Handbook of Utility Theory

by Barbera, Salvador; Hammond, Peter J.; Seidl, Christian

• ISBN13: 9781402077142
• ISBN10: 1402077149
• Format: Hardcover
• Copyright: 2004-03-01
• Publisher: Kluwer Academic Pub

Summary

The main purpose of the Handbook of Utility Theory is to make more widely available some recent developments in the area. The editors selected a list of topics that seemed ripe enough to be covered by review articles. Then they invited contributions from researchers whose expert work had come to their attention. So the list of topics and contributors is largely the editors' responsibility. Each contributor's chapter has been refereed, and revised according to the referees' remarks. Whereas Volume I of the Handbook of Utility Theory is largely concentrated on basic theory, the present volume is concerned with extensions and applications to other branches of economic theory. Taken together, these first two volumes contain all the purely theoretical material that the editors planned to cover. The chapters on experimental and empirical research on utility and the chapters on the history of utility theory will appear in Volume III.

Table of Contents

Preface	vii
Contributors List	xi
14 Alternatives to Expected Utility: Foundations	685	(72)
Robert Sugden
1 Introduction	687	(2)
2 Choice Under Risk: The von Neumann-Morgenstern Framework	689	(37)
2.1 Expected Utility Theory	689	(5)
2.2 The Common Consequence and Common Ratio Effects, and Simultaneous Insuring and Gambling	694	(5)
2.3 Moments of Utility, Disappointment Theory and Risk-Value Theory	699	(2)
2.4 Weighted Utility Theory and SSB Utility Theory	701	(3)
2.5 Lottery-Dependent Expected Utility	704	(1)
2.6 Machina's Generalized Expected Utility Theory	705	(3)
2.7 Transformations of Probabilities	708	(2)
2.8 Prospective Reference Theory	710	(2)
2.9 Rank-Dependent Utility Theory	712	(4)
2.10 Ordinal Independence	716	(1)
2.11 Gut's Theory of Disappointment Aversion	717	(2)
2.12 Cumulative Prospect Theory	719	(3)
2.13 Similarity Theory	722	(1)
2.14 Case-Based Decision Theory	723	(3)
3 Choice Under Uncertainty: The Savage Framework	726	(14)
3.1 Savage's Conceptual Framework	726	(1)
3.2 Savage's Subjective Expected Utility Theory	727	(3)
3.3 Probabilistic Sophistication	730	(2)
3.4 Ambiguity and the Ellsberg Paradox	732	(2)
3.5 Choquet Expected Utility Theory	734	(2)
3.6 Rank-Dependent Theory as a Special Case of Choquet Expected Utility Theory	736	(2)
3.7 Regret Theory	738	(2)
4 Dynamic Choice	740	(8)
4.1 Dynamic Consistency and the Common Ratio Effect	740	(4)
4.2 Relaxing Separability	744	(2)
4.3 Reduction by the Substitution of Certainty Equivalents	746	(1)
4.4 Relaxing Timing Independence	746	(2)
5 Conclusion	748	(2)
References	750	(7)
15 Alternatives to Expected Utility: Formal Theories	757	(82)
Ulrich Schmidt
1 Introduction	758	(1)
2 The General Framework	759	(2)
3 Expected Utility Theory	761	(10)
3.1 Axioms for Expected Utility	761	(3)
3.2 Representation Theorems	764	(2)
3.3 Properties of Expected Utility	766	(3)
3.4 Violations of Independence	769	(2)
4 Generalizations of Expected Utility	771	(48)
4.1 Utility Theories with the Betweenness Property	771	(12)
4.2 Rank-Dependent Utility Theory	783	(16)
4.3 Local Expected Utility Analysis	799	(4)
4.4 Hybrid Models	803	(7)
4.5 Discontinuous Models	810	(9)
5 Conclusions	819	(1)
References	820	(19)
16 State-Dependent Utility and Decision Theory	839	(54)
Jacques H. Dreze and Aldo Rustachini
1 Technical Summary	841	(2)
2 Introduction, Retrospect and Preview	843	(7)
2.1 Retrospect: Theory	843	(2)
2.2 Retrospect: Applications and Moral Hazard	845	(2)
2.3 One-Person Games with Moral Hazard	847	(1)
2.4 Motivation and Organisation	848	(2)
3 A General Framework	850	(1)
4 Games Against Nature	851	(2)
5 Hypothetical Preferences	853	(6)
6 Games with Moral Hazard	859	(7)
