  In two-sided markets, Myerson and Satterthwaite's impossibility theorem
states that one can not maximize the gain-from-trade while also satisfying
truthfulness, individual-rationality and no deficit. Attempts have been made to
circumvent Myerson and Satterthwaite's result by attaining
approximately-maximum gain-from-trade: the double-sided auctions of McAfee
(1992) is truthful and has no deficit, and the one by Segal-Halevi et al.
(2016) additionally has no surplus --- it is strongly-budget-balanced. They
consider two categories of agents --- buyers and sellers, where each trade set
is composed of a single buyer and a single seller. The practical complexity of
applications such as supply chain require one to look beyond two-sided markets.
Common requirements are for: buyers trading with multiple sellers of different
or identical items, buyers trading with sellers through transporters and
mediators, and sellers trading with multiple buyers. We attempt to address
these settings. We generalize Segal-Halevi et al. (2016)'s
strongly-budget-balanced double-sided auction setting to a multilateral market
where each trade set is composed of any number of agent categories. Our
generalization refines the notion of competition in multi-sided auctions by
introducing the concepts of external competition and trade reduction. We also
show an obviously-truthful implementation of our auction using multiple
ascending prices.
