Dynamics under Full
Contracts are often repeated over time. Examples of such long-term relationships abound and span all areas of contract theory. Let us describe a few. The insurance contract of an agent entails bonuses and maluses that link his current coverage and risk premium to his past history of accidents. Labor contracts often continue to reward the past performances of an agent in the future, either in monetary terms or by means of promotions. Lastly, in many regulated sectors, regulatory contracts often stipulate the current price caps that apply to a given firm as a function of the past realizations of its costs.
In view of the analysis of the previous chapters, the general framework to understand those repeated contractual relationships must be one where the principal controls several activities performed by the agent at different points in time. In an adverse selection setting, the reader will probably have recognized the multi-output framework of section 2.10.3. Under moral hazard, the setting is akin to a multitask model along the lines of section 5.2. With