7 Conditional Expected Utility	866	(5)
7.1 Representation Theorem	866	(3)
7.2 Extensions and Remarks	869	(2)
8 Risk Aversion	871	(4)
8.1 State-Independent Preferences, or Single Commodity	871	(1)
8.2 State-Dependent Preferences, or Many Commodities	872	(3)
9 Applications: Life Insurance and Value of Life	875	(20)
9.1 Life Insurance	876	(2)
9.2 Value of Life	878	(5)
10 Conclusion	883	(1)
Appendix	884	(4)
References	888	(5)
17 Ranking Sets of Objects	893	(86)
S. Barbera. W. Bossert and P.K. Pattanaik
1 Introduction	895	(3)
2 An Overview	898	(3)
3 Complete Uncertainty	901	(21)
3.1 Basic Concepts	901	(3)
3.2 Best and Worst Elements	904	(6)
3.3 Impossibility Results	910	(2)
3.4 Characterizations	912	(10)
4 Opportunities	922	(37)
4.1 Indirect Utility	922	(2)
4.2 Freedom of Choice	924	(19)
4.3 Well-Being	943	(6)
4.4 Flexibility and Consequences	949	(10)
5 Sets As Final Outcomes	959	(9)
5.1 Conceptual Issues	959	(1)
5.2 Fixed-Cardinality Rankings	959	(3)
5.3 Additive Representability and Separability	962	(3)
5.4 Signed Orderings	965	(3)
6 Concluding Remarks	968	(1)
References	969	(10)
18 Expected Utility In Non-Cooperative Game Theory	979	(86)
Peter J. Hammond
1 Introduction and Outline	982	(4)
1.1 Background	982	(1)
1.2 Normative Theory and Consequentialism	982	(1)
1.3 Normal Form Invariance and Equilibrium	983	(1)
1.4 The Zero Probability Problem	984	(1)
1.5 Subjective Probabilities and Rationalizability	985	(1)
1.6 Rationalizable Dominance	986	(1)
2 Normal Form Invariance	986	(7)
2.1 Games in Normal Form	986	(1)
2.2 Consequentialist Game Forms	987	(1)
2.3 Games in Extensive Form	988	(1)
2.4 Perfect Recall	988	(1)
2.5 The Agent Normal Form	989	(1)
2.6 The Absent-Minded Driver	990	(1)
2.7 Consequentialist Normal Form Invariance	991	(2)
3 Objective Probabilities and Best Responses	993	(5)
3.1 Expected Utility and Best Responses	993	(2)
3.2 Dominance by Pure Strategies	995	(1)
3.3 Dominance by Mixed Strategies	996	(1)
3.4 Strategies not Strictly Dominated must be Best Responses	996	(1)
3.5 Strategies not Weakly Dominated must be Cautious Best Responses	997	(1)
4 Objective Probabilities and Equilibrium	998	(6)
4.1 Two-Person Strictly Competitive Games	998	(2)
4.2 Nash Equilibrium	1000	(1)
4.3 Bayesian Nash Equilibrium	1001	(2)
4.4 Correlated Equilibrium	1003	(1)
5 Perfect and Proper Equilibrium	1004	(5)
5.1 Subgame Imperfection of Nash Equilibrium	1004	(1)
5.2 Trembling-Hand Perfection	1005	(1)
5.3 E-Perfect and Perfect Equilibrium	1006	(1)
5.4 Proper Equilibrium	1007	(2)
5.5 Importance of Best Responses	1009	(1)
6 Quantal Response Equilibrium	1009	(7)
6.1 Motivation	1009	(1)
6.2 Ordinality	1010	(1)
6.3 Luce's Superstrong Transitivity Axiom	1011	(1)
6.4 Luce's Model	1012	(1)
6.5 Equilibrium	1013	(1)
6.6 Strategic Choice versus Consequentialism	1014	(1)
6.7 Consequentialist Stochastic Choice Is Trivial	1014	(2)
6.8 Assessment	1016	(1)
7 Beyond Equilibrium	1016	(2)
7.1 Is Equilibrium Attainable?	1016	(2)
7.2 The Zero Probability Problem	1018	(1)
7.3 Beyond Objective Probability	1018	(1)
8 Subjectively Expected Utility in Game Theory	1018	(8)
8.1 The Mariotti Problem	1018	(3)
8.2 Battigalli's Construction	1021	(1)
8.3 Players' Type Spaces	1022	(2)
8.4 Subjective Expectations	1024	(2)
8.5 Arbitrage Choice Theory	1026	(1)
9 Rationalizable Expectations	1026	(41)
9.1 Rationalizable Strategies	1026	(2)
9.2 Iterated Removal of Strictly Dominated Strategies	1028	(1)
9.3 Strictly Rationalizable Strategies	1029	(1)
9.4 The Centipede Game	1030	(2)
10 Hierarchies of Beliefs	1032	(1)
10.1 Rationalizable Types	1032	(1)
10.2 Mathematical Preliminaries	1033	(1)
10.3 A Sequence of Type Spaces	1034	(1)
10.4 The Limit Space	1035	(1)
11 Trembling Best Responses	1036	(1)
11.1 The Zero Probability Problem	1036	(2)
11.2 B-Perfect Rationalizability	1038	(2)
11.3 Borgers' Example	1040	(1)
11.4 W-Perfect Rationalizability	1041	(2)
