Incomplete Information VCG Contracts for Common Agency

Tal Alon, Inbal Talgam-Cohen, Ron Lavi, Elisheva Shamash

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We study contract design for welfare maximization in the well-known “common agency” model introduced in 1986 by Bernheim and Whinston. This model combines the challenges of coordinating multiple principals with the fundamental challenge of contract design: that principals have incomplete information of the agent’s choice of action. Our goal is to design contracts that satisfy truthfulness of the principals, welfare maximization by the agent, and two fundamental properties of individual rationality (IR) for the principals and limited liability (LL) for the agent. Our results reveal an inherent impossibility. Whereas for every common agency setting there exists a truthful and welfare-maximizing contract, which we refer to as “incomplete information Vickrey–Clarke–Groves contracts,” there is no such contract that also satisfies IR and LL for all settings. As our main results, we show that the class of settings for which there exists a contract that satisfies truthfulness, welfare maximization, LL, and IR is identifiable by a polynomial-time algorithm. Furthermore, for these settings, we design a polynomial-time computable contract: given valuation reports from the principals, it returns, if possible for the setting, a payment scheme for the agent that constitutes a contract with all desired properties. We also give a sufficient graph-theoretic condition on the population of principals that ensures the existence of such a contract and two truthful and welfare-maximizing contracts, in which one satisfies LL and the other one satisfies IR.

Original languageEnglish
Pages (from-to)288-299
Number of pages12
JournalOperations Research
Issue number1
Early online date18 Jul 2023
Publication statusPublished - 31 Jan 2024


  • common agent
  • contract
  • equilibrium
  • individual rationality
  • limited liability
  • polynomial complexity
  • principal
  • VCG

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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