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 principal-agent 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 polynomial-time 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 $\delta$-incentive-compatible ($\delta$-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 $\delta$-IC contracts where $\delta$ is a sufficiently rapidly-decaying function of $c$. On the positive side, we show that simple linear $\delta$-IC contracts with constant $\delta$ 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.

Keywords

  1. principal-agent problem
  2. contract theory
  3. moral hazard
  4. computational complexity
  5. hardness of approximation
  6. FPTAS

MSC codes

  1. 68W40
  2. 91B40

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Information & Authors

Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 211 - 254
ISSN (online): 1095-7111

History

Submitted: 24 February 2020
Accepted: 11 December 2020
Published online: 25 February 2021

Keywords

  1. principal-agent problem
  2. contract theory
  3. moral hazard
  4. computational complexity
  5. hardness of approximation
  6. FPTAS

MSC codes

  1. 68W40
  2. 91B40

Authors

Affiliations

Funding Information

Army Research Office https://doi.org/10.13039/100000183 : W911NF1910294
Henry and Marilyn Taub Foundation https://doi.org/10.13039/100013730
Israel Science Foundation https://doi.org/10.13039/501100003977 : 336/18
Leverhulme Trust https://doi.org/10.13039/501100000275 : SRG1819n191601
National Science Foundation https://doi.org/10.13039/100000001 : CCF-1813188

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