Dutta, Prajit K
Strategies and games : theory and practice / Prajit K Dutta and Wouter Vergote. - 2nd Ed. - Cambridge : MIT Press, 2022 - xxxiv, 671p. ; 23cm.
P A R T O N E Introduction 1
c h a p t e r 1 A First Look at the Applications 3
1.1 Games That We Play 3
1.2 Background 8
1.3 Examples 10
Exercises 15
c h a p t e r 2 A First Look at the Theory 21
2.1 Rules of the Game: Background 21
2.2 Who, What, When: The Extensive Form 23
2.2.1 Information Sets and Strategies 24
2.3 Who, What, When: The Normal (or Strategic) Form 26
2.4 How Much: Von Neumann–Morgenstern Utility Function 28
2.5 Representation of the Examples 30
Exercises 33
P A R T T W O Strategic Form Games: Theory and Practice 39
c h a p t e r 3 Strategic Form Games and Dominant Strategies 41
3.1 Strategic Form Games 41
3.1.1 Examples 42
3.1.2 Equivalence with the Extensive Form 45
3.2 Case Study: The Strategic Form of Art Auctions 46
3.2.1 Art Auctions: A Description 46
3.2.2 Art Auctions: The Strategic Form 47
3.3 Dominant Strategy Solution 48
3.4 Case Study Again: A Dominant Strategy at the Auction 50
Exercises 52
c h a p t e r 4 Dominance Solvability 57
4.1 The Idea 57
4.1.1 Dominated and Undominated Strategies 57
4.1.2 Iterated Elimination of Dominated Strategies 59
4.1.3 More Examples 60
4.2 Case Study: Electing The United Nations
Secretary-General 63
4.3 A More Formal Definition 64
4.4 A Discussion 66
Exercises 68
c h a p t e r 5 Nash Equilibrium 75
5.1 The Concept 75
5.1.1 Intuition and Definition 75
5.1.2 Nash Parables 77
5.2 Examples 79
5.3 Case Study: Nash Equilibrium in the Animal Kingdom 81
5.4 Relation Between the Solution Concepts 83
Exercises 85
c h a p t e r 6 An Application: Cournot Duopoly 89
6.1 Background 89
6.2 The Basic Model 90
6.3 Cournot Nash Equilibrium 91
6.4 Cartel Solution 93
6.5 Case Study: OPEC 95
6.6 Variants on the Main Theme I: A Graphical Analysis 97
6.6.1 The IEDS Solution to the Cournot Model 99
6.7 Variants on the Main Theme II: Stackelberg Model 100
6.8 Variants on the Main Theme III: Generalization 101
Exercises 103
c h a p t e r 7 Voting and Elections 107
7.1 Elections, Voting, and Game Theory 107
7.2 Voting Procedures 108
7.2.1 Majority Voting 108
7.2.2 Agenda Setting: an Example 109
7.3 Individual Rationality versus Collective Rationality 110
7.3.1 The Condorcet Paradox 110
7.3.2 A Way Out: Single-Peaked Preferences 111
7.3.3 Beyond the Condorcet Paradox 114
7.4 Competing for Votes 114
7.4.1 The Hotelling-Downs Model of Political Competition 114
7.4.2 Courting the Median Voter 115
7.4.3 Discussion 117
7.5 More on Voting Procedures 117
Exercises 119
c h a p t e r 8 An Application: The Commons Problem 125
8.1 Background: What Is the Commons? 125
8.2 A Simple Model 127
8.3 Social Optimality 129
8.4 The Problem Worsens in a Large Population 130
8.5 Case Study: Global Warming 131
8.6 Averting a Tragedy 133
Exercises 135
c h a p t e r 9 Mixed Strategies 139
9.1 Definition and Examples 139
9.1.1 What Is a Mixed Strategy? 139
9.1.2 Yet More Examples 142
9.2 An Implication 144
9.3 Mixed Strategies Can Dominate Some Pure Strategies 145
9.3.1 Implications for Dominant Strategy Solution and IEDS 146
9.4 Mixed Strategies Are Good for Bluffing 147
9.5 Mixed Strategies and Nash Equilibrium 148
9.5.1 Mixed-Strategy Nash Equilibria in an Example 150
9.6 Case Study: Random Drug Testing 151
Exercises 153
c h a p t e r 10 Two Applications: Natural Monopoly and Bankruptcy Law 161
10.1 Chicken, Symmetric Games, and Symmetric Equilibria 161
10.1.1 Chicken 161
10.1.2 Symmetric Games and Symmetric Equilibria 162
10.2 Natural Monopoly 164
10.2.1 The Economic Background 164
10.2.2 A Simple Example 164
10.2.3 War of Attrition and a General Analysis 166
10.3 Bankruptcy Law 168
10.3.1 The Legal Background 168
10.3.2 A Numerical Example 168
10.3.3 A General Analysis 170
Exercises 173
c h a p t e r 11 Zero-Sum Games 179
11.1 Definition And Examples 179
11.2 Playing Safe: Maxmin 182
11.2.1 The Concept 182
11.2.2 Examples 183
11.3 Playing Sound: Minmax 185
11.3.1 The Concept and Examples 185
