Bilevel Optimization and the Principal-agent Problem

Abstract: 

The principal-agent problem is a well-known problem in economics, in which one party (the “agent”) acts on behalf of another party (the “principal”). In many cases, the agent has incentive to act against the principal’s best interests. The problem may be modelled as a bilevel programming problem, where the principal maximises their expected utility subject to the constraint that the agent also maximises their expected utility.

Under the assumption that the expected utility functions are polynomial, we develop a convergent global optimization approach to solve the principal-agent problem using a sequence of semidefinite programming (SDP) relaxations.

Aidan is an Applied Mathematics Honours student working with Jeya Jeyakumar.