Unilateral Actions the Case of International Environmental Problems

3. Cost uncertainty

Next, private information about reduction costs is introduced. The main purpose
of this section is to show how to determine an expected (or Bayesian) Nash
equilibrium and how revelation of information can result in changes in reduc-
tions by the other countries. This model serves as a (benchmark) framework for
the following, focusing exclusively on the effect stemming from information
transmission.

Assume two possible cost types, low cost countries, denoted L and high cost
countries, denoted H, i.e., θi ∈ {L,H} . Let ρj = prob(θj = L) be the (common)
prior probability that the cost parameter of country j is low, with
θ= (θ₁,θ₂,...,θ_n) . Let ρ= (ρ₁,ρ₂,...,ρ_n) be the vector of common prior beliefs
about the types of the n countries.

The reaction function of country i, in the most general form, is given by
q_i = q_i(θ_i,q_-i(ρ),ρ) , which says that the best reply function by country i is de-
pendent on own type, θi , expected choice of reductions of the other countries,
q-i(ρ) , and the common prior belief vector, ρ. In a two country version,
q₁ = q₁ (θ₁ ,q₂ (θ),θ) denotes the reaction function for country 1 under full in-
formation, while q₁ = q₁(q₂(ρ), ρ) is the situation with complete uncertainty.
The non-cooperative (Nash) equilibrium is given by qi^nc = qi^nc (ρ) under com-
plete uncertainty, and q_i^nc = q_i^nc (θ) under full information and two countries.
Most importantly, it follows from (3),⁸ that

∂q_i

8 To see this, remember that —- > 0, which says that the higher another countries costs, the
∂θ_j

higher the own reduction. Since ρ is the probability for low costs, the more likely that the other
country has low costs, the lower will be the own reduction.

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