Time-Consistent Solutions to the Stochastic Dynamic Strategic Export Subsidy Problem

In this paper we obtain the time-consistent solution to a stochastic dynamic version of the strategic export subsidy problem. The dynamic structure of the problem emanates either from an exhaustible resource or from a learning-by-doing technology. In any given period, nature ‘chooses’ the stochastic demand and cost parameters first. Then, governments choose subsidies. Lastly, firms choose output levels. We establish existence, uniqueness, and representation results for the time-consistent equilibrium of the game. Various interesting features of the solution are illustrated by simulation analysis. In particular, subsidies jump immediately to positive levels and, perhaps paradoxically, are reduced gradually to zero in the exhaustible resource case, while they keep rising in the learning-by-doing case. Subsidies are higher in the learning-by-doing case than when the good in question is an exhaustible resource. Also, they are higher in the case when only one government is active, and lower in the corresponding time-inconsistent equilibrium case.