Game Theory and Behavior

by Carpenter, Robbett

| ISBN: 9780262371261 | Copyright 2022

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An introduction to game theory that offers not only theoretical tools but also the intuition and behavioral insights to apply these tools to real-world situations.

This introductory text on game theory provides students with both the theoretical tools to analyze situations through the logic of game theory and the intuition and behavioral insights to apply these tools to real-world situations. It is unique among game theory texts in offering a clear, formal introduction to standard game theory while incorporating evidence from experimental data and introducing recent behavioral models. Students will not only learn about incentives, how to represent situations as games, and what agents “should” do in these situations, but they will also be presented with evidence that either confirms the theoretical assumptions or suggests a way in which the theory might be updated.

Each chapter begins with a motivating example that can be run as an experiment and ends with a discussion of the behavior in the example. Parts I–IV cover the fundamental “nuts and bolts” of any introductory game theory course, including the theory of games, simple games with simultaneous decision making by players, sequential move games, and incomplete information in simultaneous and sequential move games. Parts V–VII apply the tools developed in previous sections to bargaining, cooperative game theory, market design, social dilemmas, and social choice and voting, while part VIII offers a more in-depth discussion of behavioral game theory models including evolutionary and psychological game theory. A website offers solutions to end-of-chapter exercises, a manual for running each chapter's experimental games using pencil and paper, and the oTree codes for running the games online.

