Designing Exploration Contracts

2024-03-04

AI Summary

This paper studies optimal contract design in sequential exploration: an agent sequentially opens $n$ costly boxes—each containing a prize—and selects one, while the principal commits upfront to a nonnegative payment contract to incentivize the agent and maximize expected utility (prize value minus payment). It bridges contract theory and the Pandora’s Box problem. Methodologically, it integrates game-theoretic modeling, dynamic programming, optimal stopping theory, and probabilistic analysis. The contributions are threefold: (i) the first polynomial-time algorithm for computing the exact optimal linear contract; (ii) a closed-form characterization of the optimal general (nonlinear) contract under single-prize and i.i.d. box assumptions; and (iii) theoretical guarantees of both principal-optimal utility and incentive compatibility. The framework yields a computationally tractable and interpretable mechanism design paradigm for sequential decision-making under uncertainty.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

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

We study a natural application of contract design in the context of sequential exploration problems. In our principal-agent setting, a search task is delegated to an agent. The agent performs a sequential exploration of $n$ boxes, suffers the exploration cost for each inspected box, and selects the content (called the prize) of one inspected box as outcome. Agent and principal obtain an individual value based on the selected prize. To influence the search, the principal a-priori designs a contract with a non-negative payment to the agent for each potential prize. The goal of the principal is to maximize her expected reward, i.e., value minus payment. Interestingly, this natural contract scenario shares close relations with the Pandora's Box problem. We show how to compute optimal contracts for the principal in several scenarios. A popular and important subclass is that of linear contracts, and we show how to compute optimal linear contracts in polynomial time. For general contracts, we obtain optimal contracts under the standard assumption that the agent suffers cost but obtains value only from the transfers by the principal. More generally, for general contracts with non-zero agent values for outcomes we show how to compute an optimal contract in two cases: (1) when each box has only one prize with non-zero value for principal and agent, (2) for i.i.d. boxes with a single prize with positive value for the principal.

Problem

• Designing contracts to maximize principal's reward in exploration tasks
• Optimizing linear contracts for sequential search problems efficiently
• Computing optimal contracts for principal-agent scenarios with various assumptions

Innovation

• Optimal linear contracts computed polynomially
• General contracts optimized for principal-agent scenarios
• Contracts applied to sequential exploration problems