Journal ArticlePresent-biased lobbyists in linear–quadratic stochastic differential gamesLazrak, Ali; Wang, Hanxiao; Yong, JiongminWe investigate a linear–quadratic stochastic zero-sum game where two players lobby a political representative to invest in a wind farm. Players are time-inconsistent because they discount the utility 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 analyse equilibrium behaviour in both single-player and two-player cases and compare the behaviours of the game under constant and variable discount rates. The equilibrium behaviour is provided in closed-loop form, either analytically or via numerical approximation. Our numerical analysis of the equilibrium reveals that strategic behaviour leads to more intense lobbying without resulting in overshooting.Springer2023-10-0110499993Finance and Stochastics274947 to 9840949-2984https://doi.org/10.1007/s00780-023-00519-92305475National Science Foundation