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Designing Exploration Contracts

Authors Martin Hoefer , Conrad Schecker , Kevin Schewior

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Author Details

Martin Hoefer
  • Department of Computer Science, RWTH Aachen University, Germany
Conrad Schecker
  • Institute for Computer Science, Goethe University Frankfurt, Germany
Kevin Schewior
  • Department of Mathematics and Computer Science, University of Cologne, Germany
  • University of Southern Denmark, Odense, Denmark

Funding

  • Hoefer, Martin: Supported by DFG Research Unit ADYN (project number 411362735) and DFG grant Ho 3831/9-1 (project number 514505843).
  • Schewior, Kevin: Supported by the Independent Research Fund Denmark, Natural Sciences, grant DFF-0135-00018B.

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Martin Hoefer, Conrad Schecker, and Kevin Schewior. Designing Exploration Contracts. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 50:1-50:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.50

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • Exploration
  • Contract Design
  • Pandora’s Box Problem

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