Strategies and Games, 2e

Theory and Practice

by Dutta, Vergote

| ISBN: 9780262368513 | Copyright 2022

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Prajit K. Dutta is Professor in the Department of Economics at Columbia University. Wouter Vergote is Lecturer in the Discipline Economics at Columbia University.

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.

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Contents (pg. ix)
Preface (pg. xxiii)
Part One. Introduction (pg. 1)
Chapter 1. A First Look at the Applications (pg. 3)
1.1 Games That We Play (pg. 3)
1.2 Background (pg. 8)
1.3 Examples (pg. 10)
Exercises (pg. 15)
Chapter 2. A First Look at the Theory (pg. 21)
2.1 Rules of the Game: Background (pg. 21)
2.2 Who, What, When: The Extensive Form (pg. 23)
2.3 Who, What, When: The Normal (or Strategic) Form (pg. 26)
2.4 How Much: Von Neumann–Morgenstern Utility Function (pg. 28)
2.5 Representation of the Examples (pg. 30)
Exercises (pg. 33)
Part Two. Strategic Form Games: Theory and Practice (pg. 39)
Chapter 3. Strategic Form Games and Dominant Strategies (pg. 41)
3.1 Strategic Form Games (pg. 41)
3.2 Case Study: The Strategic Form of Art Auctions (pg. 46)
3.3 Dominant Strategy Solution (pg. 48)
3.4 Case Study Again: A Dominant Strategy at the Auction (pg. 50)
Exercises (pg. 52)
Chapter 4. Dominance Solvability (pg. 57)
4.1 The Idea (pg. 57)
4.2 Case Study: Electing The United Nations Secretary-General (pg. 63)
4.3 A More Formal Definition (pg. 64)
4.4 A Discussion (pg. 66)
Exercises (pg. 68)
Chapter 5. Nash Equilibrium (pg. 75)
5.1 The Concept (pg. 75)
5.2 Examples (pg. 79)
5.3 Case Study: Nash Equilibrium in the Animal Kingdom (pg. 81)
5.4 Relation Between the Solution Concepts (pg. 83)
Exercises (pg. 85)
Chapter 6. An Application: Cournot Duopoly (pg. 89)
6.1 Background (pg. 89)
6.2 The Basic Model (pg. 90)
6.3 Cournot Nash Equilibrium (pg. 91)
6.4 Cartel Solution (pg. 93)
6.5 Case Study: OPEC (pg. 95)
6.6 Variants on the Main Theme I: A Graphical Analysis (pg. 97)
6.7 Variants on the Main Theme II: Stackelberg Model (pg. 100)
6.8 Variants on the Main Theme III: Generalization (pg. 101)
Exercises (pg. 103)
Chapter 7. Voting and Elections (pg. 107)
7.1 Elections, Voting, and Game Theory (pg. 107)
7.2 Voting Procedures (pg. 108)
7.3 Individual Rationality versus Collective Rationality (pg. 110)
7.4 Competing for Votes (pg. 114)
7.5 More on Voting Procedures (pg. 117)
Exercises (pg. 119)
Chapter 8. An Application: The Commons Problem (pg. 125)
8.1 Background: What Is the Commons? (pg. 125)
8.2 A Simple Model (pg. 127)
8.3 Social Optimality (pg. 129)
8.4 The Problem Worsens in a Large Population (pg. 130)
8.5 Case Study: Global Warming (pg. 131)
8.6 Averting a Tragedy (pg. 133)
Exercises (pg. 135)
Chapter 9. Mixed Strategies (pg. 139)
9.1 Definition and Examples (pg. 139)
9.2 An Implication (pg. 144)
9.3 Mixed Strategies Can Dominate Some Pure Strategies (pg. 145)
9.4 Mixed Strategies Are Good for Bluffing (pg. 147)
9.5 Mixed Strategies and Nash Equilibrium (pg. 148)
9.6 Case Study: Random Drug Testing (pg. 151)
Exercises (pg. 153)
Chapter 10. Two Applications: Natural Monopoly and Bankruptcy Law (pg. 161)
10.1 Chicken, Symmetric Games, and Symmetric Equilibria (pg. 161)
10.2 Natural Monopoly (pg. 164)
10.3 Bankruptcy Law (pg. 168)
Exercises (pg. 173)
Chapter 11. Zero-SumGames (pg. 179)
11.1 Definition And Examples (pg. 179)
11.2 Playing Safe: Maxmin (pg. 182)
11.3 Playing Sound: Minmax (pg. 185)
11.4 Playing Nash: Playing Both Safe and Sound (pg. 188)
Exercises (pg. 190)
