Agency Contracts under Maximum-Entropy

This article proposes the application of the maximum-entropy principle (MEP) to agency contracting (where a principal hires an agent to make decisions on their behalf) in situations where the principal and agent only have partial knowledge on the probability distribution of the output conditioned on the agent’s actions. The paper characterizes the second-best agency contract from a maximum entropy distribution (MED) obtained from applying the MEP to the agency situation consistently with the information available. We show that, with the minimum shared information about the output distribution for the agency relationship to take place, the second-best compensation contract is (a monotone transformation of) an increasing affine function of output. With additional information on the output distribution, the second-best optimal contracts can be more complex. The second-best contracts obtained theoretically from the MEP cover many compensation schemes observed in real agency relationships.

Comment on “Optimal Contract to Induce Continued Effort”

In this comment, we first use a counterexample to demonstrate that the optimal contract structure proposed in section 4 of Sun and Tian (2018) can be wrong when the two players’ discount rates are different. We then specify correct optimal contract structures, which involve generalizing the contract space to allow random termination. Numerical study with a wide range of model parameters illustrates that such a random termination only occurs sparingly in optimal contracts. Moreover, the suboptimality gap, measured by the relative improvement of the optimal contract over the best contract without random termination, is extremely small. This paper was accepted by Manel Baucells, decision analysis.

Revenue sharing on the Internet

Revenue sharing contracts between Content Providers (CPs) and Internet Service Providers (ISPs) can act as leverage for enhancing the infrastructure of the Internet. ISPs can be incentivised to make investments in network infrastructure that improve Quality of Service (QoS) for users if attractive contracts are negotiated between them and CPs. The idea here is that part of the revenue of CPs is shared with ISPs to invest in infrastructure improvement. We propose a model in which CPs (leaders) determine contracts, and an ISP (follower) reacts by strategically determining the infrastructure enhancement (effort) for each CP. Two cases are studied: (i) the ISP differentiates between the CPs and puts (potentially) a different level of efforts to improve the QoS of each CP, and (ii) the ISP does not differentiate between CPs and makes equal amount of effort for all the CPs. The last scenario can be viewed as neutral behavior by the ISP. Our analysis of optimal contracts shows that preference of CPs for the neutral and non-neutral regime depends on their monetizing power - CPs which can better monetize their demand tend to prefer non-neutral regime whereas the weaker CPs tend to prefer the neutral regime. Interestingly, ISP revenue, as well as social utility, are also found to be higher under the non-neutral regime. We then propose an intermediate regulatory regime that we call "soft-neutral", where efforts put by the ISP for all the CPs need not be equal same but the disparity is not wide. We show that the soft-neutral regime alleviates the loss in social utility in the neutral regime and the outcome further improves when CPs determine their contracts through bargaining.

OPTIMAL CONTRACTS IN A MULTI-PURPOSE TASK

In the paper a famous multitask model of principal-agent relations is enhanced with the requirement that a reward is paid only if some minimal threshold in each type of workis attained. We deduce and analyze formulae for the expectedutility of an agent and propose a method to find his optimal behavior depending on the reward function parameters.

Optimal Contract for Machine Repair and Maintenance

Maintenance outsourcing is quite common in industries that rely on complex and critical equipment. Instead of investing in the maintenance facilities, firms outsource maintenance activities to specialized companies. However, it may be hard for firms (i.e., principal) to observe whether maintenance companies (i.e., agent) put sufficient resources into providing the best service, which gives rise to agency issues. In a dynamic environment in which an agent is responsible for both maintenance and repair of a critical machine, how the principal uses payments and termination to tackle agency issues is a challenging problem. In “Optimal Contract for Machine Repair and Maintenance,” F. Tian, P. Sun, and I. Duenyas provide theoretical guidance on designing the optimal contract to induce efforts from an agent to efficiently operate a machine. Although they consider the very general contract forms, the optimal contracts demonstrate simple and intuitive structures, making them easy to describe and implement in practice.

Monitoring experts

We study the design of contracts that incentivize experts to collect information and truthfully report it to a decision maker. We depart from most of the previous literature by assuming that the transfers cannot depend on the realized state or on the ex post payoff of the decision maker. The contract thus has to induce the experts to “monitor each other” by making the transfers contingent on the entire vector of reports. We characterize the least costly contract that implements any given vector of efforts and derive the cost function for the decision maker. We then study properties of optimal contracts by comparing the value of information and its cost.