11.5 The Dekel-Fudenberg Procedure	1043	(2)
11.6 Proper Rationalizability	1045	(1)
11.7 Properties	1046	(1)
12 Rationalizable Preferences over Pure Strategies	1047	(1)
12.1 Quasi-Orderings as Dominance Relations	1047	(1)
12.2 A Recursive Construction	1048	(3)
12.3 Assessment	1051	(1)
13 Conclusion: Insecure Foundations?	1052	(2)
References	1054	(11)
19 Utility Theories in Cooperative Games	1065	(34)
Mamoru Kaneko and Myrna H. Wooders
1 Introduction	1067	(1)
2 Games with Side Payments	1068	(9)
2.1 Transferable Utility and Side Payments	1070	(1)
2.2 A Market Game	1071	(3)
2.3 A Majority Voting Game with Side Payments	1074	(2)
2.4 A Cooperative Game Derived from a Strategic Form Game	1076	(1)
3 Axiomatic Characterization of Transferable Utility	1077	(6)
3.1 Transferable Utility with no Uncertainty	1077	(2)
3.2 Transferable Utility with Uncertainty	1079	(4)
4 Solution Concepts for Games with Side Payments	1083	(9)
4.1 The Core	1083	(4)
4.2 The von Neumann-Morgenstern Stable Set	1087	(2)
4.3 The Nucleolus	1089	(2)
4.4 The Shapley Value	1091	(1)
5 Games Without Side Payments and Some Solution Concepts	1092	(8)
5.1 Games Without Side Payments	1092	(1)
5.2 Examples	1093	(2)
5.3 Solution Concepts	1095	(1)
References	1096	(3)
20 Utility in Social Choice	1099	(80)
Walter Bossert and John A. Weymark
1 Introduction	1100	(2)
2 Welfarism	1102	(9)
3 Social Welfare Orderings	1111	(4)
4 Utility Comparisons Using Invariance Transforms	1115	(11)
5 Utility Comparisons As Meaningful Statements	1126	(3)
6 Cardinal Measurability and Full Comparability	1129	(4)
7 Cardinal Measurability and Unit Comparability	1133	(3)
8 Translation-Scale Measurability	1136	(1)
9 Ordinal Measurability and Full Comparability	1137	(7)
10 Ordinal and Cardinal Measurability	1144	(2)
11 Ratio-Scale Measurability	1146	(3)
12 Two-Person Situations	1149	(4)
13 Separability	1153	(11)
14 Variable-Population Social Choice	1164	(6)
15 Concluding Remarks	1170	(1)
References	1170	(9)
21 Interpersonally Comparable Utility	1179	(95)
Marc Fleurbaey and Peter J. Hammond
1 Introduction and Outline	1181
1.1 Interpersonal Comparisons: Some Background	1181	(1)
1.2 Outline of Chapter	1182	(1)
2 Welfare Economics	1183	(1)
2.1 Pareto Efficiency	1183	(1)
2.2 Pareto Improvements	1184	(1)
2.3 Private Information	1184	(2)
2.4 Measures of Individual Gain and Loss	1186	(3)
3 Social Choice without Interpersonal Comparisons	1189	(1)
3.1 Arrow's Impossibility Theorem	1189	(3)
3.2 Possibilities	1192	(5)
3.3 Welfarism	1197	(4)
3.4 Independence of Irrelevant Alternatives	1201	(3)
4 Social Choice with Interpersonal Comparisons	1204	(1)
4.1 Interpersonal Comparisons of Utility	1204	(2)
4.2 Maximin and Comparisons of Utility Levels	1206	(2)
4.3 Utilitarianism and Comparisons of Utility Difference Ratios	1208	(4)
4.4 Interpersonal Comparisons of What?	1212	(6)
5 The Basis of Interpersonal Comparisons	1218	(1)
5.1 Descriptive or Normative?	1218	(4)
5.2 Capabilities	1222	(1)
5.3 Social Indicators of Happiness	1223	(2)
5.4 Bargaining	1225	(2)
5.5 Relative Utilitarianism	1227	(2)
5.6 Fairness	1229	(2)
5.7 The Condorcet Criterion	1231	(2)
6 Interpersonally Comparable Measures of Economic Welfare	1233	(1)
6.1 Optimal Income Taxation	1233	(2)
6.2 Isomorphic Cardinal Utility Functions	1235	(9)
6.3 Exact Aggregation: Parallel Linear Engel Curves	1244	(6)
6.4 Exact Aggregation: The Translog Model	1250	(6)
6.5 An Extended Almost Ideal Demand System	1256	(3)
6.6 Assessment	1259	(1)
7 A Generalized Utilitarianism	1260	(1)
7.1 Introspective Approaches	1260	(1)
7.2 Social and Personal Consequences	1261	(2)
7.3 Individualistic Consequentialism	1263	(1)
7.4 Individual Welfarism	1264	(1)
7.5 Utilitarianism	1264	(2)
7.6 Personal Non-Existence	1266	(3)
7.7 Revealed Interpersonal Comparisons	1269	(2)
8 Concluding Remarks	1271	(3)
References	1274	(12)
Subject Index	1286	(16)
Name Index	1302