Credible Threats in Negotiations. A Game-theoretic Approach

Credible Threats in Negotiations. A Game-theoretic Approach

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English

Description

The modern theory of threats in bargaining situations is presented in a unified and systematic treatment that puts the existing literature in a new perspective. Harold Houba and Wilko Bolt provide a masterful synthesis of the fundamental results obtained in the rapidly expanding game-theoretic literature. The relative impacts of the fundamental forces on the bargaining outcome are discussed and related to the visions expressed by Nobel-laureate John Nash. Many topics -such as robustness of the results with respect to the diversity of known bargaining procedures, the role of commitment and policy bargaining situations- receive their most extensive treatment to date.
Credible Threats in Negotiations is suitable as a textbook for graduate students in economic theory and other social sciences and a necessity as a resource for scholars interested in bargaining situations.

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Published 01 January 2002
Reads 8
EAN13 0306475391
License: All rights reserved
Language English

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Contents
List of Figures List of Tables Preface Acknowledgments On the authors
1.THE ESSENCE OF NEGOTIATION 1.1.Introduction 1.2.motivating examplesReal life negotiations: 1.3.the bookOutline of 2.A BARGAINING MODEL WITH THREATS 2.1.Introduction 2.2.The bargaining problem 2.2.1The contract space 2.2.2Disagreement actions 2.2.3Utility functions 2.2.4Mutual and conflicting interests 2.2.5Pareto efficiency 2.2.6Individual rationality 2.2.7Generic uniqueness 2.2.8Utility representation 2.3.A bargaining game with threats 2.3.1The order of moves 2.3.2The players’ information 2.3.3Information sets and strategies 2.3.4Outcomes and utilities 2.3.5Reinterpretation as expected utilities
v
xi xiii xv xix xxi
1 1 3 7 15 15 16 16 18 19 20 21 23 23 26 28 29 31 32 35 36
vi
2.4.
CREDIBLE THREATS IN NEGOTIATIONS
2.3.6An appropriate equilibrium concept 2.3.7Limit sets of equilibria 2.3.8Markov strategies 2.3.9Strategies represented by tables Related Literature
Part I Exogenous disagreement outcomes 3.PROCEDURETHE ALTERNATING OFFERS 3.1. Introduction 3.2.Alternating offers 3.3. Markov perfect equilibrium 3.3.1An important fixed point problem 3.3.2Dynamic programming 3.3.3Optimal response 3.3.4Optimal proposals 3.3.5Characterization in utility representation 3.3.6Characterization in the contract space 3.4. Subgame perfect equilibrium 3.4.1The method of Shaked and Sutton 3.4.2Characterization of the SPE 3.4.3Firstmover advantage 3.4.4Computation of the SPE contract 3.5. Applications 3.5.1Dividing a dollar 3.5.2A barter economy 3.6. Related literature 4.THE NASH PROGRAM 4.1. Introduction 4.2. Nash’s bargaining solution 4.2.1Utility representation 4.2.2Two geometrical properties 4.2.3Bargaining in the contract space 4.2.4Computation of axiomatic contracts 4.2.5Two critical remarks 4.2.6A reinterpretation 4.2.7Alternative axioms for Nash’s bargaining solution
38 40 41 42 44
49 49 50 51 51 56 57 60 62 64 67 67 69 70 71 72 73 75 77
81 81 82 82 85 88 93 94 97 99
Contents
