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# Introduction to Game Theory : A Behavioral Approach

**by**Williams, Kenneth C.

### 9780199837397

0199837392

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6/14/2012

Oxford University Press

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## Summary

Game theory studies the strategic interaction of people within various institutions such as political, economic, or other social institutions that are governed by a set or rules or principals. Game theory provides solutions to these strategic interactions by developing models based onassumptions about human behavior and the institution where the interaction occurs. Game theory is an interdisciplinary method to examine decision making in the fields of economics, political science, psychology, sociology, mathematics, computer programming, and biology.This book is an introduction to game theory but differs from other excellent introduction game theory texts by taking a behavioral approach. This means that basic game theory concepts are explained by using results from laboratory experiments that examine how real people behave when they participatein the games that are modeled. This approach is referred to as behavioral game theory and it seeks to use psychological reasoning to explain deviations in the predictions of standard game theory models. Behavior game theory allows for the study of how human emotions affect decision making using theassumptions of game theory. Although the study of game theory is somewhat technical because it uses mathematics to construct the various models, the intuition behind game theory is actually normative and nontechnical. This book takes a very nontechnical approach to the study of game theory so that only minimum math skills areneeded to follow the discussion in the book. The importance of game theory lies in the deductive process of reasoning and understanding how to construct models of social interaction, and not the mathematics that are involved.

