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

2. Description of the game

In this section the players, strategies, equilibrium concept, and the pay-off function of the game
are presented, together with an interpretation of the main variables and parameters.

2.1. Players, variables, and parameters

There are two opportunistic parties and a dictator. A party is defined as opportunistic if
enjoyment of power is its only source of utility and its overriding objective is to maximise the
expected discounted gains of being in office.⁶ The two parties are called Party I (she) and
Party II (he). Depending on the electoral result, each of them can play one of two roles:
incumbent or opposition. It is assumed that at the beginning of the game Party I is the
incumbent and Party II the opposition. During each electoral period the incumbent enjoys K
utils. There is no utility for the party in opposition. Previous to the election the incumbent
chooses an action x. This action can be interpreted as expenditure in public goods.

The probability of being re-elected p(x) is an increasing function of x. It is assumed that
∂ p(X)          ∂² p(x)

—' ⁷ > 0 and —'   ⁷ < 0. The concavity of p(x) is due to diminishing marginal political

∂ x           ∂ ² x

returns of expenditure.

Voters are assumed to assess the incumbent performance retrospectively. During the electoral
period the utility of the voters is directly related to x. There are N voters (N very large), each of
them getting a utility of V_i(x). Their strategy is to co-operate with the incumbent (vote for it) as
far as the incumbent performs satisfactorily; otherwise to punish her by electing the opposition
party.⁷ Issues do not count; only results matter.

⁶ Opportunistic parties do not have an incentive to appropriate part of the rents for themselves, as in the
case where parties are selfish. Hence, eventually, voters are going to receive all the rents. This is not a zero-
sum game where by repeating elections voters (acting strategically) can increase their benefits by improving
their bargaining power. For an example of selfish parties see Freejohn (1986).

⁷ Note that when using this strategy, although acting rationally, voters do not make any prediction about
the future (or the effects of future policies).

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