Collection Auctions with Prefix Structure

We consider multi-unit auctions in which bidders submit non-decreasing (prefix) bid sequences. We prove that under prefix monotonicity, any allocation that maximizes the sum of prefix bids necessarily assigns all items to a single bidder. Hence, although the environment admits multi-winner allocations, optimal allocations collapse to a singleton outcome. This shows that prefix structure eliminates multi-winner efficient allocations in multi-unit environments. The result provides a simple structural characterization of how prefix constraints alter allocation patterns and prevent quantity splitting across bidders.