Information concentration in common value environments

We consider how information concentration affects a seller’s revenue in common value auctions. The common value is a function of $n$ random variables partitioned among $m \le n$ bidders. For each partition, the seller devises an optimal mechanism. We show that whenever the value function allows scalar sufficient statistics for each player’s signals, the mechanism design problem is well-defined. Additionally, whenever a common regularity condition is satisfied, a coarser partition always reduces revenues. In particular, any merger or collusion among bidders reduces revenue.