An Algorithm-to-Contract Framework without Demand Queries

2025-07-26

AI Summary

This paper studies incentive-compatible contract design under the budget-maximization framework: how to transform combinatorial optimization algorithms into approximately optimal, incentive-compatible contracts without access to a demand oracle. We propose a “local-to-global” transformation framework—the first generic reduction from standard algorithms to incentive-compatible contracts that does not rely on a black-box demand oracle, while preserving the original algorithm’s approximation ratio. Our approach leverages bilateral enhanced demand approximation and supports complex combinatorial constraints—including matroids, matchings, and multi-dimensional budgets—as well as extensions to multi-agent collaborative settings. Under various constraint classes, we obtain fully polynomial-time approximation schemes (FPTAS) in both multiplicative and additive senses, with approximation guarantees matching the best-known bounds for the corresponding pure algorithmic problems.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Local 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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Consider costly tasks that add up to the success of a project, and must be fitted by an agent into a given time-frame. This is an instance of the classic budgeted maximization problem, which admits an approximation scheme (FPTAS). Now assume the agent is performing these tasks on behalf of a principal, who is the one to reap the rewards if the project succeeds. The principal must design a contract to incentivize the agent. Is there still an approximation scheme? In this work, our ultimate goal is an algorithm-to-contract transformation, which transforms algorithms for combinatorial problems (like budgeted maximization) to tackle incentive constraints that arise in contract design. Our approach diverges from previous works on combinatorial contract design by avoiding an assumption of black-box access to a demand oracle. We first show how to "lift" the FPTAS for budgeted maximization to obtain the best-possible multiplicative and additive FPTAS for the contract design problem. We establish this through our "local-global" framework, in which the "local" step is to (approximately) solve a two-sided strengthened variant of the demand problem. The "global" step then utilizes the local one to find the approximately optimal contract. We apply our framework to a host of combinatorial constraints including multi-dimensional budgets, budgeted matroid, and budgeted matching constraints. In all cases we achieve an approximation essentially matching the best approximation for the purely algorithmic problem. We also develop a method to tackle multi-agent contract settings, where the team of working agents must abide to combinatorial feasibility constraints.

Problem

• Transforming algorithms for combinatorial problems to handle contract design incentives
• Avoiding demand oracle assumptions in combinatorial contract design
• Extending framework to multi-agent settings with combinatorial constraints

Innovation

• Algorithm-to-contract transformation for incentive constraints
• Local-global framework for optimal contract approximation
• Multi-agent contract method with combinatorial constraints