Collusion-proof mechanisms for multi-unit procurement

Abstract

A principal wants to procure multiple homogeneous units from finitely many agents. Each agent has an increasing and convex cost function, whose exact shape is unknown to the principal. Utility is quasilinear in money. We study which mechanisms are strategy-proof and robust to collusion, both when the agents can exchange money and physical units (reallocation-proofness) and when they cannot (group strategy-proofness). To achieve reallocation-proofness, the principal must offer the agents a fixed price per unit. While group-strategy-proof mechanisms can be more complex, they are inefficient and run the risk of procuring no units at all. We characterize the set of group-strategy-proof and anonymous mechanisms with a uniform price. A standout feature is that the number of potential prices is bounded above by the number of agents.