Strongly budget balanced auctions for multi-sided markets

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 auction of McAfee (1992) [35] is truthful and has no deficit — it is weakly-budget-balanced, and the one by Segal-Halevi et al.'s (2016) [38] 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 in areas such as supply chain requires 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 [38] 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.