Budget-Feasible Contracts

2025-04-02

AI Summary

This paper studies incentive contract design for multiple agents under budget constraints, focusing on binary and combinatorial action settings—thereby overcoming the practical limitations of traditional infinite-budget assumptions. Methodologically, it integrates combinatorial optimization, approximation algorithms, mechanism design, and analysis of submodular/gross-substitute reward functions. Key contributions include: (i) introducing the “frugality cost” metric and deriving nearly tight bounds; (ii) establishing, for the first time, the equivalence among revenue, reward, and social welfare (BEST) objectives under budget feasibility; (iii) achieving constant-factor approximations for all BEST objectives in the binary-action setting; (iv) recovering constant approximations under gross-substitute rewards; and (v) proving fundamental inapproximability—no finite approximation ratio is possible for submodular rewards. Collectively, these results provide foundational theory and sharp algorithmic boundaries for budget-feasible incentive mechanisms.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Combinatorial 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

The problem of computing near-optimal contracts in combinatorial settings has recently attracted significant interest in the computer science community. Previous work has provided a rich body of structural and algorithmic insights into this problem. However, most of these results rely on the assumption that the principal has an unlimited budget for incentivizing agents, an assumption that is often unrealistic in practice. This motivates the study of the optimal contract problem under budget constraints. We study multi-agent contracts with budget constraints under both binary and combinatorial actions. For binary actions, our contribution is threefold. First, we generalize all previously known approximation guarantees on the principal's revenue to budgeted settings. Second, through the lens of budget constraints, we uncover insightful connections between the standard objective of the principal's revenue and other objectives. We identify a broad class of objectives, which we term BEST objectives, including reward, social welfare, and revenue, and show that they are all equivalent (up to a constant factor), leading to approximation guarantees for all BEST objectives. Third, we introduce the price of frugality, which quantifies the loss due to budget constraints, and establish near-tight bounds on this measure, providing deeper insights into the tradeoffs between budgets and incentives. For combinatorial actions, we establish a strong negative result. Specifically, we show that in a budgeted setting with submodular rewards, no finite approximation is possible to any BEST objective. This stands in contrast to the unbudgeted setting with submodular rewards, where a polynomial-time constant-factor approximation is known for revenue. On the positive side, for gross substitutes rewards, we recover our binary-actions results, obtaining a constant-factor approximation for all BEST objectives.

Problem

• Study optimal contracts under budget constraints
• Analyze multi-agent contracts with binary and combinatorial actions
• Investigate approximation guarantees for BEST objectives

Innovation

• Generalizes revenue guarantees to budgeted settings
• Introduces BEST objectives equivalence concept
• Establishes price of frugality measure