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

[1 - q(r)]δs.II⁰* + K
[1 - q ( r ) δ_s ]

After substituting (9) into (8), the expression for the total expected pay-off at time t^s for the
opposition party is obtained:

[1 - p ( r )]. δ,K

(1 - δ_s )[1 + δs - 2δ_sp(r)]

Finally, the total discounted pay-off for both parties is given by:

1¹ ■■ + II⁰ ' = —K—  where δ, = δ (W,, μ)

(1 - δ, )                 s t

From this last expression the Pareto-optimum or efficient result for the level of reserves W^P can
be derived. This corresponds to the level that make the total discount factor equal to the pure
myopia value, i.e., W^p / δ_s (W, μ) = μ.

After introducing the game and characterised the non-cooperative equilibrium, the next step is
to present the conditions for the emergence of co-operation between both parties.

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