The mathematics of principal-agent problems




Liu, Bibo

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The principal-agent problem is an important model in the field of Economics of Information. In this thesis we study only a particular type of principal-agent problem which is called moral hazard model and by the principal-agent problem we mean it is moral hazard model. The moral hazard model actually belongs to the class of bilevel programming problems in Mathematics. In Economics. the first order approach is used to reduce the principal-agent problem to a single level optimization problem. However, this approach is only valid under some strong conditions. Moreover the approach can only be used under the assumption that the optimal action of the principal-agent problem and its relaxed problem appears only at an interior point. In this thesis, we consider a new relaxed problem. Under more general assumptions. we can solve the principal-agent problem without restricting the optimal action of the agent to be in the interior.



Principal agent, Moral hazard