The Progressive Second Price mechanism (PSP), recently introduced byLazar and Semret to share aninfinitely-divisible resource among users through pricing, has been shown to verifyvery interesting properties. Indeed, the incentive compatibilityproperty of that scheme, and the convergence toan efficient resource allocation where established, using the frameworkof Game Theory.Therefore, that auction-based allocation and pricing scheme seemsparticularly well-suited to solve congestion problems intelecommunication networks, where the resource to share is theavailable bandwidth on a link.This paper aims atsupplementing the existing results by highlighting some properties of thedifferent equilibria that can be reached. We precisely characterize the possible outcomes of thePSP auction game in terms of players bid price: when the bid fee (cost of a bid update) tends to zero then the bid price of all users at equilibrium gets close to the so-called market clearing price of the resource. Therefore, observing an equilibrium of the PSP auction game gives some accurate information about the market clearing price of the resource.