Part Three. Extensive Form Games: Theory and Applications (pg. 199)
Chapter 12. Extensive Form Games and Backward Induction (pg. 201)
12.1 The Extensive Form (pg. 201)
12.2 Perfect Information Games: Definition and Examples (pg. 206)
12.3 Backward Induction: Examples (pg. 209)
12.4 Backward Induction: A General Result (pg. 213)
12.5 Connection With IEDS in the Strategic Form (pg. 215)
12.6 Case Study: Poison Pills as a Vaccine Against Takeovers (pg. 217)
Exercises (pg. 219)
Chapter 13. An Application: Research and Development (pg. 225)
13.1 Background: R&D, Patents, and Oligopolies (pg. 225)
13.2 A Model of R&D (pg. 227)
13.3 Backward Induction: Analysis of the Model (pg. 229)
13.4 Some Remarks (pg. 234)
Exercises (pg. 236)
Chapter 14. Subgame Perfect Equilibrium (pg. 239)
14.1 A Motivating Example (pg. 239)
14.2 Subgames and Strategies within Subgames (pg. 242)
14.3 Subgame Perfect Equilibrium (pg. 244)
14.4 Two More Examples (pg. 245)
14.5 Some Remarks (pg. 248)
14.6 Case Study: Peace in the World War I Trenches (pg. 249)
Exercises (pg. 251)
Chapter 15. Finitely Repeated Games (pg. 257)
15.1 Examples and Applications (pg. 257)
15.2 Finitely Repeated Games (pg. 263)
15.3 Case Study: Treasury Bill Auctions (pg. 268)
Exercises (pg. 272)
Chapter 16. Infinitely Repeated Games (pg. 277)
16.1 Detour Through Discounting (pg. 277)
16.2 Analysis of Example 3: Trigger Strategies and Good Behavior (pg. 279)
16.3 The Folk Theorem (pg. 282)
16.4 Repeated Games with Imperfect Detection (pg. 285)
Exercises (pg. 288)
Chapter 17. An Application: Competition and Collusion in the NASDAQ Stock Market (pg. 295)
17.1 The Background (pg. 295)
17.2 The Analysis (pg. 297)
17.3 The Broker-Dealer Relationship (pg. 302)
17.4 The Epilogue (pg. 304)
Exercises (pg. 305)
Chapter 18. An Application: OPEC (pg. 309)
18.1 Oil: A Historical Review (pg. 309)
18.2 A Simple Model of the Oil Market (pg. 312)
18.3 Oil Prices and the Role of OPEC (pg. 314)
18.4 Repeated Games with Demand Uncertainty (pg. 316)
18.5 Unobserved Quota Violations (pg. 320)
18.6 Some Further Comments (pg. 323)
Exercises (pg. 325)
Chapter 19. An Application: Logrolling and Pork-Barrel Spending (pg. 329)
19.1 Earmarks, Pork, and Logrolling (pg. 329)
19.2 A Simple Model of Earmark Spending (pg. 331)
19.3 Bringing Home the Bacon with Grim Trigger Strategies (pg. 333)
19.4 When Bygones are Bygones (pg. 336)
Exercises (pg. 341)
Chapter 20. An Application: Trade Agreements (pg. 345)
20.1 The Purpose of Trade Agreements (pg. 345)
20.2 A Tariff-Setting Game (pg. 346)
20.3 The Repeated Game and the Design of Trade Agreements (pg. 352)
20.4 Flexible Trade Agreements (pg. 354)
Exercises (pg. 359)
Chapter 21. Dynamic Games with an Application to Global Warming (pg. 363)
21.1 Dynamic Games: A Prologue (pg. 363)
21.2 A Global Warming Game (pg. 365)
21.3 Greenhouse Gas Emissions: Global Optimum (pg. 367)
21.4 Business as Usual Emission Level and Game Equilibrium (pg. 372)
21.5 Dynamic Games: An Epilogue (pg. 379)
Exercises (pg. 381)
Chapter 22. Strategic Bargaining (pg. 385)
22.1 Introduction (pg. 385)
22.2 Unanimity Bargaining: Negotiating a Merger Deal (pg. 388)
22.3 A Generalization: Sequential Bargaining with a Finite Horizon (pg. 392)
22.4 Legislative Bargaining (pg. 396)
22.5 Epilogue: Costly Bargaining and Conflict (pg. 398)
Exercises (pg. 399)
Part Four. Asymmetric Information Games: Theory and Applications (pg. 403)
Chapter 23. Moral Hazard and Incentives Theory (pg. 405)
23.1 Moral Hazard: Examples and a Definition (pg. 405)
23.2 A Principal-Agent Model (pg. 407)
23.3 The Optimal Incentive Scheme (pg. 411)
