Monotonic Preference Aggregation Mechanisms for Purchasing a Shareable Resource

Abstract: Situations where a group of agents come together to jointly buy a resource that they individually cannot afford to buy are commonly observed in markets. For example in the US market for radio spectrum, a recent proposal invited small firms who would benefit from gaining additional access to spectrum to jointly submit bids for blocks of spectrum with the idea that its utilization could be shared. In such a scenario, the problem is to design a mechanism that truthfully elicits and aggregates the privately held preferences of these agents, and enables them to act as a single decision-making body in order to participate in the market. In this paper, we design a class of mechanisms called monotonic aggregation mechanisms that achieves this under a specific setting. We assume that the resource is being sold in a sealed-bid second-price auction that solicits bids for the entire resource. Our mechanism truthfully elicits utility functions from the buyers, prescribes a joint bid, and prescribes a division of the payment and the resource in the event that they win the resource in the auction. This mechanism further satisfies a popular notion of collusion-resistance known as coalition-strategyproofness. We give two explicit examples of this generic class for the case where the utility functions of the buyers are non-decreasing and concave.