Environment and Statecraft: The Strategy of Environmental Treaty-Making

By Scott Barrett | Go to book overview

Appendix 9.1

Derivation of Figure 9.1

Figure 9.1 assumes that payoffs are given by

with qi ∈ {0, 1}. Then, if Qi = 0, i will play qi = 0 provided c > b > 0. Suppose, however, that Qi = N − 1. Then, since N > c/b by assumption, i will play qi = 1. Indeed, depending on the parameter values, if “enough” countries play Abate, then each will prefer to play Abate. To be precise, country i will play Abate provided

The game illustrated in Figure 9.1 assumes b = 1, c = 2.5, and N = 5.


Derivation of Figure 9.2

Figure 9.2 assumes that payoffs take the form:

where α, β, γ, and δ are parameters (with non-negative values) and where ti takes on a value of 1 if i adopts the segregated ballast tank (SBT) technology and a value of 0 if it does not. The parameter α takes on a value between zero and one; α = 1 implies that the technology standard is just as effective in reducing emissions as the performance standard (assuming full compliance). The parameter γ is the cost of installing the SBT technology and the final term captures the network externality. This shows that if i does not adopt the technology, then it incurs a cost that increases in the number of countries that do adopt the technology—i's tankers are now shut out of these markets (of course, the environmental benefit to i of other countries adopting SBT is included in the bracketed term). Put differently, as long as δ is less than one, there is a benefit to i of adopting SBT that increases in the number of others that adopt SBT.

Notice that, so long as ti = 0 for all i, the above game is identical to the game studied in Chapter 7 . This is the prisoners' dilemma shown in Figure 9.2(a) . By contrast, setting qi = 0 for all i yields Figure 9.2(b) . The network externality makes this game a coordination game. The games shown in Figure 9.2 assume b = 1, c = 3.5, α = 1, γ = 5, β = 1, δ = 0.9, and N = 10.

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