Multi-Project Contracts

2025-06-06

AI Summary

This paper studies optimal contract design in a multi-task principal–agent setting: a principal assigns heterogeneous agents—each capable of undertaking at most one task—to multiple tasks, aiming to maximize expected output governed by an XOS (fractionally subadditive) valuation function over agent assignments. To address computational intractability arising from large-scale task sets, we devise the first polynomial-time constant-factor approximation algorithm for optimal contracting under XOS valuations. Our method introduces a novel approximate demand query procedure tailored to truncated subadditive functions. Technically, we integrate tools from mechanism design, combinatorial optimization, and submodular/ subadditive function theory within the value oracle model. The proposed algorithm achieves a constant-factor approximation of the optimal contract in polynomial time, thereby substantially improving both computational efficiency and theoretical guarantees for large-scale heterogeneous agent allocation.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Design contracts for multiple projects with heterogeneous agents
• Allocate agents to projects under capacity constraints
• Approximate optimal contracts for combinatorial reward functions

Innovation

• Combinatorial contract design for multi-project allocation
• Constant approximation via XOS functions analysis
• Approximate demand queries for capped subadditive functions