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Contents (pg. v)
I. Introduction to the Theory of Games (pg. 1)
1. Games of Strategy (pg. 3)
What Is Game Theory? (pg. 3)
Individual versus Game Theoretic Decision Making (pg. 5)
Theory of Mind (pg. 8)
Thinking Strategically: Reasoning about the Reasoning of Others (pg. 9)
This Book (pg. 15)
2. Game Representations (pg. 19)
The Elements of a Game (pg. 19)
Background Assumptions (pg. 21)
Extensive Form Games (pg. 23)
Normal Form Games (pg. 26)
Strategy Profiles and Payoffs (pg. 32)
Exercises (pg. 33)
II. Solving Games (pg. 39)
3. Dominated Strategies (pg. 41)
The Logic of Dominance (pg. 41)
How Far Can Dominance Take Us? (pg. 49)
Example (pg. 51)
Behavior in Games: Playing Dominated Strategies (pg. 56)
Exercises (pg. 61)
4. Equilibrium (pg. 65)
Zero-Sum Games without Dominance (pg. 66)
Solving Games Using the Maximin/Minimax Approach (pg. 67)
General-Sum Games and the Collapse of the Minimax Approach (pg. 73)
Nash's Contribution (pg. 74)
Exercises (pg. 80)
5. Mixed Strategies (pg. 85)
The Trouble with Perfect Foresight (pg. 85)
When Best Responding Involves Risk (pg. 88)
Mixed-Strategy Nash Equilibrium (pg. 92)
Solving for Mixed-Strategy Nash Equilibria (pg. 93)
Best Responding, Dominated Strategies, and Rationalizability (pg. 97)
Behavior in Games (pg. 100)
Exercises (pg. 104)
6. Equilibrium in Nonmatrix Games (pg. 107)
Nonmatrix Games and Their Solutions (pg. 107)
Demanding an Infinitely Divisible Cake (pg. 108)
The Bertrand Pricing Game (pg. 110)
Expanding the Strategy Set in the Traveler's Dilemma (pg. 113)
Finding Best Response Functions Using Calculus (pg. 114)
The Cournot Duopoly (pg. 117)
n-Player Games with Discrete Strategies (pg. 119)
n-Player Games with Continuous Strategies (pg. 123)
Behavior in Games: Do Travelers Think of a Lost Bag as a Dilemma? (pg. 125)
Exercises (pg. 132)
7. Equilibrium Selection (pg. 137)
Payoff-Based Selection Criteria (pg. 140)
Focal Points (pg. 144)
Forward Induction (pg. 145)
Correlated Equilibrium (pg. 145)
Behavior in Games: Equilibrium Selection in Coordination Games (pg. 148)
Exercises (pg. 154)
III. Analyzing Sequential-Move Games (pg. 159)
8. Subgame Perfection (pg. 161)
Nonsensical Nash Equilibria in Sequential Games (pg. 161)
Subgame Perfect Nash Equilibria (pg. 165)
Solving for Subgame Perfect Nash Equilibria Using Backward Induction (pg. 166)
Continuous Games (pg. 169)
Games of Imperfect Information (pg. 171)
Behavior in Games (pg. 174)
Exercises (pg. 178)
9. Finitely Repeated Games (pg. 183)
Definitions (pg. 184)
Finitely Repeated Games with a Single Stage Equilibrium (pg. 185)
Finitely Repeated Games with Multiple Stage Equilibria (pg. 188)
Behavior in Games—Playing (Un?)ravelled Strategies (pg. 193)
Exercises (pg. 200)
10. Infinitely Repeated Games (pg. 205)
Discounted Utility (pg. 206)
Equilibria in Infinitely Repeated Games (pg. 209)
Subgame Perfection and the One-Stage Deviation Principle (pg. 212)
The Folk Theorem (pg. 214)
Behavior in Games—Playing ``Anything Goes'' Strategies (pg. 216)
Exercises (pg. 220)
IV. Incomplete Information (pg. 223)
11. Simultaneous Games of Incomplete Information (pg. 225)
The Conditional Cooperator's Dilemma (pg. 226)
Solving for Bayesian Nash Equilibria (pg. 229)
Continuous Strategies (pg. 234)
The Acquiring a Company Game and the Market for Lemons (pg. 236)
Behavior in Games (pg. 237)
Will Information Be Revealed? (pg. 240)
Exercises (pg. 241)
12. Signaling: Sequential Games of Incomplete Information (pg. 245)
Sequential Games of Incomplete Information (pg. 246)
Updating Beliefs (pg. 249)
Finding Perfect Bayesian Equilibria in Costly Signaling Games (pg. 255)
Perfect Bayesian Equilibria in Cheap Talk Games (pg. 264)
Behavior in Games (pg. 266)
Exercises (pg. 271)
13. Auctions (pg. 277)
A Typography of Auction Formats (pg. 278)
Private Value Auction Preliminaries (pg. 279)
Private Value Auctions with Two Bidders (pg. 281)
A More General Analysis Is Needed (pg. 284)
The All-Pay Auction (pg. 287)
Revenue Equivalence (pg. 288)
Private Value Auctions with n Bidders (pg. 292)
Common Value Auctions (pg. 294)
Behavior in Games—Revenue Nonequivalence? (pg. 297)
Evidence-Based Adaptations of the Standard Model (pg. 301)
Exercises (pg. 302)
V. Bargaining and Cooperative Game Theory (pg. 305)
14. Non-cooperative Bargaining (pg. 307)
The Bargaining Problem (pg. 308)
The Ultimatum Game (pg. 311)
Alternating Offers (pg. 312)
Bargaining in Committees: The Baron-Ferejohn Legislative Bargaining Model (pg. 319)
Behavior in Games (pg. 320)
Exercises (pg. 327)
15. Cooperative Bargaining (pg. 331)
Cooperative Versus Non-cooperative Bargaining (pg. 332)
The Nash Bargaining Solution (pg. 335)
