Consider a situation where a group of buyers would like to jointly purchase a particular resource with the intention of sharing it. For example, suppose two individuals who are sharing a living space would like to purchase an object, say an air conditioner or a television, which is available in the market for a certain price. How do they agree upon a division of this price amongst themselves when their utilties for using that object are private? Any scheme that recommends some notion of fair division of this price has to rely on the ability of the scheme to elicit the true utilities of the individuals, which is difficult since each individual wants to minimize his share of the payment. More generally, the resource in question may be congestible, and the utilities may depend on the proportion in which it is shared between the two users. In that case they not only have to decide how to divide the price of the resource but also how it will be shared, and the two decisions would naturally have to go hand in hand. Moreover, it may not be a simple question of paying a given price, but the resource itself may be offered in an auction, in which case the two buyers need to decide how they will jointly bid in the auction, along with the terms of sharing the resource and the division of payment in the event that they win. Embracing the classical perspective of mechanism design, we can transfer the onus of coming up with a solution to this problem from the buyers to the seller herself. This leads us to consider the converse problem from the perspective of the seller in the market. She intends to sell a resource and several competing groups of buyers are interested in purchasing that resource for their respective groups. Her problem is thus to design a mechanism to allocate the resource to one of the competing groups, along with a proposed division of the resource within the group. The key aspect of this design problem is the kind of incentive properties such a mechanism needs to satisfy. The buyers in a single group are expected to collude in their utility reports and hence such a mechanism needs to be robust to any collusive behavior within a particular group, but perhaps not necessarily across groups. A practical example, which is our primary motivation for studying this kind of a market, is the market for radio spectrum. Recently there has been a debate concerning the merits and demerits of allocating newly opened blocks of spectrum for free unlicensed use (like WiFi) as opposed to selling them for exclusive licensed use (e.g., to cellular ser-