Unilateral Actions the Case of International Environmental Problems

5. Information structure and correlation of costs

Consider the following information structure. Initially, the countries are at q^nc.
No country wants to initiate further reductions. Costs of further reductions are
uncertain, with probability ρ, θ=L and with probability (1-ρ), θ=H, but most
importantly, costs are fully correlated between countries. This information
structure is common knowledge to the countries. Next, a country undertakes an
assessment of the costs of reductions and it is assumed that it gets fully, but pri-
vately, informed. If it is revealed that costs are low, the country will initiate
full-scale unilateral actions, if those actions indisputably reveal that costs are
low. If it is revealed that costs are high, no further reductions will be made if all
other countries believe that costs are high (but it will make unilateral actions, if
it could convince the other countries that costs are low). Given this information
structure, it is possible to state conditions where unilateral actions are indeed
profitable.

Formally, the following 4 assumptions are made regarding the information
structure:

Assumption A1 (correlation of costs): The cost-parameter is fully correlated
between countries, i.e. θi =θj ,∀i, j ∈ I .

Assumption A2 (assessment of costs): Any country i can get fully (but pri-
vately) informed about θi. The cost of doing so, is Di > 0.

Assumption A3 (profitability of unilateral actions for one country):

a) Let q(p ) = q(ρ² ) for all p < ρ and ρ² < p and let p < p.

b) Let ∃i ∈ I : NB_i(ρ,q_i(ρ),q_-i(ρ)) ≤ NB_i(L,q_i(L),q_-i(L))+D_i and

∀j ≠ i : NBj⁽ρ^, q_j ⁽ρ)^, q—j⁽ρ)) ≤ NBj⁽L^, q_j ⁽L)^, q—j⁽L)) + Dj.

Assumption A4 (Information-transmission): No verification technologies exist.

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