Abstract
In the last few decades game theory has emerged as a powerful tool for examining a broad range of philosophical issues. It is unsurprising, then, that game theory has been taken up as a tool to examine issues in the philosophy of religion. Economist Steven Brams (1982), (1983) and (2007), for example, has given a game theoretic analysis of belief in God, his main argument first published in this journal and then again in both editions of his book, Superior Beings. I have two main aims in this paper, one specific and one general. My specific aim is to show that Brams’ application of game theory to examine belief in God is, in particular, deeply flawed in two respects. My general aim is to show that any game-theoretic model in which a human being and God are players can only succeed at the cost of abandoning the assumption that God is omnibenevolent.
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Notes
Since only one player—God—has a dominant strategy (Don’t reveal Himself), Brams’ Belief Game differs from a standard prisoners’ dilemma in which both players have a dominant strategy (defect). This sort of dilemma, in which one player has a dominant strategy and the players end up at a Pareto-inferior outcome is what is known as a “common-knowledge prisoners” dilemma. In his entry on the Stanford Encyclopedia of Philosophy, “Prisoner’s Dilemma,” Kuhn identifies the conditions of a common knowledge prisoners’ dilemma. He begins by laying out a standard prisoners’ dilemma as follows: Standard prisoners’ dilemma
Here R represents the reward for both players if they both cooperate, S represents the “sucker” payoff for the player who, alone, cooperates, T represents the temptation payoff for the player who, alone, defects, and P represents the punishment that each player receives if both players defect. In a standard prisoners’ dilemma, the following inequalities hold true, and both players have a dominant strategy of defection:-
(a)
Tr \(>\) Rr and Pr \(>\) Sr
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(b)
Tc \(>\) Rc and Pc \(>\) Sc
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(c)
Rr \(>\) Pr and Rc \(>\) Pc
However, Kuhn points out that “the force of the [prisoner’s] dilemma can be felt under weaker conditions”—the conditions of the common knowledge prisoners’ dilemma. In a common knowledge prisoners’ dilemma, either (a) or (b)—but not both—fails to hold. We can see that in the Belief Game (b) is not satisfied. If God reveals Himself, “Man’s” payoff if he doesn’t believe in God’s existence (1) is not greater than “Man’s” payoff if he does believe in God’s existence (4), so Tc is not greater than Rc. This entails that “Man” does not have a dominant strategy; however, since both players are rational and since both players know the ordering of the other player’s preferences, the players end up at a Pareto-inferior equilibrium, as in the standard prisoners’ dilemma. The Belief Game, then, is a common knowledge prisoners’ dilemma.
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(a)
This is actually a bit of an oversimplification. Christopher Morris (1991 pp. 76–95) distinguishes the concepts of mutual unconcern, egoism, asociality, and private consumerism from non-tuism. Each of these other assumptions is stronger than the assumption of non-tuism (for example, mutual unconcern—or Rawls’ mutual disinterest—requires that agents not take an interest in the preferences of others). I have cashed my argument out in terms of non-tuism to show that even on the weakest assumption, God’s omnibenevolence is undermined if we attempt to cast Him as a player in a game theoretic model.
Another point of clarification: I take it that game theorists, in assuming that agents have non-tuistic preferences, do not take themselves to be describing the real preferences of real agents. In other words, the assumption of non-tuism is a simplifying assumption that need not, and does not, in fact track the behavior of real agents facing real situations.
While Wicksteed spelled out the concept of “non-tuism” in earlier works, he first used the term “non-tuism” in The Common Sense of Political Economy and Selected Papers and Reviews on Economic Theory.
Thanks to Steve Kuhn for thinking of this possibility.
Here R represents the reward for both players if they both cooperate, S represents the “sucker” payoff for the player who, alone, cooperates, T represents the temptation payoff for the player who, alone, defects, and P represents the punishment that each player receives if both players defect. In a standard prisoners’ dilemma, the following inequalities hold true, and both players have a dominant strategy of defection:References
Binmore, K. (1994). Playing fair: Game theory and the social contract. Cambridge, MA: MIT Press.
Binmore, K. (2008). Natural justice. Oxford: Oxford University Press.
Brams, S. (1982). Belief in God: A game-theoretic paradox. International Journal of Philosophy of Religion, 13(3), 121–129.
Brams, S. (1983). Superior beings: If they exist, how would we know?. New York: Springer.
Brams, S. (2007). Superior beings, IF they exist, how would we know? (2nd ed.). New York: Springer.
Kuhn, S. (2009). Prisoner’s dilemma. In E. N. Zalta (ed.), The Stanford encyclopedia of philosophy, Online Edn. http://plato.stanford.edu/entries/prisoner-dilemma/. Accessed 24 July 2012
Lewis, D. (1969). Convention: A philosophical study. Cambridge: Harvard University Press.
Gauthier, D. (1986). Morals by agreement. Oxford: Oxford University Press.
Moore, G. E. (1903). Principia ethica. Cambridge: Cambridge University Press.
Morris, C. (1991). Moral standing and rational choice contractarianism. In P. Vallentyne (Ed.), Contractarianism and rational choice: essays on David Gauthier’s morals by agreement (pp. 76–95). Cambridge: Cambridge University Press.
Murphy, M. (2001). Natural law and practical rationality. Cambridge: Cambridge University Press.
Scanlon, T. (1998). What do we owe to each other?. Harvard: Belknap Press.
Wicksteed, P. (1910). The common sense of political economy: Including a study of the human basis of economic law. London: Macmillan.
Wicksteed, P. (1933). The common sense of political economy and selected papers and reviews on economic theory. New York: Routledge and Kegan.
Acknowledgments
For helpful comments and discussions, I would like to thank Nick Casalbore, Steve Kuhn, Anne Langhorne, Mark Murphy, Travis Rieder, and the audience of the 2011 South Carolina Society for Philosophy/ North Carolina Philosophical Society annual meeting.
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McShane, P.J. Game theory and belief in God. Int J Philos Relig 75, 3–12 (2014). https://doi.org/10.1007/s11153-013-9396-3
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DOI: https://doi.org/10.1007/s11153-013-9396-3