Abstract : Flat-rate charging of telecommunication networks does not seem relevant anymore as it creates congestion (like in the Internet). Among usage-based charging schemes, auctionning for bandwidth looks very relevant anymore as it creates congestion (like in the Internet). Among usage-based charging schemes, auctionning for bandwidth looks very promising. We review here the tremendous work called progressive second price auction and give a modification in the allocation rule in order to prove and improve the results published in the literature.