Sukanya Kudva

Sukanya Kudva, Edward Dowling, Anil Aswani

We consider a multi-unit auction of identical items with single-minded bidders, where a subset of bidders may collude by coordinating bids and transferring payments and items among themselves. Classical collusion-proof mechanisms are largely restricted to posted-price formats, which fail to guarantee even approximate efficiency. We therefore adopt a learning-augmented approach to leverage side information about which bidders are colluding and obtain improved welfare and revenue guarantees. In our setting, colluding bidders optimally shade their bids to suppress prices. Using this characterization, we establish a Bulow-Klemperer type result showing that recruiting more honest bidders is better than the best collusion-proof auction mechanism. We then consider a setting in which a black-box collusion detection algorithm labels bidders as colluding or non-colluding, and propose a VCG Posted Price (V-PoP) mechanism that applies VCG to non-colluding bidders and posted prices to colluding bidders. We show that V-PoP is ex-post dominant-strategy incentive compatible (DSIC) even when it uses select bidder information to calculate an optimal split of items between the subgroups. Additionally, we derive probabilistic guarantees on expected welfare and revenue under both known and unknown valuation distributions, and analyze the robustness of V-PoP to bidder misclassification errors. Numerical experiments across several distributions demonstrate that V-PoP consistently outperforms VCG restricted to non-colluding bidders and approaches the performance of the ideal VCG mechanism assuming universal truthfulness. Our results provide a principled framework for incorporating collusion detection into mechanism design, advancing the theory of auctions under collusion.

Xin Chen, Sukanya Kudva, Yongzheng Dai et al.

The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical algorithms to compute the corresponding solution, or have polynomial-time algorithms that require an exponentially-larger number of samples for low estimation error. This paper develops a novel tensor completion algorithm that resolves this tension by achieving both provable convergence (in numerical tolerance) in a linear number of oracle steps and the information-theoretic rate. Our approach formulates tensor completion as a convex optimization problem constrained using a gauge-based tensor norm, which is defined in a way that allows the use of integer linear optimization to solve linear separation problems over the unit-ball in this new norm. Adaptations based on this insight are incorporated into a Frank-Wolfe variant to build our algorithm. We show our algorithm scales-well using numerical experiments on tensors with up to ten million entries.