Imperfect Monitoring May Be Perfectly Fine: Differential Game Theory and an Application to Climate Change

Abstract

We study a class of finite-horizon differential games with control-state separable objective functionals and state equations. In this context, we introduce simple mechanisms that give a dynamic payoff to agents that only depends on the current value of the state variable. Thus, in many applications their implementation requires moderate monitoring capability. We are able to show that these mechanisms induce, in Markov-perfect equilibrium, any economically meaningful control path that is continuously differentiable and satisfies certain mild regularity assumptions. Moreover, if the target control-state path represents a Pareto improvement over an inefficient unregulated outcome, a suitably chosen ex-ante cost-sharing scheme ensures ex-post individual rationality, in addition to budget balance. At the same time, if the differential game has pre-existing linear cost structure no such agreement is necessary. Our results extend to an infinite time horizon and a multi-dimensional state space. We apply our analysis to a simple differential-game model of global climate change and exhibit a mechanism, which induces the globally optimal emissions path in Markov-perfect equilibrium.

Keywords: differential games, imperfect monitoring, mechanism design, climate change, Volterra integral equations

JEL Classification: C72, C73, Q53