3. The possibility of co-operation
Sequential games differ significantly from repeated games because there is a state variable that
changes in response to players’ actions. Therefore, whether or not an early-stopping
equilibrium12 can be enforced by using grim strategies depends not only on the discount rate
but also on the level of the state variable. In this particular game, the discount factor becomes
partially an endogenous variable being determined by the level of reserves. There are mutual
gains if both parties decide to co-operate in maintaining or improving the level of reserves and,
in that way, reducing the risk of a take over. More generally it provides an illustration of the link
between the country’s wealth and the incumbent's willingness of postponing consumption when
electoral incentives are present. As an illustration of the co-operative problem consider the
following metaphor:
"Driving on a highway"
There is a car with two occupants, both wanting to be the driver. They are on a highway with
lanes of different length. The driver has an expected driving period equal to p(r), which she can
increase(reduce) by moving down(up) to the immediate lane below(above). There are two
special lanes in the highway: a lane in which there is no incentive to change (stationary lane), and
the longest lane (Pareto-Optimum). Due to myopia, the driver might not distinguish lanes of
different length, as illustrated in Figure 4 with lanes 1 and 2 at the point marked by the dotted
line. For an amount of reserves lower than W E , the incumbent has the incentive to increase the
stock unilaterally and, consequently, to generate a move in the direction of the equilibrium
position. By contrast, when the level of reserves is above W E , the incumbent is tempted to
consume part of the stock in order to boost her electoral prospects. This behaviour causes a
downward movement towards the stationary lane.
12 Here associated with an efficient equilibrium of the supergame.