Present-Biased Lobbyists in Linear Quadratic Stochastic Differential Games

TL;DR

This paper studies a stochastic zero-sum game involving lobbying for wind farm investment, focusing on time-inconsistent players with non-constant discount rates, and derives equilibrium strategies both analytically and numerically.

Contribution

It introduces a novel analysis of equilibrium behavior in a time-inconsistent lobbying game with non-constant discounting, providing closed-form and numerical solutions.

Findings

Strategic lobbying increases intensity without overshooting.

Equilibrium strategies are derived in closed-loop form.

Non-constant discount rates significantly affect lobbying behavior.

Abstract

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.