an action. This introduces a tension among the n noncooperative principals to coordinate the

agent’s choice of action, on top of the usual tension between each principal and the self-interested

agent. What constitutes a desirable action depends on the principals’ valuations and on the design

objective (welfare, revenue, etc.). In this work we focus on welfare, as detailed below.

The game. Fix a common agency setting. A contract t and valuation proﬁle v deﬁne the following
two-stage game. First, principals simultaneously report their bids b = (b1, ..., bn). After perceiving
the bids, the agent chooses a hidden action a, which imposes a distribution F|a over the outcomes.
An outcome o is realized according to this distribution, and each principal (cid:96) pays the agent t(cid:96)(b, o).
We assume quasi-linear utilities and risk neutrality for all parties. The utilities of the game are as
(cid:96)∈[n] t(cid:96)(b, o) −
Incomplete Information VCG Contracts for Common Agency