Unilateral Actions the Case of International Environmental Problems

Result 2: There exist only one undominated separating sequential equilib-
rium, (q¹L ,q¹H ) = (q_i (L,1 ), qUA ).              Proof, see appendix 2.

Result 2 is intuitive, since the H-type uses costly actions in order to try to sepa-
rate from the shadow of the L-type. A rational player chooses this particular
strategy, which implies the minimum necessary costs in order to separate, and,
hence, the Pareto-optimal separating equilibrium is obtained implying the
minimum possible distortion from the full information (first best) allocation.

Compared to Hoel (1991), unilateral actions are fully explained as a rational
move to reveal that costs are high. However, from (2) and (3) it follows that al-
though revelation of costs can increase the response of the other country, in this
model it cannot be the case that, un-coordinated, both increase their reductions.
Moreover, compared to what should be required for an action to serve as a
‘good example’, the action is in the wrong direction, since in our model, the
high cost country reduces less in order to trigger an increase in the other coun-
tries’ reduction. Most importantly, however, the unilateral actions do not ‘set a
good example’ and do not establish any move forward solving the underlying
environmental problem.

Proposition 1: In Hoel’s (1991) model, simply adding private information
about costs and allowing unilateral actions to reveal such costs
does not result in ‘setting a good example’.

Hence, the information structure of signalling game 1 does not yield a better
prospect for unilateral actions than does the original analysis of Hoel (1991).
The reason why the other countries reduce more in the non-cooperative setting
is that country i reduces less, due to it having high costs, and hence, it strategi-
cally exploits information. In this respect this looks more like an act of free rid-
ing. The signalling game model 1 however shows what is needed in order for a
unilateral move to ‘set a good example’.

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