arXiv subjects

Yonglei Yan

Publications and source records attributed to Yonglei Yan.

4 recordsLinked to original sources

arXiv2026

Settling the Complexity of Hylland--Zeckhauser Equilibria

The Hylland--Zeckhauser (HZ) mechanism is a foundational framework for allocating indivisible goods in one-sided matching markets via lotteries supported by competitive prices and equal artificial budgets. We resolve the exact computational complexity of the HZ scheme by proving that computing an exact HZ equilibrium is FIXP-complete, thereby settling a conjecture of Vazirani and Yannakakis. Notably, this hardness persists even when computing the equilibrium allocation alone. We establish our hardness result via a reduction that encodes quadratic fixed-point equations into a reciprocal variational inequality. On the algorithmic side, we present a deterministic polynomial-time approximation algorithm that achieves an additive error of $0.0755211 + δ$ for any $δ> 0$, significantly improving upon the previous $1/e$ guarantee.

cs.GT↗

arXiv2026

On the Complexity of Exact Autobidding Equilibria

Autobidding equilibria link advertisers' value multipliers or participation probabilities through aggregate budget and return-on-investment (ROI) constraints. We establish the exact computational complexity of finding these equilibria across several canonical settings: exact equilibrium computation is $\mathsf{FIXP}$-complete for second-price ROI pacing, budget- or ROI-constrained generalized second-price (GSP) sponsored shopping, and second-price throttling. Furthermore, approximating the equilibrium control vector in distance to a true equilibrium is $\mathsf{FIXP}_{a}$-complete when the target accuracy is provided as input.

cs.GT↗

arXiv2026

GSP Autobidding Equilibria with Few Advertisers or Slots

In sponsored-shopping auctions, one advertiser may win several positions, and a product that is never displayed may determine the prices of several winners. Under generalized second-price (GSP) pricing without self-pricing, these interactions couple allocation and payment through a single global ranking. We prove that exact autobidding equilibria under budget and return-on-investment (ROI) constraints can be computed in polynomial time whenever either the number $n$ of advertisers or the number $K$ of display slots is fixed. Our algorithms rely on two structural reductions. With few advertisers, the payment polytopes of tied bid layers combine by a Minkowski sum, giving a fixed-dimensional representation of exponentially many rankings. With few slots, budget equilibria admit threshold recovery and an exact submodular description of attainable payments at the display boundary. For ROI, we prove that every group-consecutive equilibrium has a representative with at most $K+2$ nonunit multipliers, preserving the item and price in every displayed slot. In each case, the reduction leads to polynomially many systems of polynomial equations and inequalities in bounded dimension. The algorithms compute exact multipliers and explicit distributions over valid group-consecutive rankings, with support at most $n+1$; for ROI with few slots, this improves to $\min\{n+1,K+3\}$.

cs.GT↗

arXiv2026

Pacing Equilibria in Second-Price Auctions with Few Goods

In this paper, we investigate the computation of second-price pacing equilibria (SPPEs), a foundational model in online advertising auctions. We present a polynomial-time algorithm for computing exact SPPEs in instances with a constant number of goods. Our core technique maps buyers' pacing multipliers to the highest bids on each good, effectively partitioning the parameter space into a set of distinct geometric cells. By enumerating these cells, we fix the relative ordering of the bids and reduce the problem of equilibrium computation to a linear feasibility program. Finally, we demonstrate that this tractability extends to large-scale markets with an arbitrary number of goods, provided the goods can be aggregated into a constant number of valuation types.

cs.GT↗