Incomplete Information VCG Contracts for Common Agency

TL;DR

This paper extends VCG contracts to incomplete information settings in common agency models, ensuring welfare maximization, truthfulness, and participation, while analyzing the inherent tradeoffs and providing polynomial-time algorithms for their implementation.

Contribution

It introduces and characterizes incomplete information VCG (IIVCG) contracts, proving their uniqueness and designing polynomial-time algorithms for their existence and construction.

Findings

IIVCG contracts guarantee truthfulness and welfare maximization.

A polynomial-time algorithm determines the existence of IIVCG contracts.

A graph-theoretic condition ensures the existence of IIVCG contracts.

Abstract

We study contract design for welfare maximization in the well known "common agency" model of [Bernheim and Whinston, 1986]. 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. Motivated by the significant social inefficiency of standard contracts for such settings (which we formally quantify using a price of anarchy/stability analysis), we investigate whether and how a recent toolbox developed for the first set of challenges under a complete-information assumption, VCG contracts [Lavi and Shamash, 2019], can be extended to incomplete information. We define and characterize the class of "incomplete information VCG contracts (IIVCG)", and show it is the unique class guaranteeing truthfulness of the principals and welfare maximization by the agent. Our results reveal an inherent tradeoff between two important properties required to ensure participation in the contract: individual rationality (for the principals) and limited liability (for the agent). We design a polynomial-time algorithm for determining whether a setting has an IIVCG contract with both properties. As our main result we design a polynomial-time "algorithmic IIVCG" contract: given valuation reports from the principals it returns, if possible for the setting, a payment scheme for the agent that constitutes an IIVCG contract with all desired properties. We also give a sufficient graph-theoretic condition on the population of principals that ensures the existence of such an IIVCG contract.