Acknowledgments ................................................ xi
In Memoriam .................................................. xiii
Introduction: The Economics of Uncertainty and Information ...... 1
PART I
1 Elements of Decision under Uncertainty ..................... 7
1.1 The Menu of Acts ........................................... 9
1.2 The Probability Distribution ............................... 9
1.2.1 Risk versus Uncertainty ............................ 10
1.2.2 "Hard" versus "Soft" Probabilities ................. 11
1.3 The Utility Function ...................................... 13
1.4 The Expected-Utility Rule ................................. 13
1.4.1 An Informal Presentation ........................... 16
1.4.2 The Independence Axiom ............................. 22
1.5 Risk Aversion ............................................. 26
1.6 Utility Paradoxes and Rationality ......................... 35
1.6.1 Probability Matching ............................... 35
1.6.2 Framing the Question ............................... 36
1.6.3 Allais Paradox ..................................... 38
1.6.4 Ellsberg Paradox ................................... 41
2 Risk Bearing: The Optimum of the Individual ............... 46
2.1 The Risk-Bearing Optimum: Basic Analysis .................. 47
2.1.1 Contingent-Claims Markets .......................... 49
2.1.2 Regimes of Asset Markets - Complete and
Incomplete ......................................... 51
2.1.3 Productive Opportunities ........................... 58
2.2 Choosing Combinations of Mean and Standard Deviation
of Income ................................................. 62
2.2.1 μ, σ. Preferences .................................. 62
2.2.2 Opportunity Set and Risk-Bearing Optimum ........... 66
2.3 State-Dependent Utility ................................... 77
2.3.1 An Application: The "Value of Life" ................ 80
3 Comparative Statics of the Risk-Bearing Optimum ........... 86
3.1 Measures of Risk Aversion ................................. 86
3.2 Endowment and Price Effects ............................... 95
3.2.1 Complete Markets ................................... 95
3.2.2 Incomplete Markets ................................. 98
3.3 Changes in the Distribution of Asset Payoffs ............. 103
3.4 Stochastic Dominance ..................................... 108
3.4.1 Comparison of Different Consumption Prospects ..... 108
3.4.2 Responding to Increased Risk* ..................... 116
4 Market Equilibrium under Uncertainty ..................... 123
4.1 Market Equilibrium in Pure Exchange ...................... 123
4.1.1 Application to Share Cropping ..................... 127
4.1.2 Application to Insurance .......................... 130
4.2 Production and Exchange .................................. 137
4.2.1 Equilibrium with Production: Complete Markets ..... 137
4.2.2 Stock Market Equilibrium* ......................... 145
4.2.3 Monopoly Power in Asset Markets* .................. 150
4.3 The Capital Asset Pricing Model ..................... 156
PART II
5 Information and Informational Decisions .................. 169
5.1 Information - Some Conceptual Distinctions ............... 169
5.2 Informational Decision Analysis .......................... 172
5.2.1 The Use of Evidence to Revise Beliefs ............. 172
5.2.2 Revision of Optimal Action and the Worth of
Information ....................................... 181
5.2.3 More Informative versus Less Informative Message
Services* ......................................... 189
5.2.4 Differences in Utility Functions and the Worth
of Information .................................... 199
5.2.5 The Worth of Information: Flexibility versus
Range of Actions .................................. 203
5.3 Multi-Person Decisions ................................... 208
5.3.1 The Use of Experts ................................ 209
5.3.2 Group Choices ..................................... 213
6 Information and Markets .................................. 224
6.1 The Inter-related Equilibria of Prior and Posterior
Markets .................................................. 225
6.1.1 Complete Contingent Markets ....................... 225
6.1.2 Incomplete Regimes of Markets ..................... 232
6.2 Speculation and Futures Trading .......................... 240
6.3 The Production and Dissemination of Information .......... 247
6.3.1 Private Information and the Leakage Problem ....... 248
6.3.2 Partial Leakage with Constant Absolute Risk
Aversion* ......................................... 257
6.4 Rational Expectations .................................... 264
7 Strategic Uncertainty and Equilibrium Concepts ........... 270
7.1 Dominant Strategy ........................................ 270
7.2 Nash Equilibrium ......................................... 272
7.3 Subgame-Perfect Equilibrium .............................. 278
7.4 Further Refinements ...................................... 284
7.5 Games with Private Information ........................... 292
7.6 Evolutionary Equilibrium ................................. 297
8 Informational Asymmetry and Contract Design .............. 308
8.1 Hidden Actions ("Moral Hazard") and Contract Design ...... 309
8.2 Hidden Knowledge ......................................... 320
8.2.1 Adverse Selection ................................. 321
8.2.2 Screening ......................................... 327
8.2.3 Monopoly Price Discrimination with Hidden
Knowledge* ........................................ 332
9 Competition and Hidden Knowledge ......................... 343
9.1 Screening ................................................ 343
9.1.1 Screening by Means of a Non-Productive Action ..... 344
9.1.2 Screening with Productive Actions ................. 350
9.2 Reactive Equilibrium ..................................... 356
9.3 Signaling ................................................ 359
10 Market Institutions ...................................... 367
10.1 Posted-Price Markets ..................................... 367
10.2 Auctions ................................................. 370
10.2.1 Bidders'Valuations Are Known ...................... 371
10.2.2 Bidders' Valuations Are Independent and
Privately Known ................................... 376
10.2.3 Optimal Mechanisms* ............................... 381
10.2.4 Bidders' Valuations Are Correlated* ............... 392
10.3 Bargaining ............................................... 404
10.4 Efficient Allocation with Private Information* ........... 410
11 Long-Run Relationships and the Credibility of Threats
and Promises ............................................. 422
11.1 The Multi-Period Prisoners' Dilemma ...................... 422
11.1.1 The Finitely Repeated Prisoners' Dilemma .......... 423
11.1.2 The Infinitely Repeated Prisoners'Dilemma ......... 424
11.2 Subgame-Perfect Equilibria in Infinitely Repeated Games .. 428
11.3 The Folk Theorem for Infinitely Repeated Games ........... 432
11.4 The Role of Chivalry ..................................... 439
11.5 Building a Reputation .................................... 442
12 Information Transmission, Acquisition, and Aggregation ... 453
12.1 Strategic Information Transmission and Delegation ........ 454
12.1.1 Strategic Information Transmission ................ 455
12.1.2 Strategic Delegation .............................. 459
12.2 Strategic Information Acquisition ........................ 461
12.2.1 Efficient Information Acquisition ................. 462
12.2.2 Overinvestment in Information ..................... 466
12.3 Information Cascades ..................................... 469
12.4 The Condorcet Jury Theorem* .............................. 477
Index ......................................................... 487
* Starred sections represent more difficult or specialized
materials that can be omitted without significant loss of
continuity
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