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We consider a game in which one player (the principal) seeks to incentivize another player (the agent) to exert effort that is costly to the agent. Any effort exerted leads to an outcome that is a stochastic function of the effort. The amount of effort exerted by the agent is private information for the agent and the principal observes only the outcome; thus, the agent can misreport his effort to gain higher payment. Further, the cost function of the agent is also unknown to the principal and the agent can also misreport a higher cost function to gain higher payment for the same effort. We pose the problem as one of contract design when both adverse selection and moral hazard are present. We show that if the principal and agent interact only finitely many times, it is always possible for the agent to lie due to the asymmetric information pattern and claim a higher payment than if he were unable to lie. However, if the principal and agent interact infinitely many times, then the principal can utilize the observed outcomes to update the contract in a manner that reveals the private cost function of the agent and hence leads to the agent not being able to derive any rent. The result can also be interpreted as saying that the agent is unable to keep his information private if he interacts with the principal sufficiently often.
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On the (In)approximability of Combinatorial Contracts. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)
We study two recent combinatorial contract design models, which highlight different sources of complexity that may arise in contract design, where a principal delegates the execution of a costly project to others. In both settings, the principal cannot observe the choices of the agent(s), only the project’s outcome (success or failure), and incentivizes the agent(s) using a contract, a payment scheme that specifies the payment to the agent(s) upon a project’s success. We present results that resolve open problems and advance our understanding of the computational complexity of both settings. In the multi-agent setting, the project is delegated to a team of agents, where each agent chooses whether or not to exert effort. A success probability function maps any subset of agents who exert effort to a probability of the project’s success. For the family of submodular success probability functions, Dütting et al. [2023] established a poly-time constant factor approximation to the optimal contract, and left open whether this problem admits a PTAS. We answer this question on the negative, by showing that no poly-time algorithm guarantees a better than 0.7-approximation to the optimal contract. For XOS functions, they give a poly-time constant approximation with value and demand queries. We show that with value queries only, one cannot get any constant approximation. In the multi-action setting, the project is delegated to a single agent, who can take any subset of a given set of actions. Here, a success probability function maps any subset of actions to a probability of the project’s success. Dütting et al. [2021a] showed a poly-time algorithm for computing an optimal contract for gross substitutes success probability functions, and showed that the problem is NP-hard for submodular functions. We further strengthen this hardness result by showing that this problem does not admit any constant factor approximation. Furthermore, for the broader class of XOS functions, we establish the hardness of obtaining a n^{-1/2+ε}-approximation for any ε > 0.
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- Award ID(s):
- 1928930
- PAR ID:
- 10514362
- Editor(s):
- Guruswami, Venkatesan
- Publisher / Repository:
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Date Published:
- Volume:
- 287
- Page Range / eLocation ID:
- 44:1-44:22
- Subject(s) / Keyword(s):
- algorithmic contract design combinatorial contracts moral hazard Theory of computation → Algorithmic game theory
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.4230/LIPIcs.ITCS.2024.44
