It is the expected pay-off for Party I acting as opposition party at time t+1
p(xI ) and q(xII) mean that Party I and Party II is in office respectively.
Likewise, at time t the opposition party (Party II) expects to obtain:
(3) IIt = [1 - P(x∣ι )] ⅛+1 II1+1 + p(xt )δt+1 II0+1
(4) II1+1 = q ( xI+1) δt+2 II1+ 2 + [1 - q ( x≈1)] δt+2 II^ + K
where: II1+1 = II1 (Wt+1 + r - x 1 ) ; IIt1+ 2 = II1 (Wt+1 + 2 r - x 1 - x2 )
IIt0 stands for the expected gains for Party II being in opposition at time t.
An amount of expenditure (x) different from current revenues (r) has two contrary effects on the
incumbent's discounted expected revenues. The first effect is related to the value of the dictator
factor. When the incumbent spends more than she receives she finances the extra spending with
reserves, otherwise she accumulates reserves. A drop(increase) in reserves
increases(decreases) the probability of a dictator's take over and consequently
reduces(increases) the expected gains. The second one is linked to the probability of re-
election. An increase(decrease) of expenditure over r improves(worsens) the incumbent's
chances of re-election, and consequently the expected gains, but worsens(improves) the
expected pay-off of the opposition party.
Player I(II)'s problem at time t is to maximise her(his) expected pay-off, taking into account the
decision of Party II(I) in that case where he(she) happens to be in office, subject to the no-
∞
borrowing constraint ∑ ( xi - ri ) ≤ W0 and the motion equation Wt = Wt+1 + r - xt .
i = 1
Of particular interest for the analysis is the expected pay-offs the incumbent will obtain when the
stock reaches a stationary state, i.e., values of the state variable that will be preserved once it is
achieved. This resting point corresponds naturally to the economic notion of long-run