A Dual Approach to Agency Problems

This paper presents a dual approach to the standard agency model. We formulate the dual of the principal-agent problem under the assumption that the incentive constraint can be replaced by a local constraint (the first-order approach), to examine whether the relaxed agency problem yields a candidate solution. The dual formulation generates a distinctive form of convex conjugate, which transforms the agent's utility from compensation into a dual functional. The dual problem features a simple convex structure, which enables us to perform a comprehensive analysis for the agency problem. We derive novel and more tractable conditions for existence and uniqueness of a solution to the problem with the dual elements. Furthermore, the approach to the dual problem provides illuminating insights into the previous nonexistence results