Liquid Welfare and Revenue Monotonicity in Adaptive Clinching Auctions

TL;DR

This paper investigates how adaptive clinching auctions behave when the number of bidders changes, showing that in symmetric cases, liquid welfare and revenue tend to increase with more bidders, but this does not hold for asymmetric budgets.

Contribution

It provides the first theoretical analysis of monotonicity properties in adaptive clinching auctions under different bidder scenarios.

Findings

Liquid welfare and revenue weakly increase with more bidders in symmetric settings.

Monotonicity properties do not hold in asymmetric budget scenarios.

The results extend to online bidder arrivals, offering insights into social network dynamics.

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.