Incentive compatibility constraints and dynamic programming in continuous time

Abstract

This paper is devoted to the study of infinite horizon continuous time optimal control problems with incentive compatibility constraints that arise in many economic problems, for instance in defining the second best Pareto optimum for the joint exploitation of a common resource, as in Benhabib and Radner [Benhabib, J., Radner, R., 1992. The joint exploitation of a productive asset: a game theoretic approach. Economic Theory, 2: 155–190]. An incentive compatibility constraint is a constraint on the continuation of the payoff function at every time. We prove that the dynamic programming principle holds, the value function is a viscosity solution of the associated Hamilton–Jacobi–Bellman (HJB) equation, and that it is the minimal supersolution satisfying certain boundary conditions. When the incentive compatibility constraint only depends on the present value of the state variable, we prove existence of optimal strategies, and we show that the problem is equivalent to a state constraints problem in an endogenous state region which depends on the data of the problem. Some economic examples are analyzed.