1 See, for example, Sugden, Robert, “Consistent Conjectures and Voluntary Contributions to Public Goods: Why the Conventional Theory Does Not Work,” Journal of Public Economics, vol. 27 (1984), pp. 117–24; Andreoni, James, “Privately Provided Public Goods in a Large Economy: The Limits of Altruism,” Journal of Public Economics, vol. 35 (1988), pp. 57–73; and Covven, Tyler, “Altruism and the Argument from Offsetting Transfers,” in this volume.
2 I present this argument, and summarize the econometric evidence, in Sugden, Robert, “On the Economics of Philanthropy,” Economic Journal, vol. 92 (1982), pp. 341–50.
3 Andreoni, James, “Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving,” Economic Journal, vol. 100 (1990), pp. 464–77.
4 Olson, Mancur, Tiie Logic of Collective Action (Cambridge: Harvard University Press, 1965), p. 60; Becker, Gary S., “A Theory of Social Interactions,” Journal of Political Economy, vol. 82 (1974), p. 1083.
5 For example, Regan, Donald, Utilitarianism and Cooperation (Oxford: Clarendon Press, 1980); Sugden, Robert, “Reciprocity: The Supply of Public Goods through Voluntary Contributions,” Economic Journal, vol. 94 (1984), pp. 772–87.
6 The argument I present here is similar to those of Hodgson, D. H., Consequences of Utilitarianism (Oxford: Clarendon Press, 1967); and Regan, , Utilitarianism and Cooperation.
7 Sugden, Robert, The Economics of Rights, Co-operation, and Welfare (Oxford: Basil Black-well, 1986).
8 To see why, let p be the probability that B will stay silent. Then if A stays silent, A's expected utility is –10(1 – p). If A confesses, A's expected utility is – 10p – (1 – p). The former expected utility is greater than the latter if p is greater than 9/19.
9 This feature is brought out by Hodgson, who considers a game similar to the Prisoners' Coordination Problem (see his Consequences of Utilitarianism). Hodgson's game is played by two act utilitarians, each of whom seeks to maximize the sum of all persons' utilities. Hodgson argues that act-utilitarian players would have no reason to cooperate. Regan discusses the same game and reaches a similar conclusion in his Utilitarianism and Cooperation.
10 Schelling, Thomas, The Strategy of Conflict (Cambridge: Harvard University Press, 1960), especially pp. 54–58.
11 These are among the findings of some experimental work I have done with Judith Mehta and Chris Starmer, which has not yet been published.
12 Lewis, David, Convention: A Philosophical Study (Cambridge: Harvard University Press, 1969), pp. 35–36.
13 Keynes, John Maynard, The General Theory of Employment, Interest, and Money (London: Macmillan, 1936), p. 156.
14 Strictly speaking, Keynes's competition is not a coordination game, since it is zerosum (the object is to beat the other competitors). However, the first sentence in the quotation from Keynes could apply equally well to a coordination game, and this may be what Schelling has in mind.
15 Schelling, , Strategy of Conflict, p. 94
16 This was part of the experimental work referred to in footnote 11.
17 Gauthier, David, “Coordination,” Dialogue, vol. 14 (1975), pp. 195–221; Bacharach, Michael, “Games with Context-Sensitive Strategy Spaces,” paper presented at International Conference on Game Theory, Florence, 06 1991.
18 Gauthier's Principle of Coordination is, in fact, slightly stronger than the principle I have just attributed to him. Gauthier's principle states that if an outcome is (i) a Nash equilibrium, (iii) Parelo optimal, and (iii) strictly Pareto preferred to all other Nash equilibria, then it is rational for each player to choose the strategy that allows this outcome to be brought about. (A Nash equilibrium is a combination of strategies, one for each player, such that each player's strategy is optimal for him, given the strategies of the others. One outcome is strictly Pareto preferred to another if all players prefer the former to the latter. An outcome x is Pareto optimal if there exists no feasible outcome y such that at least one player prefers y to x, and no player prefers x to y.) Since any outcome which is strictly Pareto preferred to all other outcomes must be a Nash equilibrium, Gauthier's Principle of Coordination implies the principle I have attributed to him.
19 Gauthier, , “Coordination,” p. 200.
20 Ibid., p. 196. In later work, Gauthier has developed a theory of “constrained maximization” which implies, among other things, that (in certain circumstances) it is rational to cooperate in the Prisoner's Dilemma; see Gauthier, David, Morals by Agreement (Oxford: Oxford University Press, 1986). A somewhat similar conception of rationality is proposed by McClennen, Edward F. in Rationality and Dynamic Choice (Cambridge: Cambridge University Press, 1990). it is possible that the Principle of Coordination is a valid implication of this kind of theory.
21 A similar criticism is made by Gilbert, Margaret in “Rationality and Salience,” Philosophical Studies, vol. 57 (1989), pp. 61–77.
22 Hurley, Susan L., Natural Reasons (Oxford: Oxford University Press, 1989), p. 148.
23 In contrast, Hurley (ibid., pp. 136–70) argues that, in games like the Prisoners' Coordination Problem, it is irrational for the players not to think as a team or, as she puts it, it is irrational for them not to participate in “collective agency.” Her argument is that the unit of agency should itself be a matter of rational choice; if “it is a good thing for such collective agency to exist,” then it is rational to participate in collective agency, and irrational not to (p. 157). I am inclined to think that the idea of rational choice is not meaningful until the unit of agency has been specified.