  We investigate a linear quadratic stochastic zero-sum game where two players
lobby a political representative to invest in a wind turbine farm. Players are
time-inconsistent because they discount performance with a non-constant rate.
Our objective is to identify a consistent planning equilibrium in which the
players are aware of their inconsistency and cannot commit to a lobbying
policy. We analyze the equilibrium behavior in both single player and
two-player cases, and compare the behavior of the game under constant and
non-constant discount rates. The equilibrium behavior is provided in
closed-loop form, either analytically or via numerical approximation. Our
numerical analysis of the equilibrium reveals that strategic behavior leads to
more intense lobbying without resulting in overshooting.
