Multi-Project Contracts

TL;DR

This paper introduces a novel contract design framework for multiple projects with heterogeneous agents, providing polynomial-time approximation algorithms for complex reward functions and advancing combinatorial contract theory.

Contribution

It develops the first polynomial-time approximation method for multi-project contracts with XOS reward functions, including new demand query techniques for capped subadditive functions.

Findings

Constant approximation for XOS functions in polynomial time

Development of approximate demand queries for capped subadditive functions

Framework enabling richer combinatorial contract design

Abstract

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 analyze this problem under different assumptions on the structure of the expected reward functions. As our main result, for XOS functions we show how to derive a constant approximation to the optimal multi-project contract in polynomial time, given access to value and demand oracles. Along the way (and of possible independent interest), we develop approximate demand queries for \emph{capped} subadditive functions, by reducing to demand queries for the original functions. Our work paves the way to combinatorial contract design in richer settings.