  We study the problem of designing mechanisms for trading networks that
satisfy four desired properties: dominant-strategy incentive compatibility,
efficiency, weak budget balance (WBB), and individual rationality (IR).
Although there exist mechanisms that simultaneously satisfy these properties ex
post for combinatorial auctions, we prove the impossibility that such
mechanisms do not exist for a broad class of trading networks. We thus propose
approaches for computing and learning the mechanisms that satisfy the four
properties, in a Bayesian setting, where WBB and IR, respectively, are relaxed
to ex ante and interim. For computational and sample efficiency, we introduce
several techniques, including game theoretical analysis to reduce the input
feature space. We empirically demonstrate that the proposed approaches
successfully find the mechanisms with the four properties for those trading
networks where the impossibility holds ex post.
