Contract Design for Sequential Actions

2024-03-14

AI Summary

This paper studies optimal contract design in a principal–agent framework where the agent sequentially and adaptively performs multi-step actions: selecting an action, observing its outcome, and dynamically deciding whether to continue or stop, ultimately submitting a realized outcome to trigger payment. It innovatively integrates sequential decision-making and the Pandora’s Box model into contract theory to capture adaptive, information-dependent behavior with multiple attempts. Methodologically, it models the agent’s exploration as an optimal stopping problem under uncertainty, with outcomes drawn from known distributions. Theoretical contributions include: (1) proving that linear contracts are efficiently optimal under outcome independence, yielding a polynomial-time algorithm; (2) providing a polynomial-time optimal algorithm for general contracts when the number of possible outcomes is fixed; and (3) establishing computational hardness by showing that constant-factor approximation is impossible under outcome correlation, thereby characterizing the complexity boundary of the problem.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

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 introduce a novel model of contracts with combinatorial actions that accounts for sequential and adaptive agent behavior. As in the standard model, a principal delegates the execution of a costly project to an agent. There are $n$ actions, each one incurring a cost to the agent and inducing a probability distribution over $m$ outcomes; each outcome generates some reward for the principal. The principal incentivizes the agent through a contract that specifies a payment for each potential outcome. Unlike the standard model, the agent chooses actions sequentially. Following each action, the agent observes the realized outcome, and decides whether to stop or continue with another action. Upon halting, the agent chooses one of the realized outcomes, which determines both his payment and the principal's reward. This model captures common scenarios where the agent can make multiple attempts in the course of executing a project. We study the optimal contract problem in this new setting, namely the contract that maximizes the principal's utility. We first observe that the agent's problem - (adaptively) finding the sequence of actions that maximizes his utility for a given contract - is equivalent to the well-known Pandora's Box problem. Using this insight, we provide algorithms and hardness results for the optimal contract problem, under both independent and correlated actions, and for both linear and general contracts. For independent actions, we provide a poly-time algorithm for the optimal linear contract, and establish that finding the optimal general contract is NP-hard. In cases where the number of outcomes is constant, we devise a poly-time algorithm even for the optimal general contract. For correlated actions, we find that, for both linear and general contracts, approximating the optimal contract within any constant ratio is NP-hard.

Problem

• Designing contracts for sequential agent actions
• Optimizing principal's utility in adaptive settings
• Solving NP-hard contract problems efficiently

Innovation

• Sequential and adaptive agent behavior model
• Pandora's Box problem equivalence
• Poly-time and NP-hard algorithms analysis