23.4 Some General Conclusions (pg. 413)
23.5 Case Study: The Rise and Fall of Capitation to Compensate Primary Care Physicians in an HMO (pg. 416)
Exercises (pg. 419)
Chapter 24. Games with Incomplete Information (pg. 423)
24.1 Some Examples (pg. 423)
24.2 A Complete Analysis of Example 4 (pg. 428)
24.3 More General Considerations (pg. 433)
24.4 Dominance-Based Solution Concepts (pg. 436)
24.5 Case Study: “Final Jeopardy!" (pg. 439)
Exercises (pg. 442)
Chapter 25. Mechanism Design, the Revelation Principle, and Sales to an Unknown Buyer (pg. 447)
25.1 Mechanism Design: The Economic Context (pg. 447)
25.2 A Simple Example: Selling to a Buyer with an Unknown Valuation (pg. 449)
25.3 Mechanism Design and the Revelation Principle (pg. 454)
25.4 A More General Example: Selling Variable Amounts (pg. 457)
Exercises (pg. 461)
Chapter 26. An Application: Auctions (pg. 465)
26.1 Background and Examples (pg. 465)
26.2 Second-Price Auctions (pg. 467)
26.3 First-Price Auctions (pg. 469)
26.4 Optimal Auctions (pg. 471)
26.5 Final Remarks (pg. 475)
Exercises (pg. 476)
Chapter 27. An Application: Price Competition with Cost Uncertainty (pg. 481)
27.1 A Procurement Procedure (pg. 481)
27.2 Bridging Price Competition and Auctions (pg. 490)
27.3 Bertrand Price Competition with Incomplete Information (pg. 492)
Exercises (pg. 496)
Chapter 28. Signaling Games and the Lemons Problem (pg. 501)
28.1 Motivation and Two Examples (pg. 501)
28.2 A Definition, an Equilibrium Concept, and Examples (pg. 505)
28.3 Signaling Product Quality (pg. 509)
28.4 Case Study: Used Cars—A Market for Lemons? (pg. 513)
28.5 Concluding Remarks (pg. 514)
Exercises (pg. 516)
Chapter 29. An Application: Crisis Bargaining and Escalation (pg. 521)
29.1 Tales of Conflict (pg. 521)
29.2 Unknown Military Strength and War (pg. 523)
29.3 To Bluff or not to Bluff? (pg. 525)
29.4 Escalation and Audience Costs (pg. 530)
29.5 Case Study: Audience Costs Drivers and the Impact on Conflict (pg. 534)
Exercises (pg. 537)
Part Five. Cooperative Games and Matching (pg. 541)
Chapter 30. Cooperative Games (pg. 543)
30.1 Cooperative versus Noncooperative Games (pg. 543)
30.2 Modeling Coalitional Games (pg. 546)
30.3 Solution Concept I: Stability and the Core (pg. 550)
30.4 Solution Concept II: The Shapley Value (pg. 554)
Exercises (pg. 561)
Chapter 31. Matching Problems (pg. 567)
31.1 Motivating Examples (pg. 567)
31.2 One-To-One Matching Problems (pg. 570)
31.3 One-Sided One-to-One Matching: The Roommate Problem (pg. 580)
31.4 Many-to-One Two-Sided Matching Problems: School Choice (pg. 582)
31.5 Epilogue: The Game Theorist as an Engineer (pg. 585)
Exercises (pg. 586)
Part Six. Foundations (pg. 593)
Chapter 32. Calculus and Optimization (pg. 595)
32.1 A Calculus Primer (pg. 595)
32.2 An Optimization Theory Primer (pg. 601)
Exercises (pg. 607)
Chapter 33. Probability and Expectation (pg. 613)
33.1 Probability (pg. 613)
33.2 Random Variables and Expectation (pg. 618)
Exercises (pg. 621)
Chapter 34. Utility and Expected Utility (pg. 625)
34.1 Decision Making Under Certainty (pg. 625)
34.2 Decision Making Under Uncertainty (pg. 628)
34.3 Risk Aversion (pg. 633)
Exercises (pg. 636)
Chapter 35. Existence of Nash Equilibria (pg. 641)
35.1 Definition and Examples (pg. 641)
35.2 Existence of Nash Equilibria: Results and Intuition (pg. 648)
Exercises (pg. 651)
Index (pg. 655)

Prajit K. Dutta

Prajit Dutta is Professor in the Department of Economics at Columbia University.

Wouter Vergote

Wouter Vergote is Lecturer in the Discipline Economics at Columbia University.

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