11.3.2 Two Results 187
11.4 Playing Nash: Playing Both Safe and Sound 188
Exercises 190
c h a p t e r 12 Extensive Form Games and Backward Induction 201
12.1 The Extensive Form 201
12.1.1 A More Formal Treatment 203
12.1.2 Strategies, Mixed Strategies, and Chance Nodes 205
12.2 Perfect Information Games: Definition and Examples 206
12.3 Backward Induction: Examples 209
12.3.1 The Power of Commitment 211
12.4 Backward Induction: A General Result 213
12.5 Connection With IEDS in the Strategic Form 215
12.6 Case Study: Poison Pills as a Vaccine Against Takeovers 217
Exercises 219
c h a p t e r 13 An Application: Research and Development 225
13.1 Background: R&D, Patents, and Oligopolies 225
13.1.1 A Patent Race: 8K Television 226
13.2 A Model of R&D 227
13.3 Backward Induction: Analysis of the Model 229
13.4 Some Remarks 234
Exercises 236
c h a p t e r 14 Subgame Perfect Equilibrium 239
14.1 A Motivating Example 239
14.2 Subgames and Strategies within Subgames 242
14.3 Subgame Perfect Equilibrium 244
14.4 Two More Examples 245
14.5 Some Remarks 248
14.6 Case Study: Peace in the World War I Trenches 249
Exercises 251
c h a p t e r 15 Finitely Repeated Games 257
15.1 Examples and Applications 257
15.1.1 Three Repeated Games and a Definition 257
15.1.2 Six Applications 260
15.2 Finitely Repeated Games 263
15.2.1 Some General Conclusions 267
15.3 Case Study: Treasury Bill Auctions 268
Exercises 272
c h a p t e r 16 Infinitely Repeated Games 277
16.1 Detour Through Discounting 277
16.2 Analysis of Example 3: Trigger Strategies and
Good Behavior 279
16.3 The Folk Theorem 282
16.4 Repeated Games with Imperfect Detection 285
Exercises 288
c h a p t e r 17 An Application: Competition and Collusion in the NASDAQ
Stock Market 295
17.1 The Background 295
17.2 The Analysis 297
17.2.1 A Model of the NASDAQ Market 297
17.2.2 Collusion 298
17.2.3 More on Collusion 300
17.3 The Broker-Dealer Relationship 302
17.3.1 Order Preferencing 302
17.3.2 Dealers Big and Small 302
17.4 The Epilogue 304
Exercises 305
c h a p t e r 18 An Application: OPEC 309
18.1 Oil: A Historical Review 309
18.1.1 Production and Price History 310
18.2 A Simple Model of the Oil Market 312
18.3 Oil Prices and the Role of OPEC 314
18.4 Repeated Games with Demand Uncertainty 316
18.5 Unobserved Quota Violations 320
18.6 Some Further Comments 323
Exercises 325
c h a p t e r 19 An Application: Logrolling and Pork-Barrel Spending 329
19.1 Earmarks, Pork, and Logrolling 329
19.2 A Simple Model of Earmark Spending 331
19.3 Bringing Home the Bacon with Grim Trigger Strategies 333
19.3.1 Equilibrium Conditions 333
19.3.2 Comparative Statics 335
19.4 When Bygones are Bygones 336
19.4.1 Renegotiation: A Good Idea? 336
19.4.2 Hoisted by Your Own Petard? Renegotiation Proofness 336
19.4.3 Penance Strategy: Renegotiation Proofness 337
19.4.4 Penance Strategy: Subgame Perfection 339
Exercises 341
c h a p t e r 20 An Application: Trade Agreements 345
20.1 The Purpose of Trade Agreements 345
20.2 A Tariff-Setting Game 346
20.2.1 Free Trade 347
20.2.2 Tariffs 347
20.2.3 Government Welfare and the Nash Equilibrium 349
20.2.4 The Prisoner’s Dilemma 351
20.3 The Repeated Game and the Design of Trade Agreements 352
20.4 Flexible Trade Agreements 354
20.4.1 Free Trade Agreement with No Flexibility 355
20.4.2 Free Trade Agreement with an Escape Clause 356
Exercises 359
c h a p t e r 21 Dynamic Games with an Application to Global Warming 363
21.1 Dynamic Games: A Prologue 363
21.2 A Global Warming Game 365
21.3 Greenhouse Gas Emissions: Global Optimum 367
21.3.1 A Computation of the Global Optimum 367
21.3.2 An Explanation of the Global Optimum 371
21.3.3 Recommended Global Optimum GHG Levels 372
21.4 Business as Usual Emission Level and Game Equilibrium 372
21.4.1 A Computation of the BAU Equilibrium 373
21.4.2 An Explanation of the BAU Emission Levels 375
21.4.3 A Comparison of the Globally Optimal and the BAU Outcomes 376
21.4.4 Special Feature of the Globally Optimal and BAU Strategies 378
21.5 Dynamic Games: An Epilogue 379
