconvex bargaining games	p. 152
Bargaining on economic environments	p. 163
Axiomatic bargaining over time	p. 166
Ordinal bargaining	p. 167
Continuity of bargaining solutions	p. 168
Noncooperative models for bargaining solutions	p. 169
Introduction	p. 169
The Harsanyi-Zeuthen procedure	p. 170
The Nash demand game	p. 171
Perfect equilibrium in an alternating Nash demand game	p. 174
A one-shot bargaining problem	p. 180
Consistency and subgame perfectness for the RKS solution	p. 180
Noncooperative comparison of solutions	p. 186
Arbitration games	p. 191
Solutions for coalitional bargaining games	p. 193
Introduction	p. 193
Coalitional bargaining games and solutions	p. 194
The Shapley solution	p. 198
The Harsanyi solution	p. 201
The proportional solutions	p. 203
Related literature	p. 205
Elements from utility theory	p. 207
Introduction	p. 207
Von Neumann-Morgenstern utility functions	p. 207
Risk aversion	p. 210
A criterion for comparing strength of preference	p. 214
Additive utility	p. 216
Multiplicative utility	p. 218
References	p. 221
Author index	p. 231
Subject index	p. 233
Notation and symbols	p. 237
Table of Contents provided by Blackwell. All Rights Reserved.

Axiomatic Bargaining Game Theory

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Hardcover

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