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,...,θn) . Let ρ= (ρ1,ρ2,...,ρn) 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
qi = qi(θi,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 qinc = qinc (ρ) under com-
plete uncertainty, and qinc = qinc (θ) under full information and two countries.
Most importantly, it follows from (3),8 that
dqj
dPi
<0
(4)
∂qi
8 To see this, remember that —- > 0, which says that the higher another countries costs, the
∂θj
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.
14
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