Exercises 381
c h a p t e r 22 Strategic Bargaining 385
22.1 Introduction 385
22.1.1 Tales of Bargaining 385
22.1.2 The Bargaining Problem and Bargaining Theory 386
22.2 Unanimity Bargaining: Negotiating a Merger Deal 388
22.2.1 Two-Stage Negotiations 389
22.2.2 Three-Stage Negotiations 390
22.2.3 Discussion 391
22.3 A Generalization: Sequential Bargaining with
a Finite Horizon 392
22.3.1 The Unique Subgame Perfect Equilibrium 392
22.3.2 Some Observations 394
22.3.3 Experimental Evidence: The Ultimatum Game 395
22.4 Legislative Bargaining 396
22.4.1 Three Legislators and Two-Stage Negotiations 396
22.4.2 N Legislators and Two-Stage Negotiations 397
22.4.3 Qualified Majority Rule 397
22.5 Epilogue: Costly Bargaining and Conflict 398
Exercises 399
P A R T F O U R Asymmetric Information Games: Theory
and Applications 403
c h a p t e r 23 Moral Hazard and Incentives Theory 405
23.1 Moral Hazard: Examples and a Definition 405
23.2 A Principal-Agent Model 407
23.2.1 Some Examples of Incentive Schemes 409
23.3 The Optimal Incentive Scheme 411
23.3.1 No Moral Hazard 411
23.3.2 Moral Hazard 412
23.4 Some General Conclusions 413
23.4.1 Extensions and Generalizations 415
23.5 Case Study: The Rise and Fall of Capitation to
Compensate Primary Care Physicians in an HMO 416
Exercises 419
c h a p t e r 24 Games with Incomplete Information 423
24.1 Some Examples 423
24.1.1 Some Analysis of the Examples 427
24.2 A Complete Analysis of Example 4 428
24.2.1 Bayes-Nash Equilibrium 428
24.2.2 Pure-Strategy Bayes-Nash 430
24.2.3 Mixed-Strategy Bayes-Nash Equilibria 430
24.3 More General Considerations 433
24.3.1 A Modified Example 433
24.3.2 A General Framework 435
24.4 Dominance-Based Solution Concepts 436
24.5 Case Study: “Final Jeopardy!” 439
Exercises 442
c h a p t e r 25 Mechanism Design, the Revelation Principle, and Sales
to an Unknown Buyer 447
25.1 Mechanism Design: The Economic Context 447
25.2 A Simple Example: Selling to a Buyer with an
Unknown Valuation 449
25.2.1 Known Passion 450
25.2.2 Unknown Passion 450
25.3 Mechanism Design and the Revelation Principle 454
25.3.1 Single Player 454
25.3.2 Many Players 456
25.4 A More General Example: Selling Variable Amounts 457
25.4.1 Known Type 457
25.4.2 Unknown Type 458
Exercises 461
c h a p t e r 26 An Application: Auctions 465
26.1 Background and Examples 465
26.1.1 Basic Model 467
26.2 Second-Price Auctions 467
26.3 First-Price Auctions 469
26.4 Optimal Auctions 471
26.4.1 How Well Do the First- and Second-Price Auctions Do? 473
26.5 Final Remarks 475
Exercises 476
c h a p t e r 27 An Application: Price Competition with Cost Uncertainty 481
27.1 A Procurement Procedure 481
27.1.1 Bayes-Nash Equilibrium: Preliminary Observations 482
27.1.2 Bayes-Nash Equilibrium 484
27.2 Bridging Price Competition and Auctions 490
27.2.1 First-Price Sealed-Bid Auction 490
27.2.2 Key Takeaway 492
27.3 Bertrand Price Competition with Incomplete
Information 492
Exercises 496
c h a p t e r 28 Signaling Games and the Lemons Problem 501
28.1 Motivation and Two Examples 501
28.1.1 A First Analysis of the Examples 504
28.2 A Definition, an Equilibrium Concept, and Examples 505
28.2.1 Definition 505
28.2.2 Perfect Bayesian Equilibrium 506
28.2.3 A Further Analysis of the Examples 508
28.3 Signaling Product Quality 509
28.3.1 The Bad Can Drive Out the Good 510
28.3.2 Good Can Signal Quality 511
28.4 Case Study: Used Cars—A Market for Lemons? 513
28.5 Concluding Remarks 514
Exercises 516
c h a p t e r 29 An Application: Crisis Bargaining and Escalation 521
29.1 Tales of Conflict 521
29.2 Unknown Military Strength and War 523
29.2.1 Complete Information: No War 523
29.2.2 Incomplete Information: Bayes-Nash Equilibrium 523
29.3 To Bluff or not to Bluff? 525
29.3.1 Signaling Military Strength 525
29.3.2 In Search of Perfect Bayesian Equilibria That Lead to War 526
29.3.3 When Challenging Is a Costly Signal 529
29.4 Escalation and Audience Costs 530
29.4.1 Finding Perfect Bayesian Equilibria 531
29.5 Case Study: Audience Costs Drivers and
the Impact on Conflict 534
