The complexity of contracts

Dütting, Paul, Roughgarden, Tim and Talgam-Cohen, Inbal (2021) The complexity of contracts. SIAM Journal on Computing, 50 (1). 211 - 254. ISSN 0097-5397

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Abstract

We initiate the study of computing (near-)optimal contracts in succinctly representable principal-agent settings. Here optimality means maximizing the principal's expected payoff over all incentive-compatible contracts-known in economics as "second-best"solutions. We also study a natural relaxation to approximately incentive-compatible contracts. We focus on principalagent settings with succinctly described (and exponentially large) outcome spaces. We show that the computational complexity of computing a near-optimal contract depends fundamentally on the number of agent actions. For settings with a constant number of actions, we present a fully polynomialtime approximation scheme (FPTAS) for the separation oracle of the dual of the problem of minimizing the principal's payment to the agent, and we use this subroutine to efficiently compute a δ-incentive-compatible (δ-IC) contract whose expected payoff matches or surpasses that of the optimal IC contract. With an arbitrary number of actions, we prove that the problem is hard to approximate within any constant c. This inapproximability result holds even for δ-IC contracts where δ is a sufficiently rapidly-decaying function of c. On the positive side, we show that simple linear δ-IC contracts with constant δ are sufficient to achieve a constant-factor approximation of the "first-best"(full-welfare-extracting) solution, and that such a contract can be computed in polynomial time.

Item Type:	Article
Official URL:	https://epubs.siam.org/journal/smjcat
Additional Information:	© 2021 Society for Industrial and Applied Mathematics
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	15 Dec 2020 15:42
Last Modified:	16 Nov 2024 02:09
URI:	http://eprints.lse.ac.uk/id/eprint/107917

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