Problem
Research questions and friction points this paper is trying to address.
Auto-bidding Auctions
PPAD hardness
Equilibrium Computation
Nonatomic Distributions
Generalized Nash Equilibrium
Beyond the PPAD hardness of Auto-bidding Auctions
🤖 AI Summary
This work addresses the apparent paradox that equilibrium computation in auto-bidding auctions is PPAD-complete in the worst case yet exhibits rapid convergence in practice. To resolve this discrepancy, the authors propose a diffuse analysis framework that models bidder valuations as non-atomic distributions, thereby reformulating the equilibrium problem as a separable monotone generalized Nash equilibrium (GNE). This framework reveals, for the first time, that the PPAD-hardness stems from atomicity assumptions, and establishes a polynomial-time solvability theory for non-atomic markets. Building on this insight, they design the first GNE solver with linear convergence in the last iterate, unifying budget pacing and throttling equilibria under a single algorithmic framework and thereby explaining the empirically observed efficiency of real-world auction markets.
📝 Abstract
Computing certain autobidding equilibria is PPAD complete in the worst case. Yet such instances rarely arise in practice, where advertisers running simple, decentralized learning strategies usually converge quickly. We show there is no contradiction: the hardness requires atomicity and vanishes once the value distribution is nonatomic, as it is in real world markets.
To bridge worst case hardness and practical convergence, we introduce diffuse analysis, a beyond worst case framework that studies equilibrium computation when bidder values are drawn from general nonatomic distributions. Under this framework, the autobidding equilibrium becomes a separately monotone generalized Nash equilibrium (GNE). For this GNE, we give the first solver with last iterate linear convergence. Thus, the equilibrium has polynomial diffuse complexity, matching the convergence observed in real-world markets.
Concretely, our framework subsumes the budget pacing and the throttling equilibrium as special cases when the payment rule is a convex combination of first and second price.
Innovation
Methods, ideas, or system contributions that make the work stand out.
diffuse analysis
autobidding equilibrium
nonatomic distribution
generalized Nash equilibrium
linear convergence
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