intersection of the reaction curves.5 Assume that in the case of no coordination,
these levels will result.6
The immediate question arises of how to define a unilateral action, since unilat-
eral movement away from a Nash-equilibrium is not a self-enforcing move? In
Hoel (1991), this is accomplished by assuming that one country acts as if it is
not maximizing (1), but instead NBi = Bi (q ) - C (qi ) + h ■ ∑ qi , where h>0 in-
dicates that the country also benefits from reduction in ways not covered by the
cost and benefit relations defined in (1).7 Hoel (1991) stresses that h are not a
choice variable.
Figure 1. The effect of a unilateral increase in reductions by country 1
Given the definition given above, what happens in Hoel’s case is easily deter-
∂qi(qj)
mined. Since reductions are strategic substitutes, i.e. ——— < 0, any unilateral
increase in reductions by one country will be responded to by a decrease in re-
ductions by all other countries. This is illustrated in a two-country version, in
5 We occasionally use vector notation Bi(qi,q-nic) , which, due to the assumption of a uniformly
mixed pollutant, is equal to B (q +∑ qnc) .
i i j≠i j
6 This is a common observation; see e.g. Hoel (1997).
7 See Hoel (1991) for a precise definition of h. In this way Hoel defines that any reduction above
the Nash equilibrium is a unilateral action, and at the same time it is in a sense a new stable
situation since there will be no further adjustments.
12
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