Exercises 537
P A R T F I V E Cooperative Games and Matching 541
c h a p t e r 30 Cooperative Games 543
30.1 Cooperative versus Noncooperative Games 543
30.1.1 A Tale of Two Games 543
30.1.2 Motivating Examples 544
30.2 Modeling Coalitional Games 546
30.2.1 Games with Transferable Utility 546
30.2.2 Games with Nontransferable Utility 548
30.2.3 Solution Concepts 549
30.3 Solution Concept I: Stability and the Core 550
30.4 Solution Concept II: The Shapley Value 554
Exercises 561
c h a p t e r 31 Matching Problems 567
31.1 Motivating Examples 567
31.1.1 How to Allocate Indivisible Goods without Prices? 570
31.2 One-To-One Matching Problems 570
31.2.1 Two-Sided One-to-One Matching Problems: Definitions 570
31.2.2 Two-Sided One-to-One Matching Problems: Stability 573
31.2.3 The Boy-Proposing Deferred Acceptance Algorithm 574
31.2.4 Boy-Optimal versus Girl-Optimal Stable Matchings 577
31.2.5 Strategic Behavior and Mechanism Design 579
31.3 One-Sided One-to-One Matching: The Roommate Problem 580
31.4 Many-to-One Two-Sided Matching Problems:
School Choice 582
31.4.1 Many-to-One Matching Problems: Definitions 582
31.4.2 Deferred Acceptance Algorithm 584
31.5 Epilogue: The Game Theorist as an Engineer 585
Exercises 586
P A R T S I X Foundations 593
c h a p t e r 32 Calculus and Optimization 595
32.1 A Calculus Primer 595
32.1.1 Functions 596
32.1.2 Slopes 598
32.1.3 Some Formulas 599
32.1.4 Concave Functions 600
32.2 An Optimization Theory Primer 601
32.2.1 Necessary Conditions 601
32.2.2 Sufficient Conditions 602
32.2.3 Feasibility Constraints 603
32.2.4 Quadratic and Log Functions 605
Exercises 607
c h a p t e r 33 Probability and Expectation 613
33.1 Probability 613
33.1.1 Independence and Conditional Probability 617
33.2 Random Variables and Expectation 618
33.2.1 Conditional Expectation 619
Exercises 621
c h a p t e r 34 Utility and Expected Utility 625
34.1 Decision Making Under Certainty 625
34.2 Decision Making Under Uncertainty 628
34.2.1 Expected Utility Theorem and the Expected Return Puzzle 629
34.2.2 Details on the von Neumann–Morgenstern Theorem 631
34.2.3 Payoffs in a Game 633
34.3 Risk Aversion 633
Exercises 636
c h a p t e r 35 Existence of Nash Equilibria 641
35.1 Definition and Examples 641
35.1.1 Mathematical Background: Fixed Points 643
35.2 Existence of Nash Equilibria: Results and Intuition 648
Exercises 651
Index 655
This widely used introduction to game theory is rigorous but accessible, unique in its balance between the theoretical and the practical, with examples and applications following almost every theory-driven chapter. In recent years, game theory has become an important methodological tool for all fields of social sciences, biology and computer science. This second edition of Strategies and Games not only takes into account new game theoretical concepts and applications such as bargaining and matching, it also provides an array of chapters on game theory applied to the political arena. New examples, case studies, and applications relevant to a wide range of behavioral disciplines are now included. The authors map out alternate pathways through the book for instructors in economics, business, and political science.
The book contains four parts: strategic form games, extensive form games, asymmetric information games, and cooperative games and matching. Theoretical topics include dominance solutions, Nash equilibrium, Condorcet paradox, backward induction, subgame perfection, repeated and dynamic games, Bayes-Nash equilibrium, mechanism design, auction theory, signaling, the Shapley value, and stable matchings. Applications and case studies include OPEC, voting, poison pills, Treasury auctions, trade agreements, pork-barrel spending, climate change, bargaining and audience costs, markets for lemons, and school choice. Each chapter includes concept checks and tallies end-of-chapter problems. An appendix offers a thorough discussion of single-agent decision theory, which underpins game theory. Taken from the Publisher site.
