Game Theory and the Humanities

Game theory models are ubiquitous in economics, common in political science, and increasingly used in psychology and sociology; in evolutionary biology, they offer compelling explanations for competition in nature. But game theory has been only sporadically applied to the humanities; indeed, we almost never associate mathematical calculations of strategic choice with the worlds...

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Game theory models are ubiquitous in economics, common in political science, and increasingly used in psychology and sociology; in evolutionary biology, they offer compelling explanations for competition in nature. But game theory has been only sporadically applied to the humanities; indeed, we almost never associate mathematical calculations of strategic choice with the worlds of literature, history, and philosophy. And yet, as Steven Brams shows, game theory can illuminate the rational choices made by characters in texts ranging from the Bible to Joseph Heller's Catch-22 and can explicate strategic questions in law, history, and philosophy.

Brams's strategic exegesis of texts helps the reader relate characters' goals to their choices and the consequences of those choices. Much of his analysis is based on the theory of moves (TOM), which is grounded in game theory, and which he develops gradually and applies systematically throughout. TOM illuminates the dynamics of player choices, including their misperceptions, deceptions, and uses of different kinds of power.

Brams examines such topics as Abraham’s decision to offer his son for sacrifice when God commanded him to do so; the outcome and payoff matrix of Pascal’s wager on the existence of God; and the strategic games played by presidents and Supreme Court justices; frustration games, as illustrated by the strategic use of sexual abstinence in Aristophanes’s Lysistrata; and how information was slowly uncovered in the game played by Hamlet and Claudius. Going beyond the explication of these specific situations, Brams also derives propositions about "generic games," applicable to a broad class of situations. The reader gains not just new insights into the actions of certain literary and historical characters but also a larger strategic perspective on the choices that make us human.

Preface ix
Acknowledgments xiii
1 Game Theory and Literature : An Overview 1
1.1 Introduction 1
1.2 Method of Inquiry 4
1.3 Avoidance and Acceptance of the Minimax Theorem 5
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Preface ix
Acknowledgments xiii
1 Game Theory and Literature : An Overview 1
1.1 Introduction 1
1.2 Method of Inquiry 4
1.3 Avoidance and Acceptance of the Minimax Theorem 5
1.4 Are Zero-Sum Games Emotionless? 11
1.5 The Rationality of Tragedy 13
1.6 Coordination Problems, Signaling, and Commitment 16
1.7 The Devil and God 19
1.8 Reputation and Intrapsychic Games 21
1.9 Wherein Lies the Future? 24
2 The Bible : Sacrifi ce and Unrequited Love 29
2.1 Introduction 29
2.2 Abraham ’ s Sacrifi ce 31
2.3 What If Abraham Had Refused to Sacrifi ce Isaac? 42
2.4 Samson and Delilah 50
2.5 Theory of Moves (TOM) 57
2.6 Emotions, Feasible Moves, and Morality 65
3 Theology : Is It Rational to Believe in God? 69
3.1 Introduction 69
3.2 Pascal ’ s Wager and the Search Decision 72
3.3 The Concern Decision 77
3.4 The Revelation Game 81
3.5 Decisions versus Games 91
4 Philosophy : Paradoxes of Fair Division 93
4.1 Introduction 93
4.2 Criteria and Classifi cation 95
4.3 Effi ciency and Envy-Freeness: They May Be Incompatible 97
4.4 Unique Effi cient and Envy-Free Divisions: Their Incompatibility with
Other Criteria 100
4.5 The Desirability of Unequal Divisions (Sometimes) 102
4.6 Summary and Conclusions 108
5 Political Philosophy : How Democracy Resolves Confl ict in Diffi cult
Games 111
5.1 Introduction 111
5.2 Resolution by Voting in a 2-Person PD 113
5.3 Resolution by Voting in an n -Person PD 115
5.4 Example of an n -Person PD 117
5.5 A Biblical Tale 119
5.6 Other Diffi cult Games 121
5.7 Summary and Conclusions 125
6 Law : Supreme Court Challenges and Jury Selection 127
6.1 Introduction 127
6.2 The White House Tapes Case 128
6.3 Analysis of the White House Tapes Game 136
6.4 The Roosevelt Court and the New Deal 140
6.5 Jury Selection 146
6.6 Summary and Conclusions 152
7 Plays : Modeling Frustration and Anger 155
7.1 Introduction 155
7.2 The Frustration Game 159
7.3 Lysistrata : Overcoming Frustration with a Credible Threat 165
7.4 The Self-Frustration Game 170
7.5 Macbeth : From Self-Frustration to Murder 175
7.6 Summary and Conclusions 180
8 History : Magnanimity after Wars 185
8.1 Introduction 185
8.2 The Two-Sidedness Convention 187
8.3 Different Views on the Rationality of Magnanimity after
Wars 190
8.4 The Magnanimity Game (MG) 191
8.5 Applications of MG to Historical Cases 197
8.6 Why Did the Confederacy Initiate the U.S. Civil War? 201
8.7 Summary and Conclusions 207
9 Incomplete Information in Literature and History 209
9.1 Introduction 209
9.2 Information Revelation in Hamlet 211
9.3 Incomplete Information in the Magnanimity Game (MG) 217
9.4 Misperception in the Iran Hostage Crisis 219
9.5 The Cuban Missile Crisis: Moving, Order, and Threat Power 226
9.6 Deception in the Cuban Missile Crisis 236
9.7 The Paradox of Omniscience 240
9.8 Summary and Conclusions 244
10 Catch-22s in Literature and History 247
10.1 Introduction 247
10.2 TOM: Cyclic Games 250
10.3 Moving Power in TOM 253
10.4 The Original Catch-22 Game and the Generic Game 256
10.5 The Witch Trials 263
10.6 King-of-the-Mountain Games 268
10.7 Summary and Conclusions 270
11 Summary and Conclusions 275
Appendix 281
Glossary 287
References 295
Index 311
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