## Table of Contents

*Preface*

**CHAPTER 1. WHAT IS GAME THEORY?**

**A. The Goal of this Book**

1. Baseball stadium model example

2. Applied models vs. pure theory

3. Applied models and empirical testing using experiments

4. A simple and not very good experiment

5. Behavioral game theory and ultimatum bargaining

6. New technology used to disprove and improve old theories

**B. What Is a Game?**

1. Game theory as an interdisciplinary method

2. Game theory and equilibrium

3. A game in von Neumann's sense

4. Game theory and the importance of assumptions

5. Rationality and self-interest in a curved exam example

**C. Behavioral Assumptions**

1. What is rationality?

2. Why is rationality needed?

**D. Behavioral Game Theory**

1. Research methods of behavioral game theory

2. Historical developments in behavioral game theory

**E. Different Types of Games**

1. Cooperative vs. noncooperative games

2. Competitive vs. noncompetitive games

3. Normal form vs. extensive form games

4. Pure vs. mixed strategy games

5. Single-shot vs. repeated games

6. Complete and perfect information vs. incomplete and imperfect information

**F. Summary**

**CHAPTER 2. WHAT ARE LABORATORY EXPERIMENTS?**

**A. Why Experiments?**

1. Ben Franklin's clothes experiment

2. The need for experiments and the growth of experiments

**B. Defining a Laboratory Experiment**

1. What is a laboratory and how does it differ from the field?

2. What is the definition of an experiment?

**C. Establishing Causality**

1. Randomization of subjects to treatments and experimental controls

2. Example of the importance of randomization of subjects to treatments

3. Experimental controls and confounding factors

4. Baseline comparisons and controlling confounding factors

**D. Experimental Validity**

1. Differences among between external, internal, and ecological validities

2. Artificial vs. natural environments

3. Problems with external validity

4. Problems with internal validity

5. Benefits of an artificial environment

**E. Experimental Methods**

1. Subject motivations

2. Deception

3. Experimental environment

4. Number of trials

5. Between-subject vs. within-subject design

6. Anonymity

7. How do you design a good experiment?

**F. Summary**

**CHAPTER 3. ORDINAL UTILITY THEORY**

**A. Too Many Choices?**

**B. Strict Rationality**

**C. Utility Theory**

1. Utility

2. Graphical utility functions

**D. Ordering Alternatives**

1. Restrictions on choice

2. May's intransitive preferences experiment

3. Choice and time

4. Nonperverse selection rule and exhaustive set of alternatives

5. Ariely's Economist experiment

**E. Ordinal Utility Functions**

**F. Spatial Preferences in One Dimension**

1. Modeling ideology

2. Single-peakedness and transitivity

**G. How Utility Functions for Money Are Induced in Political Economy Experiments**

1. Payoff charts

2. Spatial payoffs

**H. Rationality, Emotions, and Social Preferences**

1. Rationality and emotions

2. Rationality used to study other types of behavior via deviations

3. Social preferences defined

4. Example of a social utility function

**I. Summary**

**CHAPTER 4. EXPECTED UTILITY THEORY**

**A. Expected Utility**

1. Expected value and slot machines

2. The St. Petersburg paradox

**B. Expected Utility Theory**

1. Using cardinal values in a utility function

2. Preferences over lotteries vs. preferences over outcomes

3. Further restrictions on choice

4. Calculating expected utility

**C. Modeling Risk**

1. What is risk?

2. Modeling risk-averse vs. risk-acceptance behavior

**D. Framing Effects and Alternative Theories of Risk**

1. Framing

2. Prospect theory

3. Regret theory

**E. Anomalies to Expected Utility Theory**

1. The Ellsberg paradox

2. Framing and reference points

3. Time inconsistency

**F. Alternative Theories to Expected Utility Theory**

1. Bounded rationality

2. The BPC model

**G. Binary Lottery Experiments**

**H. Summary**

**CHAPTER 5. SOLVING FOR A NASH EQUILIBRIUM IN NORMAL FORM GAMES**

**A. In Cold Blood**

**B. Beliefs and the Common Knowledge Assumption**

**C. Nash Equilibrium**

1. Defining a Nash equilibrium

2. Nash equilibrium behavior in other examples

3. He-think-I-think regress

4. Pareto principle

5. Nash equilibrium in a zero-sum game

**D. Prisoner's Dilemma**

**E. Elimination of Dominated Strategies and a Dominant Solvable Equilibrium**

**F. Three-Player Normal Form Games**

**G. Eliminating Dominated Strategies in an Election Game**

**H. Finding Dominate Strategies in a Spatial Election Experiment**

**I. Other Experimental Tests of Dominant Strategies**

1. Tversky and Kahneman's dominant strategy experiment

2. Beauty contest

**J. Summary**

**CHAPTER 6. CLASSIC NORMAL FORM GAMES AND EXPERIMENTS**

**A. Classic Normal Form Games**

**B. Revisiting the Prisoner's Dilemma**

1. Repeated prisoner's dilemma game

2. Example of finite repeated game with reciprocity strategies

3. Axelrod's Tournament

4. Prisoner's dilemma as a route-choice game

**C. Social Dilemmas**

1. Collective goods problem

2. Collective goods experiment

3. Volunteer dilemma

**D. Chicken Games and Brinkmanship**

1. Chicken run

2. Brinkmanship and the Cuban missile crisis

3. Hawk-dove game

4. Acme-Bolt truck experiment

**E. Battle of the Sexes Game and Coordination Games**

1. Classic story of the battle of the sexes

2. Coordination in a matching pennies game

3. Focal point equilibrium

**F. Stag Hunt or Assurance Games**

1. The Rousseau game and risk-dominant equilibrium

2. Quorum-busting

3. Experiment on stag hunt game: Communication and trust

4. Coordination and elites

**G. Summary**

**CHAPTER 7. SOLVING FOR MIXED STRATEGY EQUILIBRIUM**

**A. Rock, Paper, Scissors**

**B. Calculating Mixed Strategies**

1. Spades-hearts game

2. Mixed strategy equilibrium for spades-hearts game

3. Why would a player use a mixed strategy?

4. Mixed strategy equilibrium for the battle of the sexes game

**C. Experimental Tests of Mixed Strategy Equilibrium**

1. O'Neill's experiment

2. Ochs' experiment

**D. Probabilistic Choice Models**

**E. Testing Mixed Strategies Using Observational Data**

1. Soccer players and mixed strategies

2. Tennis players and mixed strategies

**F. Summary**

**CHAPTER 8. EXTENSIVE FORM GAMES AND BACKWARD INDUCTION**

**A. The Twenty-One Coin Game**

**B. Defining an extensive form game**

1. Follow-the-leader game redux

2. Formal definition of extensive form game

3. Twilight example

4. Three Stooges game

**C. Backward Induction**

**D. The Importance of the Order in which Players Move**

1. First mover's advantage and the chicken game

2. First mover's advantage and a collective good game

3. Second mover's advantage and RPS game

**E. Backward Induction and the Need for Refinement**

**F. Experiments on Backward induction Reasoning**

1. Race game

2. Race game and chess players

**G. Summary**

**CHAPTER 9. SUBGAME PERFECT EQUILIBRIUM**

**A. Credible vs. Noncredible Threats**

**B. Subgame Perfect Equilibrium**

1. Subgames

2. Threat game

3. Strategy mappings and Rasmussen's computer disk game

4. Player 1 moves twice game

5. Kreps and Wilson's up-down game

**C. Subgame Perfect Equilibrium and the Need for Refinement**

**D. Centipede Game**

1. How the centipede game is played

2. Centipede, reputations, and quantal response equilibrium

3. Centipede and chess players

**E. Ultimatum Bargaining Games**

1. Ultimatum bargaining and problems with subgame perfect equilibrium

2. Ultimatum bargaining and communication

3. Bargaining with social preferences turned off

4. Ultimatum bargaining and cultural effects

5. Physical attraction and ultimatum bargaining

**F. Trust Games**

**G. Neuroeconomics**

**H. Wait a Minute, Are These Really Social Preferences?**

1. Manufactured social preferences

2. Strategic ignorance

**I. Summary**

**CHAPTER 10. IMPERFECT AND INCOMPLETE INFORMATION GAMES**

**A. The Structure of Imperfect and Incomplete Information**

1. Infatuation and fickle games

2. Disney movies and incomplete and imperfect information

**B. The Structure of Incomplete Information in Game Trees**

1. Matching pennies and information sets

2. Varied information sets in a guessing game

3. Restrictions placed on information sets

**C. Incomplete Information over Player Types**

**D. Sequential Rationality**

1. Establishment of beliefs and restrictions placed on beliefs

2. Deriving a sequential equilibrium

**E. Signaling Games**

1. Truth-lying game

2. Truth-lying and games of conflict and common interest

3. Calculating a sequential equilibrium for the truth-lying game

**F. Sender-Receiver Framework Lying Experiment**

**G. Persuasion Experiment**

**H. Summary**

**CHAPTER 11. BAYESIAN LEARNING**

**A. The people of the state of California v. Collins (1968)**

**B. Conditional probabilities**

**C. Conditional probabilities and the beliefs of video game characters**

**D. Bayesian learning**

1. What is learning?

2. Updating beliefs

3. Calculating Bayes' Theorem

**E. Perfect Bayesian Equilibrium**

1. Weak consistency of beliefs

2. Solving for a perfect Bayesian Equilibrium

3. Refinements to perfect Bayesian Equilibrium

**F. Information cascade experiments**

**G. Alternative learning models**

**H. Equilibrium and learning**

**I. Summary**

Chapter Problem Sets

**Appendix 1. Solving Linear Equations**

**Appendix 2. A Short History of Game Theory and Political Economy Experiments**

**Appendix 3. Sincere vs. Strategic Voting in Agenda Games**

*References*

*Glossary*

*Index*