Dynamics of Contract Design with Screening

Abstract

We analyze a novel principal-agent problem of moral hazard and adverse selection in continuous time.The constant private shock revealed at time zero when the agent selects the contract has a long-term impact on the optimal contract. The latter is based not only on the continuation value of the agent who truthfully reports, but also contingent upon the continuation value of the agent who misreports, called temptation value. The good agent is retired when the temptation value of the bad agent becomes large, because then it is expensive to motivate the good agent. The bad agent is retired when the temptation value of the good agent becomes small, because then the future payment does not provide sufficient incentives. We also compare the efficiency of the shutdown contract and the screening contract and find that the screening contract can bring more profit to the principal only when the agent's reservation utility is sufficiently small.

Optimal Long-term Contracting with Learning

“…The topic of optimal contracting with endogenous learning also relates to the recent literature studying optimal long-term contracts with adverse selection and moral hazard (e.g., Baron and Besanko, 1984;Sung, 2005;Sannikov, 2007;Garrett and Pavan, 2012;Gershkov and Perry, 2012;Halac, Kartik, and Liu, 2012;and Cvitanic, Wan, and Yang, 2013). 7 In general, when the agent has pre-contracting private information that is persistent, a mechanism design approach naturally arises (e.g., Pavan, Segal and Toikka, 2012;Golosov, Troshkin, and Tsyvinski, 2012).…”

Bank Monitoring Incentives Under Moral Hazard and Adverse Selection

“…In this section we come back to the case in which there are two types of banks in the market, and study the so-called credible set, which is formed by the pairs of value functions of the banks under the admissible contracts. As in [14], we do not expect all the points in the feasible set to correspond to a pair of reachable values of the banks under some admissible contract. We will therefore follow the approach initiated by [14] and we will characterise the credible set.…”

“…Following the terminology of Cvitanić, Wan and Yang [14], let us discuss the so-called feasible set for the banks.…”

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In this paper, we extend the optimal securitisation model of Pagès [50] and Possamaï and Pagès [51] between an investor and a bank to a setting allowing both moral hazard and adverse selection. Following the recent approach to these problems of Cvitanić, Wan and Yang [14], we characterise explicitly and rigorously the so-called credible set of the continuation and temptation values of the bank, and obtain the value function of the investor as well as the optimal contracts through a recursive system of first-order variational inequalities with gradient constraints. We provide a detailed discussion of the properties of the optimal menu of contracts.Principal-Agent problems with moral hazard have an extremely rich history, dating back to the early static models of the 70s, see among many others Zeckhauser [68], Spence and Zeckhauser [63], or Mirrlees [42,43,44,45], as well as the seminal papers by Grossman and Hart [26], Jewitt, [33], Holmström [30] or Rogerson [57].

…”

“…In this paper, we extend the optimal securitisation model of Pagès [50] and Possamaï and Pagès [51] between an investor and a bank to a setting allowing both moral hazard and adverse selection. Following the recent approach to these problems of Cvitanić, Wan and Yang [14], we characterise explicitly and rigorously the so-called credible set of the continuation and temptation values of the bank, and obtain the value function of the investor as well as the optimal contracts through a recursive system of first-order variational inequalities with gradient constraints. We provide a detailed discussion of the properties of the optimal menu of contracts.…”