Game Theory and the Humanities

Game Theory and the Humanities: Bridging Two Worlds

Steven J. Brams
Copyright Date: 2011
Published by: MIT Press
Pages: 336
https://www.jstor.org/stable/j.ctt5hhj4n
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    Game Theory and the Humanities
    Book Description:

    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. Much of Brams's 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 the outcome and payoff matrix of Pascal's wager on the existence of God; the strategic games played by presidents and Supreme Court justices; and how information was slowly uncovered in the game played by Hamlet and Claudius. 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.

    eISBN: 978-0-262-29593-2
    Subjects: Economics

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. Preface
    (pp. ix-xii)
  4. Acknowledgments
    (pp. xiii-xiv)
  5. 1 Game Theory and Literature: An Overview
    (pp. 1-28)

    Fiction has been one of the most fertile grounds for humanistic applications of game theory. Novels, short stories, plays, narrative poems, and even the librettos of operas—all have been subject to game-theoretic exegesis, as have stories in the Bible. It is these applications, all of which involve noncooperative game theory, that I survey in this chapter.¹

    I will sketch but not present technical details of several models, in part because my primary purpose is to emphasize literary themes amenable to game-theoretic treatment, and in part because I will model in depth the choices of characters in specific literary works...

  6. 2 The Bible: Sacrifice and Unrequited Love
    (pp. 29-68)

    The Bible is a sacred document to millions of people.¹ It expresses supernatural elements of faith that do not admit of any natural explanations. At the same time, however, some of the great narratives in the Bible do not seem implausible reconstructions of historical events. Moreover, biblical characters often exhibit ordinary human failings in their behavior toward one another.

    Is it possible to reconcile natural and supernatural elements in the Bible? This would not seem an easy task, because God, in some ineffable manifestation, makes His presence felt in practically all biblical stories. A naturalistic interpretation of the Bible immediately...

  7. 3 Theology: Is It Rational to Believe in God?
    (pp. 69-92)

    Theology studies the relationship between human beings and God.¹ Game theory seems well suited for analyzing this relationship, though some may question the seemingly impious view that God plays games with us.² But the game-like view is inherent in those Western religions that presume God can be conceived of in personal terms and, more specifically, is in a one-to-one relationship with each of us.

    The idea of a personal God, especially one who is a game player, is alien to most eastern religions. I confess that the present analysis has a Western religious bias, perhaps epitomized by the view of...

  8. 4 Philosophy: Paradoxes of Fair Division
    (pp. 93-110)

    A paradox occurs when two plausible lines of reasoning lead to a contradiction.¹ A main concern of philosophy is to resolve paradoxes, especially those that raise fundamental questions, such as what constitutes a just society. A contradiction arises if we define a just society to be one that respects individual rights and maximizes social welfare, but these properties cannot be satisfied simultaneously.

    Game theory provides an important tool for addressing such questions. A game incharacteristic-function formis one in which each subset of players can ensure itself of a specified portion of some valued good like money.² In such...

  9. 5 Political Philosophy: How Democracy Resolves Conflict in Difficult Games
    (pp. 111-126)

    The dual problems of fostering cooperation in societies and choosing leaders to govern them, while briefly mentioned in the Hebrew Bible when Saul becomes the first Israelite king (Brams 1980/2003, chap. 7), are more systematically analyzed by the classical Greek philosophers, Plato and Aristotle.¹ Two thousand years later English political philosopher Thomas Hobbes (1588–1679) maintained that the only escape from anarchy was the imposition of rule by a “leviathan,” a strong central authority to whom citizens would cede their natural rights through a social contract. More recent political philosophers have suggested more benign means for forging consensus in a...

  10. 6 Law: Supreme Court Challenges and Jury Selection
    (pp. 127-154)

    The three traditional branches of government in the United States—the Presidency, the Congress, and the Supreme Court—have never been entirely at ease with each other. The most persistent and rancorous conflicts have been between the president and Congress, especially when one or both of its two houses (the House of Representatives and the Senate) are controlled by a different party from that of the president.

    The U.S. Constitution allows the president to veto bills passed by Congress, but Congress can override a presidential veto by two-thirds majority votes in both its houses. Consequences of these rules for the...

  11. 7 Plays: Modeling Frustration and Anger
    (pp. 155-184)

    Emotions, such as anger, jealousy, or love, are spontaneous feelings that practically all of us experience at one time or another.¹ Although there may be good reasons for us to be angry, jealous, or fall in love, these feelings, especially when they overtake us suddenly, seem not to be the product of rational calculation. Rather, they overpower us, so to speak, which seems the antithesis of the careful means-ends analysis that we normally associate with rational choice. Indeed, Gelernter (1994, 29) argues that “you cannot choose your emotions. Emotions choose themselves,” suggesting that emotions have no rational basis.² (I rule...

  12. 8 History: Magnanimity after Wars
    (pp. 185-208)

    History is the study of the past.¹ Typically, it involves identifying the set of events that give rise to particular outcomes, which may range from elections to social movements to wars.

    Some historians, however, take a more social-scientific view. They do not stress the peculiar or unique but instead attempt to analyze the underlying forces that produce outcomes across cultures and time, such as the rise and fall of empires. To do so, they may focus on the accumulation of wealth, the nature of political institutions, the qualities of leadership, and the like in order to try to identify key...

  13. 9 Incomplete Information in Literature and History
    (pp. 209-246)

    The classical definition of a game in extensive form (i.e., one represented by a game tree) includes the specification of the information players have about the sequence moves of the other players.¹ Although the role of information in games has always been central in game theory, it takes on special significance under the rules of TOM.

    For example, because standard game theory pays little attention to possible differences in the power of players, focusing instead on player choices and the stability of outcomes, it has little to say when there is incomplete information about power differences. Yet a player’s information...

  14. 10 Catch-22s in Literature and History
    (pp. 247-274)

    In his classic novel,Catch-22(1961, 52), Joseph Heller describes the thoroughly frustrating situation a U.S. combat pilot faced in World War II: “If he flew them [more missions] he was crazy and didn’t have to; but if he didn’t want to he was sane and had to.”¹ Unlike the frustrating situations I described in chapter 7, in which a player in an unsatisfactory state could initiate a series of moves to extricate itself, this strategy will not work if the game can cycle back to the initial state, whence the frustration and attendant anger returns.

    In this chapter, I...

  15. 11 Summary and Conclusions
    (pp. 275-280)

    Most of the applications I have made of game theory and the theory of moves (TOM) to the humanities alternate between fictional narratives and historical reconstructions. While they occur in two different worlds—made up and real—they share common ground: The players in them actrationally, in accordance with their goals.

    If Abraham’s faith in God wavers, he still can anticipate that God will renege on his command that he sacrifice Isaac, affording Abraham the opportunity to save Isaac by heeding God’s command (chapter 2).

    If, hypothetically, Abraham had refused to offer Isaac for sacrifice, he would have benefited...

  16. Appendix
    (pp. 281-286)
  17. Glossary
    (pp. 287-294)
  18. References
    (pp. 295-310)
  19. Index
    (pp. 311-319)