Complexity of Auctions with Interdependence

A team of researchers including Patrick Loiseau, Simon Mauras, and Minrui Xu has published a significant theoretical computer science paper titled "Complexity of Auctions with Interdependence" (arXiv:2603.18668). The work tackles a core problem in algorithmic game theory: designing truthful auction mechanisms where bidders' valuations are interdependent, meaning each bidder's value depends not only on their own private signal but also on others' signals. This model, introduced by Milgrom and Weber in 1982, is more realistic for many real-world scenarios like spectrum or ad slot auctions but is notoriously complex to optimize.

The researchers investigated both value-maximizing auctions (allocating a good) and the lesser-studied cost-minimizing procurement auctions (allocating a chore). Crucially, they removed two major simplifying assumptions common in prior literature: domain restrictions and the requirement for monotone valuation functions. Their central finding is a hardness result: they proved that the general problem of designing a truthful mechanism that optimizes the approximation ratio is NP-hard. This provides a theoretical explanation for why previous research focused on special cases.

Complementing the negative result, the paper provides positive characterizations for when the problem becomes tractable. The authors show that some previously considered special cases can be reduced to classical combinatorial problems, allowing for efficient algorithms. They also establish query complexity lower bounds, quantifying the minimum information needed from bidders to achieve certain approximation guarantees. This work delineates the boundary between computationally feasible and infeasible automated mechanism design.