Trading networks are an indispensable part of today's economy, but to compete successfully with others, they must be efficient in maximizing the value they provide to the external market. While the prior work relies on truthful disclosure of private information to achieve efficiency, we study the problem of designing mechanisms that result in efficient trading networks by incentivizing firms to truthfully reveal their private information to a third party. Additional desirable properties of such mechanisms are weak budget balance (WBB; the third party needs not invest) and individual rationality (IR; firms get non-negative utility). Unlike combinatorial auctions, there may not exist mechanisms that simultaneously satisfy these properties ex post for trading networks. We propose an approach for computing or learning truthful and efficient mechanisms for given networks in a Bayesian setting, where WBB and IR, respectively, are relaxed to ex ante and interim for a given distribution over the private information. We incorporate techniques to reduce computational and sample complexity. We empirically demonstrate that the proposed approach successfully finds the mechanisms with the relaxed properties for trading networks where achieving ex post properties is impossible.

We study contract design for welfare maximization in the well-known "common agency" model of Bernheim and Whinston [1986]. This model combines the challenges of coordinating multiple principals with the fundamental challenge of contract design: that principals have incomplete information of the agent's choice of action. Motivated by the significant social inefficiency of standard contracts for such settings (which we formally quantify using a price of anarchy/stability analysis), we investigate whether and how a recent toolbox developed for the first set of challenges under a complete-information assumption - VCG contracts [Lavi and Shamash, 2019] - can be extended to incomplete information.