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Axiomatic Bargaining Game Theory : THEORY AND DECISION LIBRARY SERIES C, GAME THEORY, MATHEMATICAL PROGRAMMING, AND OPERATIONS RESEARCH - Hans J.M. Peters

Axiomatic Bargaining Game Theory

THEORY AND DECISION LIBRARY SERIES C, GAME THEORY, MATHEMATICAL PROGRAMMING, AND OPERATIONS RESEARCH

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Published: 31st 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.

Preface
Preliminariesp. 1
Introductionp. 1
Basic definitions and conceptsp. 2
Examplesp. 3
Outline of this bookp. 9
Nash bargaining solutionsp. 13
Introductionp. 13
The bargaining problemp. 14
Nonsymmetric Nash solutionsp. 17
Alternative characterizations of nonsymmetric Nash solutionsp. 26
Disagreement point axiomsp. 37
Nash bargaining solutions: further resultsp. 45
Independence of irrelevant alternatives and revealed preferencesp. 47
Introductionp. 47
The role of IIAp. 48
(A)cyclicity of revealed preference without continuityp. 50
(A)cyclicity of revealed preference with continuityp. 53
Representation of revealed preferencep. 56
Concluding remarks and related literaturep. 59
Violation of SARP for n ] 2p. 59
Monotonicity propertiesp. 63
Introductionp. 63
Individual Monotonicityp. 64
Replication invariance of bargaining solutionsp. 70
Global individual monotonicityp. 73
Proportional solutionsp. 76
The equal-loss solutionp. 82
The lexicographic egalitarian solutionp. 84
The lexicographic equal-loss solutionp. 88
Further literaturep. 92
Additivity propertiesp. 93
Introductionp. 93
The super-additive solution of Perles and Maschlerp. 94
Simultaneity of issues and additivity in bargainingp. 96
Partial super-additivity and proportional solutionsp. 98
Restricted additivity and nonsymmetric Nash solutionsp. 101
Risk propertiesp. 107
Introductionp. 107
Risk properties of bargaining solutionsp. 107
Risk properties, independence of irrelevant alternatives, individual monotonicityp. 112
Risk behavior in "risky" situationsp. 115
Improvement sensitivity of bargaining solutionsp. 116
Risk sensitivity, twist sensitivity, and the slice propertyp. 118
Bargaining with a variable number of playersp. 125
Introductionp. 125
The variable population bargaining modelp. 126
Population monotonicity and the Raiffa-Kalai-Smorodinsky solutionp. 127
Stability and the Nash solutionp. 129
The egalitarian solution, weak stability and population monotonicityp. 133
Alternative models and solution conceptsp. 135
Introductionp. 135
Multivalued solutionsp. 135
Probabilistic solutionsp. 142
Nonconvex bargaining gamesp. 152
Bargaining on economic environmentsp. 163
Axiomatic bargaining over timep. 166
Ordinal bargainingp. 167
Continuity of bargaining solutionsp. 168
Noncooperative models for bargaining solutionsp. 169
Introductionp. 169
The Harsanyi-Zeuthen procedurep. 170
The Nash demand gamep. 171
Perfect equilibrium in an alternating Nash demand gamep. 174
A one-shot bargaining problemp. 180
Consistency and subgame perfectness for the RKS solutionp. 180
Noncooperative comparison of solutionsp. 186
Arbitration gamesp. 191
Solutions for coalitional bargaining gamesp. 193
Introductionp. 193
Coalitional bargaining games and solutionsp. 194
The Shapley solutionp. 198
The Harsanyi solutionp. 201
The proportional solutionsp. 203
Related literaturep. 205
Elements from utility theoryp. 207
Introductionp. 207
Von Neumann-Morgenstern utility functionsp. 207
Risk aversionp. 210
A criterion for comparing strength of preferencep. 214
Additive utilityp. 216
Multiplicative utilityp. 218
Referencesp. 221
Author indexp. 231
Subject indexp. 233
Notation and symbolsp. 237
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792318736
ISBN-10: 0792318730
Series: THEORY AND DECISION LIBRARY SERIES C, GAME THEORY, MATHEMATICAL PROGRAMMING, AND OPERATIONS RESEARCH
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 242
Published: 31st July 1992
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 17.15  x 1.91
Weight (kg): 0.61