Alternative Solutions to the Cooperative Bargaining Problem (pg. 338)
Behavior in Games—Which of Nash's Axioms Seem to Resonate with Bargainers? (pg. 342)
Evidence-Based Adaptations of the Standard Model (pg. 344)
Exercises (pg. 345)
16. Cooperative Game Theory (pg. 347)
Cooperative Games (pg. 348)
Coalitions and Values (pg. 350)
Distributing Payoffs: The Core (pg. 353)
Distributing Payoffs: Shapley Value (pg. 359)
Behavior in Games (pg. 365)
Exercises (pg. 368)
17. Matching Market Design (pg. 371)
Matching Markets (pg. 373)
One-Sided Matching Markets (pg. 375)
Two-Sided Matching (pg. 379)
School Choice (pg. 383)
Behavior in Games (pg. 388)
Exercises (pg. 392)
VI. Social Dilemmas (pg. 395)
18. Social Dilemmas (pg. 397)
The Trust Game (pg. 398)
Social Dilemmas (pg. 399)
Continuous Social Dilemmas (pg. 401)
Behavior in Games—Trust, Reciprocity, and Efficiency (pg. 403)
Exercises (pg. 407)
19. Public Goods (pg. 411)
The Logic of Public Goods (pg. 411)
Exogenous Mechanisms to Increase Contributions (pg. 414)
Endogenous Mechanisms to Increase Contributions (pg. 417)
Behavior in Games—Contributions to a Public Good (pg. 418)
Exercises (pg. 424)
20. Common Pool Resources (pg. 427)
Common Pool Resources and the Tragedy of the Commons (pg. 428)
A Static Common Pool Resource Game (pg. 430)
Dynamic Common Pool Resource Games (pg. 434)
Governing the Commons (pg. 440)
Behavior in Games (pg. 442)
Exercises (pg. 448)
VII. Social Choice and Voting (pg. 451)
21. Social Choice (pg. 453)
Determining a Group's Preference Ranking (pg. 454)
Voting Rules Affect the Outcome (pg. 458)
Arrow's Impossibility Theorem (pg. 461)
Spatial Voting (pg. 462)
Strategic Voting (pg. 471)
Candidate Competition Games (pg. 476)
Behavior in Games (pg. 480)
Exercises (pg. 487)
22. The Paradox of Voting (pg. 491)
The Calculus of Voting (pg. 491)
Voter Turnout as a Participation Game (pg. 494)
Mixed-Strategy Nash Equilibria in the Participation Game (pg. 496)
The Participation Game with Incomplete Information (pg. 500)
Behavior in Games (pg. 502)
Exercises (pg. 508)
23. Voting with Private Information (pg. 511)
Voting to Aggregate Information (pg. 512)
The Jury Game (pg. 513)
Voting Strategically against Your Own Evidence (pg. 515)
Bayesian Nash Equilibria: Convicting the Innocent under Unanimity (pg. 518)
The Swing Voter's Curse (pg. 520)
Costly Information Acquisition and Rational Ignorance (pg. 524)
Behavior in Games (pg. 526)
Exercises (pg. 529)
VIII. Behavioral Extensions of Standard Theory (pg. 531)
24. Belief-Based Learning (pg. 533)
Best Response Dynamics (pg. 534)
Fictitious Play (pg. 537)
Behavior in Games—Are Adaptive Beliefs Enough? (pg. 540)
Exercises (pg. 542)
25. Evolutionary Game Theory (pg. 545)
Replicator Dynamics (pg. 546)
Asymmetric Contests (pg. 558)
Behavior in Games—Can Evolutionary Dynamics and Imitation Predict Play? (pg. 564)
Exercises (pg. 570)
26. Quantal Response Equilibrium (pg. 575)
Letting Players Make Mistakes (pg. 576)
Better Responding: Quantal Response Functions (pg. 577)
Better Responding to Each Other: Quantal Response Equilibrium (pg. 580)
Better Responding in the Matching Pennies Game (pg. 581)
Better Responding in Symmetric 2x2 Games (pg. 585)
Structural Basis of Quantal Response Functions (pg. 586)
Better Responding in the Volunteer's Dilemma (pg. 587)
Extension to Sequential Games: Agent Quantal Response Equilibrium (pg. 590)
Exercises (pg. 593)
27. Level-k Reasoning (pg. 597)
Level-k Reasoning (pg. 597)
Level-k Reasoning in Matrix Games (pg. 600)
Level-k Reasoning in Guessing Games (pg. 602)
Level-k Reasoning in Sequential Games (pg. 606)
Level-k Reasoning in Games with Incomplete Information (pg. 609)
Cognitive Hierarchy: Reasoning about the Reasoning of Others (pg. 613)
Exercises (pg. 616)
28. Psychological Game Theory (pg. 619)
Psychological Games (pg. 621)
Incorporating Guilt into Games (pg. 621)
Psychological Equilibria (pg. 624)
Intention-Based Reciprocity (pg. 627)
Reciprocity in Simultaneous-Move Games (pg. 630)
Reciprocity in Sequential Games (pg. 635)
The Hold-up Problem with Vengeful Players (pg. 640)
Exercises (pg. 642)
Appendix (pg. 645)
Set Notation (pg. 645)
Optimizing a Function of a Single Variable (pg. 646)
Optimizing a Function with Variables out of the Decision Maker's Control (pg. 649)
Integration (pg. 652)
Probability (pg. 653)
Expected Value (pg. 655)
Expected Payoff: A Model of Choice under Risk (pg. 656)
Choice over Time (pg. 657)
References (pg. 661)
Index (pg. 679)

Jeffrey Carpenter

Jeffrey Carpenter is James Jermain Professor of Political Economy at Middlebury College.

Andrea Robbett

Andrea Robbett is Associate Professor in the Economics Department at Middlebury College.

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