Contract Design for Sequential Actions

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Tomer Ezra, Michal Feldman, Maya Schlesinger

Published: 2026, Last Modified: 07 May 2026SODA 2026EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We introduce a novel model of contracts with combinatorial actions that captures sequential and adaptive agent behavior. As in the standard setting, a principal delegates a costly project to an agent and incentivizes them via a contract specifying payments for each possible outcome. The novelty of our model lies in allowing the agent to select actions sequentially — after each action, they observe the outcome and decide whether to stop or continue. This framework captures common scenarios in which agents can make multiple attempts to achieve a desired outcome.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. We then 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 give a polynomial-time algorithm for computing the optimal linear contract and show that finding the optimal general contract is NP-hard. When the number of outcomes is constant, we provide a polynomial-time algorithm even for general contracts. In the case of correlated actions, we show that, for both linear and general contracts, approximating the optimal contract within any constant factor is NP-hard.*This project has been partially funded by the European Research Council (ERC) under the European Union’s Horizon Europe Program (grant agreement No. 101170373), by an Amazon Research Award, by the NSF-BSF (grant number 2020788), by the Israel Science Foundation Breakthrough Program (grant No. 2600/24), and by a grant from TAU Center for AI and Data Science (TAD). T. Ezra is supported by the Harvard University Center of Mathematical Sciences and Applications.