9780262046527 $125.00 0262041693
Equilibrium (Economics)
Game theory
Games of strategy (Mathematics)
330.015193 / DUT , A4/2 23
Strategies and games : theory and practice / Prajit K Dutta and Wouter Vergote. - 2nd Ed. - Cambridge : MIT Press, 2022 - xxxiv, 671p. ; 23cm.
P A R T O N E Introduction 1
c h a p t e r 1 A First Look at the Applications 3
1.1 Games That We Play 3
1.2 Background 8
1.3 Examples 10
Exercises 15
c h a p t e r 2 A First Look at the Theory 21
2.1 Rules of the Game: Background 21
2.2 Who, What, When: The Extensive Form 23
2.2.1 Information Sets and Strategies 24
2.3 Who, What, When: The Normal (or Strategic) Form 26
2.4 How Much: Von Neumann–Morgenstern Utility Function 28
2.5 Representation of the Examples 30
Exercises 33
P A R T T W O Strategic Form Games: Theory and Practice 39
c h a p t e r 3 Strategic Form Games and Dominant Strategies 41
3.1 Strategic Form Games 41
3.1.1 Examples 42
3.1.2 Equivalence with the Extensive Form 45
3.2 Case Study: The Strategic Form of Art Auctions 46
3.2.1 Art Auctions: A Description 46
3.2.2 Art Auctions: The Strategic Form 47
3.3 Dominant Strategy Solution 48
3.4 Case Study Again: A Dominant Strategy at the Auction 50
Exercises 52
c h a p t e r 4 Dominance Solvability 57
4.1 The Idea 57
4.1.1 Dominated and Undominated Strategies 57
4.1.2 Iterated Elimination of Dominated Strategies 59
4.1.3 More Examples 60
4.2 Case Study: Electing The United Nations
Secretary-General 63
4.3 A More Formal Definition 64
4.4 A Discussion 66
Exercises 68
c h a p t e r 5 Nash Equilibrium 75
5.1 The Concept 75
5.1.1 Intuition and Definition 75
5.1.2 Nash Parables 77
5.2 Examples 79
5.3 Case Study: Nash Equilibrium in the Animal Kingdom 81
5.4 Relation Between the Solution Concepts 83
Exercises 85
c h a p t e r 6 An Application: Cournot Duopoly 89
6.1 Background 89
6.2 The Basic Model 90
6.3 Cournot Nash Equilibrium 91
6.4 Cartel Solution 93
6.5 Case Study: OPEC 95
6.6 Variants on the Main Theme I: A Graphical Analysis 97
6.6.1 The IEDS Solution to the Cournot Model 99
6.7 Variants on the Main Theme II: Stackelberg Model 100
6.8 Variants on the Main Theme III: Generalization 101
Exercises 103
c h a p t e r 7 Voting and Elections 107
7.1 Elections, Voting, and Game Theory 107
7.2 Voting Procedures 108
7.2.1 Majority Voting 108
7.2.2 Agenda Setting: an Example 109
7.3 Individual Rationality versus Collective Rationality 110
7.3.1 The Condorcet Paradox 110
7.3.2 A Way Out: Single-Peaked Preferences 111
7.3.3 Beyond the Condorcet Paradox 114
7.4 Competing for Votes 114
7.4.1 The Hotelling-Downs Model of Political Competition 114
7.4.2 Courting the Median Voter 115
7.4.3 Discussion 117
7.5 More on Voting Procedures 117
Exercises 119
c h a p t e r 8 An Application: The Commons Problem 125
8.1 Background: What Is the Commons? 125
8.2 A Simple Model 127
8.3 Social Optimality 129
8.4 The Problem Worsens in a Large Population 130
8.5 Case Study: Global Warming 131
8.6 Averting a Tragedy 133
Exercises 135
c h a p t e r 9 Mixed Strategies 139
9.1 Definition and Examples 139
9.1.1 What Is a Mixed Strategy? 139
9.1.2 Yet More Examples 142
9.2 An Implication 144
9.3 Mixed Strategies Can Dominate Some Pure Strategies 145
9.3.1 Implications for Dominant Strategy Solution and IEDS 146
9.4 Mixed Strategies Are Good for Bluffing 147
9.5 Mixed Strategies and Nash Equilibrium 148
9.5.1 Mixed-Strategy Nash Equilibria in an Example 150
9.6 Case Study: Random Drug Testing 151
Exercises 153
c h a p t e r 10 Two Applications: Natural Monopoly and Bankruptcy Law 161
10.1 Chicken, Symmetric Games, and Symmetric Equilibria 161
10.1.1 Chicken 161
10.1.2 Symmetric Games and Symmetric Equilibria 162
10.2 Natural Monopoly 164
10.2.1 The Economic Background 164
10.2.2 A Simple Example 164
10.2.3 War of Attrition and a General Analysis 166
10.3 Bankruptcy Law 168
10.3.1 The Legal Background 168
10.3.2 A Numerical Example 168
10.3.3 A General Analysis 170
Exercises 173
c h a p t e r 11 Zero-Sum Games 179
11.1 Definition And Examples 179
11.2 Playing Safe: Maxmin 182
11.2.1 The Concept 182
11.2.2 Examples 183
