The Progressive Second Price Mechanism in a Stochastic Environment

We consider in this paper an auction-based pricing scheme recently introduced by Lazar and Semret to allocate bandwidth among users. This mechanism, called Progressive Second Price, was studied using tools from noncooperative game theory, for a fixed set of players (i.e., users). We compare here the results obtained in that case with the more realistic situation when players randomly enter or leave the game. We assume that they enter according to a Poisson process, and leave it after an exponentially distributed sojourn time. We show that this stochastic assumption cannot be skipped since it can lead to very different results.