We study a new class of contract design problems where a principal delegates the execution of multiple projects to a set of agents. The principal's expected reward from each project is a combinatorial function of the agents working on it. Each agent has limited capacity and can work on at most one project, and the agents are heterogeneous, with different costs and contributions for participating in different projects. The main challenge of the principal is to decide how to allocate the agents to projects when the number of projects grows in scale.

We study a generalization of both the classic single-dimensional mechanism design problem, and the hidden-action principal-agent problem of contract theory [c.f., Alon et al. 2021]. In this setting, the principal seeks to incentivize an agent with a private Bayesian type to take a costly action. The goal is to design an incentive compatible menu of contracts which maximizes the expected revenue.

Economic theory distinguishes between principal-agent settings in which the agent has a private type and settings in which the agent takes a hidden action. Many practical problems, however, involve aspects of both. For example, brand X may seek to hire an influencer Y to create sponsored content to be posted on social media platform Z. This problem has a hidden action component (the brand may not be able or willing to observe the amount of effort exerted by the influencer), but also a private type component (influencers may have different costs per unit-of-effort). This "effort" and "cost per unit-of-effort" perspective naturally leads to a principal-agent problem with hidden action and single-dimensional private type, which generalizes both the classic principal-agent hidden action model of contract theory a la Grossmann and Hart [1986] and the (procurement version) of single-dimensional mechanism design a la Myerson [1983]. A natural goal in this model is to design an incentive-compatible contract, which consist of an allocation rule that maps types to actions, and a payment rule that maps types to payments for the stochastic outcomes of the chosen action. Our main contribution is an LP-duality based characterization of implementable allocation rules for this model, which applies to both discrete and continuous types. This characterization shares important features of Myerson's celebrated characterization result, but also departs from it in significant ways. We present several applications, including a polynomial-time algorithm for finding the optimal contract with a constant number of actions. This in sharp contrast to recent work on hidden action problems with multi-dimensional private information, which has shown that the problem of computing an optimal contract for constant numbers of actions is APX-hard.

We study contract design for welfare maximization in the well-known "common agency" model of Bernheim and Whinston [1986]. This model combines the challenges of coordinating multiple principals with the fundamental challenge of contract design: that principals have incomplete information of the agent's choice of action. Motivated by the significant social inefficiency of standard contracts for such settings (which we formally quantify using a price of anarchy/stability analysis), we investigate whether and how a recent toolbox developed for the first set of challenges under a complete-information assumption - VCG contracts [Lavi and Shamash, 2019] - can be extended to incomplete information.

We consider settings where agents are evaluated based on observed features, and assume they seek to achieve feature values that bring about good evaluations. Our goal is to craft evaluation mechanisms that incentivize the agents to invest effort in desirable actions; a notable application is the design of course grading schemes. Previous work has studied this problem in the case of a single agent. By contrast, we investigate the general, multi-agent model, and provide a complete characterization of its computational complexity.