and given A4, it is optimal to take unilateral actions, since there exists no other
means of transmitting information than by the appropriate choice of qi.
7. Relaxing the assumptions
The result stated in proposition 1 builds on a number of strong assumptions.
This section is devoted to analyzing how the assumptions influence the prob-
ability of unilateral actions. First and foremost, it is interesting to investigate the
role of the correlation of costs for the result in proposition 2. Let γ be the corre-
lation, i.e. γ=1 means fully positive correlation. Common sense suggests that
the higher the correlation, the more likely are unilateral actions. The analysis of
this paper verifies this intuition.
Result 5: Given A2-A4, there exists a γ > 0 such that for all γ > γ, unilateral
actions are profitable if costs are low, and for γ ≤ γ, unilateral ac-
tions are not profitable. Proof, see Appendix 2.
First, it is important to recognize that unilateral actions are more likely to be
profitable the more a given increase in beliefs increases the response in terms of
increased reductions. The reason for this is that a country will only engage in
unilateral actions if the expected gain of doing so outweighs the costs of be-
coming informed. Note, however, that this is not an obvious conclusion. Both
types prefer a high response and since unilateral actions are used by the low
cost country to separate from the shadow of the high cost type, a higher re-
sponse only makes unilateral actions more likely (i.e. separation more likely)
when the low cost type profits more from a better response than does the high
cost country. But this is exactly what the single crossing condition implies: The
low cost country will need less costly effort to separate. Now it is easy to verify
that the assumption of high correlation is important. If the informed country’s
signal is only an imperfect signal (imperfectly correlated costs), then the updat-
ing of beliefs will never reach 1. Hence, more reduction efforts are needed to
get a response at all, and once the response appears, it is to a less extent. The
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