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

In comparison, in a situation where parties play co-operatively, the incumbent's expected pay-

off is given by:¹⁸

L (1 - δc )[1+δ c - 2δc. p_r ]_|

Note that, regarding the incumbent's discounting, a difference is made between three values for
the political factor: in the first place, δN = δ(WE, μ) stands for the discount that applies when
the system is at stationary equilibrium with reserves equal to W^E ; in the second place, the
discount factors during the period of deviation during which reserves are falling; finally,
δ c= δ ( W0, μ ) is the value for the discount factor under co-operation, assuming that reserves
are kept constant at the level shown at t=0.¹⁹

How can co-operation be sustained?

Co-operation can emerge in this game if appropriate values for the parameters of interest (in this
case combinations of μ and p(r) ) can be found that makes the gains of co-operation equal or
greater than those of defection. To check under which circumstances this is the case, I will study
the incentive compatible condition

(13) 1¹D - 1¹C = 0

which, after substituting (11) and (12) and rearranging, results in:

The ICC is expressed as the combination of three terms. The first one is the gains the incumbent
expects to receive for remaining in office without interruption after deviation has occurred. This
term captures the temptation for deviating from co-operation, being positively related to the
initial amount of reserves and current revenues. The second term stands for the non co-
operative pay-off for the party currently in office from period t=n+1 onwards. The third
component gives the expression for the incumbent's expected gains under co-operation. The

¹⁸ This expression is obtained following the same procedure employed to obtain eq.(7).

¹⁹ In the particular case where the spirit of co-operation is to minimise the risk of a take over by keeping the
level of reserves W equal to W , the discount factor only accounts for time preferences (i.e., δ = μ ).

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