A monopolist platform (the principal) shares profits with a population of affiliates (the agents), heterogeneous in skill, by offering them a common nonlinear contract contingent on individual revenue. The principal cannot discriminate across individual skill but knows its distribution and aims at maximizing profits. This paper identifies the optimal contract, its implied profits, and agents' effort as the unique solution to an equation depending on skill distribution and agents' costs of effort. If skill is Pareto-distributed and agents' costs include linear and power components, then closed-form solutions highlight two regimes: If linear costs are low, the principal's share of revenues is insensitive to skill distribution and decreases as agents' costs increase. If linear costs are high, then the principal's share is insensitive to the agents' costs and increases as inequality in skill increases.


  1. optimal contracts
  2. principal-agent
  3. hidden type
  4. adverse selection

MSC codes

  1. 91B41
  2. 91B43

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Information & Authors


Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 3559 - 3585
ISSN (online): 1095-7138


Submitted: 8 April 2019
Accepted: 16 September 2020
Published online: 1 December 2020


  1. optimal contracts
  2. principal-agent
  3. hidden type
  4. adverse selection

MSC codes

  1. 91B41
  2. 91B43



Funding Information

H2020 European Research Council https://doi.org/10.13039/100010663 : 279582
National Science Foundation https://doi.org/10.13039/100000001 : DMS-1412529
Science Foundation Ireland https://doi.org/10.13039/501100001602 : 16/IA/4443, 16/SPP/3347

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