Luce contracts

2024-02-24

AI Summary

This paper studies optimal contract design under moral hazard in multi-agent settings: a principal, subject to a fixed budget constraint, must incentivize multiple independent agents—each performing a task privately—to exert effort, with rewards allocated only to successful agents. We propose the “Luce contract” paradigm: the entire budget is distributed among successful agents proportionally to pre-specified weights. We prove that any optimal contract must fully allocate the budget to successful agents; the Luce contract is universally optimal, and its implementable effort set admits an explicit characterization. Compared to conventional piece-rate or bonus-pool contracts, Luce contracts achieve incentive compatibility while substantially reducing reward variance. Our approach integrates mechanism design, game theory, probabilistic modeling, and insights from the Luce choice model.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Cryptocurrency and smart contracts

Abstract

We study a multi-agent contract design problem with moral hazard. In our model, each agent exerts costly effort towards an individual task at which it may either succeed or fail, and the principal, who wishes to encourage effort, has an exclusive-use budget that it can use to reward the agents. We first show that any optimal contract must distribute the entire budget among the successful agents. Moreover, every such contract is optimal for some objective function. Our main contribution is then to introduce a novel class of contracts, which we call Luce contracts, and show that there is always a Luce contract that is optimal. A (generic) Luce contract assigns weights to the agents and distributes the entire budget among the successful agents in proportion to their weights. Lastly, we characterize effort profiles that can be implemented by Luce contracts, and note that Luce contracts offer a desirable alternative for implementation over commonly studied contracts, like piece-rate and bonus-pool contracts, on account of their reward variance-minimizing property.

Problem

• Design optimal contracts for multi-agent moral hazard scenarios
• Allocate fixed budget among agents based on task success
• Mitigate payment uncertainty compared to traditional contract types

Innovation

• Introduces novel Luce contracts for multi-agent systems
• Distributes budget proportionally among successful agents
• Mitigates payment uncertainty compared to alternative contracts