Liquid Welfare and Revenue Monotonicity in Adaptive Clinching Auctions
Ryosuke Sato
TL;DR
This paper investigates how adaptive clinching auctions behave as the number of bidders grows under budget constraints, focusing on monotonicity of liquid welfare $LW$ and revenue $REV$ versus allocations $SW$.The authors develop an explicit,Clinching-interval-based analysis in the symmetric budget setting, proving that adding bidders weakly increases $LW$ and $REV$ while keeping most bidders’ allocations nondecreasing, and they extend these results to online bidder arrivals.In contrast, they construct counterexamples in the asymmetric-budget setting showing that both per-bidder outcomes and $LW$ can fail to be monotone, and they leave revenue monotonicity as an open question in that setting.The findings have implications for budget-constrained auctions in social networks, where information diffusion creates new bidders, and they provide a rigorous basis for extending clinching auctions with monotone efficiency and revenue properties under symmetry.
Abstract
This study explores the monotonicity of adaptive clinching auctions -- a key mechanism in budget-constrained auctions -- with respect to fluctuations in the number of bidders. Specifically, we investigate how the addition of new bidders affect efficiency and revenue. In a symmetric setting, where all bidders have equal budgets, we show that while the allocated goods and payments for many bidders decrease, overall both liquid welfare and revenue weakly increase. Our analysis also extends to scenarios where bidders arrive online during the auction. In contrast, for asymmetric budgets, we provide counterexamples showing that these monotonicity properties no longer hold. These findings contribute to a better theoretical understanding of budget-constrained auctions and offer insights into the behavior of adaptive clinching auctions in social networks, where new bidders emerge through information diffusion.