Second-Price Ad Auctions with Binary Bids and markets with good competition

Given a bipartite graph G=(U,V,E)G=(U,V,E) with U={1,…,n}U={1,…,n}, and a positive budget BvBv for each v in V, a B-matching M in G is a second-price B-matching if, for every edge uv in M, there is an edge uw in E   so that less than BwBw edges u′wu′w with u′