4.2.8Alternative axiomatic solutions 4.3. Strategic bargaining and Nash’s bargaining solution 4.3.1Nash’s demand game 4.3.2Interpretation of demands 4.3.3Convergence in alternating offers 4.3.4Convergence in the contract space 4.4. The two approaches are complementary 4.5. Related Literature 5.COMPREHENSIVE BARGAINING PROBLEMS 5.1. Introduction 5.2. Comprehensive bargaining problems 5.3. Markov perfect equilibrium 5.3.1The fixed point problem 5.3.2MPE in utility representation 5.4. Subgame perfect equilibrium 5.4.1Bounds for SPE utilities 5.4.2Equilibrium switching 5.4.3SPE with equilibrium switching 5.4.4SPE with delay 5.5. Nash program 5.5.1Generalized Nash’s solutions 5.5.2SPE utility pairsLimit set of 5.5.3Convergence or nonconvergence, that’s the question 5.6. Contract space 5.6.1SPE contracts 5.6.2Sufficient conditions for uniqueness 5.7. Related Literature 6.COMPARATIVE STATICS 6.1. Introduction 6.2. Utility functions and the contract space 6.2.1Mutual and conflicting interests 6.2.2Imperfectly divisible goods 6.3. Nonstationary bargaining problems 6.3.1Alternating probabilities of breakdown 6.3.2Alternating disagreement points 6.4. Alternative bargaining procedure
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101 102 103 105 107 110 112 114 117 117 118 120 120 122 124 124 126 127 130 132 132 134 137 138 138 139 141
145 145 146 146 149 152 152 155 160
viii
6.5.
CREDIBLE THREATS IN NEGOTIATIONS
6.4.1Markov process 6.4.2proposalsStrategic timing of Related Literature
Part II Endogenous Threats 7.COMMITMENT AND ENDOGENOUS THREATS 7.1.Introduction 7.2.Optimal threats with commitment 7.2.1variablethreat gameNash’s original 7.2.2The variablethreat game with alternating offers 7.3.Credible threats without commitment 7.3.1Nash’s variablethreat game: no commitment 7.3.2Variable threats with alternating offers: no commitment 7.3.3Bounds for SPE utilities 7.3.4The set of SPE utility pairs 7.3.5SPE with delay 7.3.6A comparison between models 7.4.Numerical examples 7.5.Related literature 8.BARGAINING OVER WAGES 8.1.Introduction 8.2.A model of wage negotiations 8.2.1Wage bargaining: some facts and assumptions 8.2.2The wage bargaining model 8.3.Wage bargaining with efficient holdouts 8.3.1Markov perfect equilibrium 8.3.2The minimumwage and maximumwage contract 8.3.3Equilibria with lengthy strikes 8.3.4discount factorsIntermezzo: unequal 8.4.an applicationDutch wage bargaining: 8.4.1Worktorule as a substitute for strike 8.4.2Equilibria with lengthy worktorule 8.4.3Backdating 8.5.Related literature
160 163 167
175 175 177 177 180 184 185
188 190 192 196 197 198 200 203 203 204 205 207 209 210 210 213 214 217 218 220 223 225
Contents
9.THE POLICY BARGAINING MODEL 9.1.Introduction 9.2.Subgame perfect equilibria 9.2.1Markov perfect equilibrium 9.2.2Worst SPE strategies: Example 9.2.3General caseWorst SPE strategies: 9.2.4Optimal disagreement actions 9.2.5Conditions for uniqueness 9.2.6SPE utilitiesCharacterization of 9.3.Policy Bargaining 9.3.1The policy bargaining model 9.3.2Characterization of SPE utilities 9.3.3Renegotiation of Agreements 9.3.4Nonbinding agreements 9.4.Numerical Examples 9.5.Related literature 10.DESTRUCTIVE THREATS 10.1.Introduction 10.2.Difference games 10.2.1General framework 10.2.2The great fish war 10.2.3Linearquadratic difference games 10.2.4Pareto efficient joint policies 10.3.Negotiations for quota 10.3.1Optimal disagreement catches 10.3.2Optimal proposals 10.3.3Numerical Solutions 10.3.4The set of SPE utility pairs 10.4.Multiple state variables 10.4.1Motivating Example 10.4.2Optimal disagreement actions 10.4.3Optimal proposals 10.4.4Breakdown quadratic value functions 10.4.5To negotiate or not? 10.5.Concluding remarks 10.6.Related literature Appendices
ix
229 229 230 230 231 233 237 241 242 244 245 246 247 248 251 253 257 257 258 259 261 263 266 268 268 270 271 273 275 276 278 279 280 281 283 286 291
x
Proofs of Selected Theorems References
Index
CREDIBLE THREATS IN NEGOTIATIONS
291 311
317