The Customary International Law Supergame February 23, 200 made it easier in some circumstance to monitor and to organize retaliation. Our model provides a broader context in which to consider these, and other, parameters Oye identifies three slightly different ways in which increasing the number of players reduces the likelihood of cooperation: (i)increasing transaction costs, (ii) increased heterogeneity of discount factors among larger numbers of players, and (iii) the second order collective action problem, suggesting that players would not retaliate against a defector. The transaction cost problem, compared to transaction benefits, with ncreasing numbers of players is merely a conjecture and seems to be countervailed by the possibility of economies of scale and scope. The second order collective action problem is based on the collective rationality issue discussed above. With respect to and the degree of variation among players. Generally, cooperation would depend on th heterogeneous discount rates, much depends on the ability to discriminate among play discount rate of the least patient state, which would result in the possibility that states with high discount factors (low discount rates)would find it useful to exclude states with low discount factors from certain cooperative arrangements c. Information The relative scale of information in the international system is somewhat different from that in a municipal setting. That is, the cost of producing and distributing information regarding state behavior may be a much smaller fraction of the utility of cooperation in the international setting than it may be in municipal inter-firm contexts Furthermore, there are significant asymmetries among states in terms of the relative cost and value of producing information. Epistemic communities among government officials may play an important role in information transmission See Arthur Lupia gisela Sin, Which Public Goods are Endangered? How ing Communication Technologies Affect the Logic of Collective Action, 117 PUBLIC CHOICE 315(2003); Ronald B. Mitchell, Sources of Transparency: Information Systems in International Regimes, 42 INT'L STUDS. Q. 109(1998) a"discount factor"is a mathematical factor structured to reflect the degree atience of a player. It represents the present value today of a payoff in a future period a discount factor of l means that future payoffs are valued equally to present payoffs discount factor of 75 means that future payoffs are valued at 75%o of present payoffs. A high discount factor indicates patience, while a low discount factor indicates impatience Discount factors should be contrasted with"discount rates"applied to future payoffs in order to reduce them to a present value, where the discount factor equals 1/(1+r), with r representing the discount rate. Therefore, discount factors are less than 1(assuming a positive discount rate). A low discount rate corresponds to a high discount factor. For example, a discount rate of 10% would result in a discount factor of approximately 91%0 We discuss below the circumstances under which a state might be thought to have a high r low discount factor Oye, supra note 63, at 18-19The Customary International Law Supergame February 23, 2004 21 made it easier in some circumstance to monitor and to organize retaliation. 66 Our model provides a broader context in which to consider these, and other, parameters. Oye identifies three slightly different ways in which increasing the number of players reduces the likelihood of cooperation: (i) increasing transaction costs, (ii) increased heterogeneity of discount factors 67 among larger numbers of players, and (iii) the second order collective action problem, suggesting that players would not retaliate against a defector. 68 The transaction cost problem, compared to transaction benefits, with increasing numbers of players is merely a conjecture and seems to be countervailed by the possibility of economies of scale and scope. The second order collective action problem is based on the collective rationality issue discussed above. With respect to heterogeneous discount rates, much depends on the ability to discriminate among players, and the degree of variation among players. Generally, cooperation would depend on the discount rate of the least patient state, which would result in the possibility that states with high discount factors (low discount rates) would find it useful to exclude states with low discount factors from certain cooperative arrangements. c. Information The relative scale of information in the international system is somewhat different from that in a municipal setting. That is, the cost of producing and distributing information regarding state behavior may be a much smaller fraction of the utility of cooperation in the international setting than it may be in municipal inter-firm contexts. Furthermore, there are significant asymmetries among states in terms of the relative cost and value of producing information. Epistemic communities among government officials may play an important role in information transmission. 66 See Arthur Lupia & Gisela Sin, Which Public Goods are Endangered?: How Evolving Communication Technologies Affect the Logic of Collective Action, 117 PUBLIC CHOICE 315 (2003); Ronald B. Mitchell, Sources of Transparency: Information Systems in International Regimes, 42 INT’L STUDS. Q. 109 (1998).. 67 A “discount factor” is a mathematical factor structured to reflect the degree of patience of a player. It represents the present value today of a payoff in a future period. A discount factor of 1 means that future payoffs are valued equally to present payoffs. A discount factor of .75 means that future payoffs are valued at 75% of present payoffs. A high discount factor indicates patience, while a low discount factor indicates impatience. Discount factors should be contrasted with “discount rates” applied to future payoffs in order to reduce them to a present value, where the discount factor equals 1/(1+r), with r representing the discount rate. Therefore, discount factors are less than 1 (assuming a positive discount rate). A low discount rate corresponds to a high discount factor. For example, a discount rate of 10% would result in a discount factor of approximately 91%. We discuss below the circumstances under which a state might be thought to have a high or low discount factor. 68 Oye, supra note 63, at 18-19