The Dictator and the Parties A Study on Policy Co-operation in Mineral Economies

equilibrium. Also, as will be presented later on in the chapter, a co-operative behaviour will
require that the level of reserves will be kept constant at a certain level. ¹¹

The stationary state

During the stationary state the incumbent sets x_t = r. Vt, in which case
I^l_t = Ii₊₁ = I'_t+2 = I^s for i = 0 and 1; δ_{t+ i} = δ_{t+ i+1} = δ_s = δ (W, μ) V i ; where the
t t I t I                                                                                                                               t t i t i i I s

symbol S is used to mean stationary state. Also, p(r) = q(r), i.e., it is expected that for a
given expenditure both parties will obtain the same probability of re-election and will implement
the same strategy once in office. The time t^s at which x_t = r, depends on the path followed by
the incumbents as reflected in the history of the game h^t.

Regarding the incumbent party at time t^s (which it is assumed to be Party I), the continuation
pay-off becomes:
(5) 1^{1 s} = p(r) δs. 1^{1 s} i [1 - p(r)]δs. 1^0s i K

1^0s = [1 - q(r)]δs.1^{1 s} I q(r) δs.1^0s

∩_v [1 - q ( r )] δ _ιv

(6) 10S = ^l -Z у 7-1 s 11S

[1 - q ( r ) δs ]

After substituting (6) into (5), I find the expression for the total expected pay-off for the
incumbent party in the stationary state:

(1 - δs )[11 δs - 2 δs.p(r )]

On the other hand, following a similar procedure, I obtain the expected pay-off at time t^s for the
party in opposition (Party II).

(8) II^0s = [1 - p(r)]δs.II^{1 s} i p(r)δ.II^0s

II^{1 s} = q(r ) δs. II^{1 s} I [1 - q(r )]δs. II^0s IK

¹¹ Regarding the analysis on uniqueness and stability of the game, it can be shown that there is
convergence towards a unique stationary state for the level of reserves ( W^E ), and that the system is stable
in the sense that for an amount of reserves different than W^E , the incumbent changes the level of the
stock generating a move in the direction of the equilibrium position. See Astorga, 1996.

<<   10   11   12   13   14   15   16   >>

More intriguing information