11.3 Playing Sound: Minmax 185
11.3.1 The Concept and Examples 185
11.3.2 Two Results 187
11.4 Playing Nash: Playing Both Safe and Sound 188
Exercises 190
c h a p t e r 12 Extensive Form Games and Backward Induction 201
12.1 The Extensive Form 201
12.1.1 A More Formal Treatment 203
12.1.2 Strategies, Mixed Strategies, and Chance Nodes 205
12.2 Perfect Information Games: Definition and Examples 206
12.3 Backward Induction: Examples 209
12.3.1 The Power of Commitment 211
12.4 Backward Induction: A General Result 213
12.5 Connection With IEDS in the Strategic Form 215
12.6 Case Study: Poison Pills as a Vaccine Against Takeovers 217
Exercises 219
c h a p t e r 13 An Application: Research and Development 225
13.1 Background: R&D, Patents, and Oligopolies 225
13.1.1 A Patent Race: 8K Television 226
13.2 A Model of R&D 227
13.3 Backward Induction: Analysis of the Model 229
13.4 Some Remarks 234
Exercises 236
c h a p t e r 14 Subgame Perfect Equilibrium 239
14.1 A Motivating Example 239
14.2 Subgames and Strategies within Subgames 242
14.3 Subgame Perfect Equilibrium 244
14.4 Two More Examples 245
14.5 Some Remarks 248
14.6 Case Study: Peace in the World War I Trenches 249
Exercises 251
c h a p t e r 15 Finitely Repeated Games 257
15.1 Examples and Applications 257
15.1.1 Three Repeated Games and a Definition 257
15.1.2 Six Applications 260
15.2 Finitely Repeated Games 263
15.2.1 Some General Conclusions 267
15.3 Case Study: Treasury Bill Auctions 268
Exercises 272
c h a p t e r 16 Infinitely Repeated Games 277
16.1 Detour Through Discounting 277
16.2 Analysis of Example 3: Trigger Strategies and
Good Behavior 279
16.3 The Folk Theorem 282
16.4 Repeated Games with Imperfect Detection 285
Exercises 288
c h a p t e r 17 An Application: Competition and Collusion in the NASDAQ
Stock Market 295
17.1 The Background 295
17.2 The Analysis 297
17.2.1 A Model of the NASDAQ Market 297
17.2.2 Collusion 298
17.2.3 More on Collusion 300
17.3 The Broker-Dealer Relationship 302
17.3.1 Order Preferencing 302
17.3.2 Dealers Big and Small 302
17.4 The Epilogue 304
Exercises 305
c h a p t e r 18 An Application: OPEC 309
18.1 Oil: A Historical Review 309
18.1.1 Production and Price History 310
18.2 A Simple Model of the Oil Market 312
18.3 Oil Prices and the Role of OPEC 314
18.4 Repeated Games with Demand Uncertainty 316
18.5 Unobserved Quota Violations 320
18.6 Some Further Comments 323
Exercises 325
c h a p t e r 19 An Application: Logrolling and Pork-Barrel Spending 329
19.1 Earmarks, Pork, and Logrolling 329
19.2 A Simple Model of Earmark Spending 331
19.3 Bringing Home the Bacon with Grim Trigger Strategies 333
19.3.1 Equilibrium Conditions 333
19.3.2 Comparative Statics 335
19.4 When Bygones are Bygones 336
19.4.1 Renegotiation: A Good Idea? 336
19.4.2 Hoisted by Your Own Petard? Renegotiation Proofness 336
19.4.3 Penance Strategy: Renegotiation Proofness 337
19.4.4 Penance Strategy: Subgame Perfection 339
Exercises 341
c h a p t e r 20 An Application: Trade Agreements 345
20.1 The Purpose of Trade Agreements 345
20.2 A Tariff-Setting Game 346
20.2.1 Free Trade 347
20.2.2 Tariffs 347
20.2.3 Government Welfare and the Nash Equilibrium 349
20.2.4 The Prisoner’s Dilemma 351
20.3 The Repeated Game and the Design of Trade Agreements 352
20.4 Flexible Trade Agreements 354
20.4.1 Free Trade Agreement with No Flexibility 355
20.4.2 Free Trade Agreement with an Escape Clause 356
Exercises 359
c h a p t e r 21 Dynamic Games with an Application to Global Warming 363
21.1 Dynamic Games: A Prologue 363
21.2 A Global Warming Game 365
21.3 Greenhouse Gas Emissions: Global Optimum 367
21.3.1 A Computation of the Global Optimum 367
21.3.2 An Explanation of the Global Optimum 371
21.3.3 Recommended Global Optimum GHG Levels 372
21.4 Business as Usual Emission Level and Game Equilibrium 372
21.4.1 A Computation of the BAU Equilibrium 373
21.4.2 An Explanation of the BAU Emission Levels 375
21.4.3 A Comparison of the Globally Optimal and the BAU Outcomes 376
21.4.4 Special Feature of the Globally Optimal and BAU Strategies 378
21.5 Dynamic Games: An Epilogue 379
