Incentive compatible and stable trade mechanisms on networks

We study a network of buyers and sellers where each seller owns an indivisible object and has no incentive to keep it, while each buyer has a downward sloping demand curve which is private information. Only the connected buyer-seller pairs can engage in trade. We search for trade mechanisms that are efficient, strategy-proof, bilateral trade stable and individually rational. In general, there does not exist a trade mechanism simultaneously satisfying these properties. The tension between strategy-proofness and bilateral trade stability is generated by the intersection between sets of competitors of a buyer at different sellers. Such intersections often allow the buyer to manipulate (via demand reductions) the prices paid in the network. The observed tension can be resolved if and only if the underlying network is cycle-free. In such a case, there is a unique trade mechanism which satisfies our four properties, a generalized Vickrey auction.