1 ‘Gauthier, Property Rights, and Future Generations,’ Canadian Journal of Philosophy 25 (1995) 163-76

2 See Gauthier, David Morals by Agreement (Oxford: Clarendon Press 1986), 299Google Scholar. In this respect, the implied model is similar to the ones that have become standard in the discussion of Rawls's conception of intergenerational distributive justice. See Dasgupta, Partha ‘On Some Alternative Criteria for Justice Between Generations,' Journal of Public Economics 3 (1974) 405–23CrossRefGoogle Scholar, and Arrow, Kenneth J. ‘Rawls's Principle of Just Saving,’ Swedish Journal of Economics 75 (1973) 323–35Google Scholar.

3 Normally, a discount factor is introduced that reduces the present value of future payoffs. This is required in order to be able to rank strategies (since the simple sum of every infinite series of positive payoffs is the same). However, because the model that I am developing here has players ‘living’ for only a finite period, I have taken the liberty of dropping the discount factor. Also, it should be noted that the introduction of a discount factor enables one to use a model of the type I am presenting here not only to represent infinitely repeated games, but also finitely repeated games in which there is some uncertainty as to when the game will end. Thus the possibility that there may not be an infinite number of future generations need not affect the results of this model. See, e.g. Rasmusen, Eric Games and Information (Cambridge, MA: Blackwell 1989), 108–10Google Scholar.

4 See Drew Fudenberg and Tirole, Jean Game Theory (Cambridge, MA: The MIT Press 1991), 110Google Scholar.

5 This is a weak version of the so-called folk theorem. For non-technical discussion, see Rasmusen, Games and Information, 121-9.

6 The assumption that players know with certainty how long they will live is introduced for simplicity only, and has no significant impact on the results of this model. A more realistic account would assign players a certain probability of dying at each stage, and then have them discount future payoffs in accordance with life-expectancy.

7 For further discussion, see Fudenberg and Tirole, Game Theory, 171. It is worth noting that depletionary investment policies are excluded, not because existing generations have some obligation to posterity, but through a simple combination of their self-interest and the assumption that future generations will act rationally. Otherwise put, the elimination of depletionary investment policies is a deductive consequence of the assumption that all individuals maximize expected utility. Because of this, Parfit's non-identity problem does not arise. See Parfit, Derek Reasons and Persons (Oxford: Clarendon Press 1984)Google Scholar.

8 Naturally, introducing some form of time-discounting would lower this.

9 I am not entirely confident about this restriction. Although it seems quite reasonable, our intuitions about such things are notoriously suspect in strategic contexts.

10 For an interpretation of the social contract as an equilibrium-selection device, see Binmore, Ken Playing Fair (Cambridge, MA: The MIT Press 1994), 334–40Google Scholar.

11 Furthermore, there is no in principle limit on the number of other issues that could be introduced into these negotiations. For instance, each generation could also make its cooperation dependent upon an acceptable population policy. This would resolve the intergenerational PD that Derek Parfit thought would lead to overpopulation. See Reasons and Persons, 383.

12 Although in Morals by Agreement, Gauthier tries to suggest that his bargaining solution follows directly from the instrumental model. He has since retracted this claim, acknowledging that his bargaining solution lacks microfoundations. See his 'Uniting Separate Persons,’ in Gauthier, David and Sugden, Robert eds., Rationality, Justice and the Social Contract (Hemel Hempstead: Harvester Wheatsheaf 1993)Google Scholar.

13 Gauthier, Morals by Agreement, 167. Thus Sauvé directly begs the question against Gauthier when he claims that: ‘The only cases in which new generations will find it irrational to continue the social contract are cases where the benefits of continued cooperation no longer outweigh the benefits available in the state of nature’ (168). In Gauthier's terms, while broadly compliant agents would reject only depletionary policies, narrowly compliant agents would reject all policies that are unfair (Gauthier, Morals by Agreement, 178). Similarly, Sauvé's claim that consumption will ‘ratchet down’ as the social contract is renegotiated across generations, slowing but not stopping resource depletion, is incorrect. Once the cooperative equilibrium is selected, it determines the rational strategy for all players in all generations, so there will be no renegotiation.

14 Elsewhere, I have argued that Gauthier's introduction of constrained maximization as a special choice disposition is superfluous across the board, because the ‘contemporaneous' choice problem that he considers should also be modelled as a repeated game. See Heath, Joseph ‘A Multi-Stage Game Model of Morals by Agreement,' Dialogue 35 (1996) 529–52CrossRefGoogle Scholar.

15 In Gauthier's actual model, each generation makes a claim upon all previous generations. In my corn-berry model this complication is not necessary because the production level can be maximized in a single stage.

16 Gauthier, Morals by Agreement, 304-5. The claim about Rawls is incorrect because the 'zero-investment’ policy results only in models with no generational overlap, and occurs only if one ignores Rawls's stipulation that the difference principle not be applied to intergenerational contracts.

17 Those who are troubled by the fact that the non-utilitarian savings policies create Pareto-inefficient outcomes might like to rig up a model so that all minimum and maximum claims coincide.

18 Furthermore, my production function assumes that the returns on investment are enjoyed in the very next stage. A more realistic model, in which payoffs may only arise several turns later, gives rise to the possibility of investment policies in which short-term decreases in production can create a greater long-run average. There is, however, no justification whatsoever for Sauvé's claim that a rational choice model of this type entails a preference for short-term rather than long-term investments.

19 For discussion see Kotlikoff, Laurence J. Generational Accounting (New York: The Free Press 1992)CrossRefGoogle Scholar.lt is worth noting that the current pressure from some members of the ‘baby boom’ generation to defect from the Canada Pension Plan is not a result of their own contribution level being too high. On the contrary, it is because their own contribution level is so low. Their underfunding of the plan amounts to an attempt to effect a massive transfer of wealth from members of younger generations to themselves. However, the scale of this proposed redistribution is so large that many boomers have come to anticipate the defection of these generations. It is this anticipated defection that supplies them with the current motivation to defect from the plan. This would appear to be an example of the ‘unraveling’ that can occur when savings arrangements are adopted that are predictably unacceptable to future generations.

20 I would like to thank Gustaf Arrhenius, Kevin Sauvé, Margaret Schabas, and three anonymous CJP referees for commenting on this paper, and the Social Sciences and Humanities Research Council of Canada for financial assistance during the period in which it was written.