Exercises 381
c h a p t e r 22 Strategic Bargaining 385
22.1 Introduction 385
22.1.1 Tales of Bargaining 385
22.1.2 The Bargaining Problem and Bargaining Theory 386
22.2 Unanimity Bargaining: Negotiating a Merger Deal 388
22.2.1 Two-Stage Negotiations 389
22.2.2 Three-Stage Negotiations 390
22.2.3 Discussion 391
22.3 A Generalization: Sequential Bargaining with
a Finite Horizon 392
22.3.1 The Unique Subgame Perfect Equilibrium 392
22.3.2 Some Observations 394
22.3.3 Experimental Evidence: The Ultimatum Game 395
22.4 Legislative Bargaining 396
22.4.1 Three Legislators and Two-Stage Negotiations 396
22.4.2 N Legislators and Two-Stage Negotiations 397
22.4.3 Qualified Majority Rule 397
22.5 Epilogue: Costly Bargaining and Conflict 398
Exercises 399
P A R T F O U R Asymmetric Information Games: Theory
and Applications 403
c h a p t e r 23 Moral Hazard and Incentives Theory 405
23.1 Moral Hazard: Examples and a Definition 405
23.2 A Principal-Agent Model 407
23.2.1 Some Examples of Incentive Schemes 409
23.3 The Optimal Incentive Scheme 411
23.3.1 No Moral Hazard 411
23.3.2 Moral Hazard 412
23.4 Some General Conclusions 413
23.4.1 Extensions and Generalizations 415
23.5 Case Study: The Rise and Fall of Capitation to
Compensate Primary Care Physicians in an HMO 416
Exercises 419
c h a p t e r 24 Games with Incomplete Information 423
24.1 Some Examples 423
24.1.1 Some Analysis of the Examples 427
24.2 A Complete Analysis of Example 4 428
24.2.1 Bayes-Nash Equilibrium 428
24.2.2 Pure-Strategy Bayes-Nash 430
24.2.3 Mixed-Strategy Bayes-Nash Equilibria 430
24.3 More General Considerations 433
24.3.1 A Modified Example 433
24.3.2 A General Framework 435
24.4 Dominance-Based Solution Concepts 436
24.5 Case Study: “Final Jeopardy!” 439
Exercises 442
c h a p t e r 25 Mechanism Design, the Revelation Principle, and Sales
to an Unknown Buyer 447
25.1 Mechanism Design: The Economic Context 447
25.2 A Simple Example: Selling to a Buyer with an
Unknown Valuation 449
25.2.1 Known Passion 450
25.2.2 Unknown Passion 450
25.3 Mechanism Design and the Revelation Principle 454
25.3.1 Single Player 454
25.3.2 Many Players 456
25.4 A More General Example: Selling Variable Amounts 457
25.4.1 Known Type 457
25.4.2 Unknown Type 458
Exercises 461
c h a p t e r 26 An Application: Auctions 465
26.1 Background and Examples 465
26.1.1 Basic Model 467
26.2 Second-Price Auctions 467
26.3 First-Price Auctions 469
26.4 Optimal Auctions 471
26.4.1 How Well Do the First- and Second-Price Auctions Do? 473
26.5 Final Remarks 475
Exercises 476
c h a p t e r 27 An Application: Price Competition with Cost Uncertainty 481
27.1 A Procurement Procedure 481
27.1.1 Bayes-Nash Equilibrium: Preliminary Observations 482
27.1.2 Bayes-Nash Equilibrium 484
27.2 Bridging Price Competition and Auctions 490
27.2.1 First-Price Sealed-Bid Auction 490
27.2.2 Key Takeaway 492
27.3 Bertrand Price Competition with Incomplete
Information 492
Exercises 496
c h a p t e r 28 Signaling Games and the Lemons Problem 501
28.1 Motivation and Two Examples 501
28.1.1 A First Analysis of the Examples 504
28.2 A Definition, an Equilibrium Concept, and Examples 505
28.2.1 Definition 505
28.2.2 Perfect Bayesian Equilibrium 506
28.2.3 A Further Analysis of the Examples 508
28.3 Signaling Product Quality 509
28.3.1 The Bad Can Drive Out the Good 510
28.3.2 Good Can Signal Quality 511
28.4 Case Study: Used Cars—A Market for Lemons? 513
28.5 Concluding Remarks 514
Exercises 516
c h a p t e r 29 An Application: Crisis Bargaining and Escalation 521
29.1 Tales of Conflict 521
29.2 Unknown Military Strength and War 523
29.2.1 Complete Information: No War 523
29.2.2 Incomplete Information: Bayes-Nash Equilibrium 523
29.3 To Bluff or not to Bluff? 525
29.3.1 Signaling Military Strength 525
29.3.2 In Search of Perfect Bayesian Equilibria That Lead to War 526
29.3.3 When Challenging Is a Costly Signal 529
29.4 Escalation and Audience Costs 530
29.4.1 Finding Perfect Bayesian Equilibria 531
29.5 Case Study: Audience Costs Drivers and
the Impact on Conflict 534
Exercises 537
P A R T F I V E Cooperative Games and Matching 541
