Positional queuetions
Vladimir Yankovskiy
TL;DR
The paper studies revenue bounds for VCG and GSP positional auctions applied to queueing systems, where each participant has a service time and a value per unit time. It formulates a general queueing mechanism, identifies the optimal sorting by value density $v_i=w_i/t_i$, and derives equilibrium conditions for VCG and GSP in this setting. It provides computable lower and upper bounds on the organizer's revenue in Nash equilibria for VCG, and analogous equilibrium conditions and a closed-form upper bound for GSP with preference. These results yield practical, computable revenue bounds for queue-based position auctions in marketplaces and service systems.
Abstract
In this work, we consider properties of VCG and GSP positional auctions in queues. The work is a continuation of "Position Auctions for Sponsored Search in Marketplaces" by the same author.