A Fixed-point Method for Solving Principal-Agent Problems: Beyond the First-order Approach (Preliminary)

Abstract

Abstract This paper generalizes Ke's (2010) …xed-point method and develops a uni…ed solution method for principal-agent problems with moral hazard under a general setting (i.e., multi-task and multi-signal). We show that the principal's problem with a complicated incentive compatibility constraint, which consists of in…nitely many inequalities, is equivalent to a Lagrangian dual problem with routine equality and inequality constraints. The discovered Lagrangian dual representation only includes the least necessary constraints for individual rationality and incentive compatibility. Thus, we can characterize the optimal contract and solve the principal-agent problem by a routine parametric programming. We provide a set of Kuhn-Tucker optimality conditions that can be applied to …nd a solution, regardless of the validity of the …rst-order approach. We also provide some examples and a comparative static analysis