c h a p t e r 30 Cooperative Games 543
30.1 Cooperative versus Noncooperative Games 543
30.1.1 A Tale of Two Games 543
30.1.2 Motivating Examples 544
30.2 Modeling Coalitional Games 546
30.2.1 Games with Transferable Utility 546
30.2.2 Games with Nontransferable Utility 548
30.2.3 Solution Concepts 549
30.3 Solution Concept I: Stability and the Core 550
30.4 Solution Concept II: The Shapley Value 554
Exercises 561
c h a p t e r 31 Matching Problems 567
31.1 Motivating Examples 567
31.1.1 How to Allocate Indivisible Goods without Prices? 570
31.2 One-To-One Matching Problems 570
31.2.1 Two-Sided One-to-One Matching Problems: Definitions 570
31.2.2 Two-Sided One-to-One Matching Problems: Stability 573
31.2.3 The Boy-Proposing Deferred Acceptance Algorithm 574
31.2.4 Boy-Optimal versus Girl-Optimal Stable Matchings 577
31.2.5 Strategic Behavior and Mechanism Design 579
31.3 One-Sided One-to-One Matching: The Roommate Problem 580
31.4 Many-to-One Two-Sided Matching Problems:
School Choice 582
31.4.1 Many-to-One Matching Problems: Definitions 582
31.4.2 Deferred Acceptance Algorithm 584
31.5 Epilogue: The Game Theorist as an Engineer 585
Exercises 586
P A R T S I X Foundations 593
c h a p t e r 32 Calculus and Optimization 595
32.1 A Calculus Primer 595
32.1.1 Functions 596
32.1.2 Slopes 598
32.1.3 Some Formulas 599
32.1.4 Concave Functions 600
32.2 An Optimization Theory Primer 601
32.2.1 Necessary Conditions 601
32.2.2 Sufficient Conditions 602
32.2.3 Feasibility Constraints 603
32.2.4 Quadratic and Log Functions 605
Exercises 607
c h a p t e r 33 Probability and Expectation 613
33.1 Probability 613
33.1.1 Independence and Conditional Probability 617
33.2 Random Variables and Expectation 618
33.2.1 Conditional Expectation 619
Exercises 621
c h a p t e r 34 Utility and Expected Utility 625
34.1 Decision Making Under Certainty 625
34.2 Decision Making Under Uncertainty 628
34.2.1 Expected Utility Theorem and the Expected Return Puzzle 629
34.2.2 Details on the von Neumann–Morgenstern Theorem 631
34.2.3 Payoffs in a Game 633
34.3 Risk Aversion 633
Exercises 636
c h a p t e r 35 Existence of Nash Equilibria 641
35.1 Definition and Examples 641
35.1.1 Mathematical Background: Fixed Points 643
35.2 Existence of Nash Equilibria: Results and Intuition 648
Exercises 651
Index 655
This widely used introduction to game theory is rigorous but accessible, unique in its balance between the theoretical and the practical, with examples and applications following almost every theory-driven chapter. In recent years, game theory has become an important methodological tool for all fields of social sciences, biology and computer science. This second edition of Strategies and Games not only takes into account new game theoretical concepts and applications such as bargaining and matching, it also provides an array of chapters on game theory applied to the political arena. New examples, case studies, and applications relevant to a wide range of behavioral disciplines are now included. The authors map out alternate pathways through the book for instructors in economics, business, and political science.
The book contains four parts: strategic form games, extensive form games, asymmetric information games, and cooperative games and matching. Theoretical topics include dominance solutions, Nash equilibrium, Condorcet paradox, backward induction, subgame perfection, repeated and dynamic games, Bayes-Nash equilibrium, mechanism design, auction theory, signaling, the Shapley value, and stable matchings. Applications and case studies include OPEC, voting, poison pills, Treasury auctions, trade agreements, pork-barrel spending, climate change, bargaining and audience costs, markets for lemons, and school choice. Each chapter includes concept checks and tallies end-of-chapter problems. An appendix offers a thorough discussion of single-agent decision theory, which underpins game theory. Taken from the Publisher site.
9780262046527 $125.00 0262041693
Equilibrium (Economics)
Game theory
Games of strategy (Mathematics)
330.015193 / DUT , A4/2 23