Sequential equilibrium
We restrict attention to pure strategy equilibria. Consequently, there remains
two different kinds of equilibria; separating equilibria, where each type send
different signals, and pooling equilibria where the two types send the same sig-
nal. Since the analysis focuses on the prospects of unilateral actions, focus is
exclusively on sequential separating equilibrium, or more precisely, interest is
on finding condition for a separating equilibrium to exist. In a separating equi-
librium, the receiver can perfectly infer the type of the sender. Formally, a col-
lection of reduction levels and beliefs {qH ,qL,ρ(q)} forms a sequential equi-
librium if the following conditions are satisfied:
i) Optimality for the country with costs θ:
Qθ ∈ arg max NBi (θ, Qi, p(Qi ))
ii) Beliefs are Bayes-consistent:
a) If qH ≠ qL then ρ(qH ) = 0 and ρ(qL) = 1
b) If Qh = Ql then ρ(qH) = ρ( qL) = Po
c) If qθ ≠ {qh , ql } then any ρ(qθ ) is admissible
After observing qi, the receiver must form a belief about which types could
have sent qi. These posterior beliefs are denoted ρ(θ∣qi) with
ρ(L ∣qi)+ρ(H ∣qi)=1. The first requirement of strategies that form a sequential
equilibrium is sequential rationality, which amounts to saying that for each qi, qj
must maximise expected payoffs, given the beliefs. Regarding the optimality of
beliefs, if qH ≠ qL and the receiver observes, e.g., qH, then it must be that costs
are high, and the only consistent belief is ρ(qH ) = 0 and given this belief, it is
optimal for the high cost type to play qH . In this particular signalling game the
requirement of consistency of beliefs does not place any restrictions on beliefs
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