A seller may sell advertisements, such as banner ads, to a buyer pursuant to a request made by the buyer to the seller. Each request has a value. The seller may accept the request from the buyer to provide a banner ad for the buyer at a later time. A request, once accepted, may be revoked at a cost which may be a fixed fraction of the request value. The cost may be referred to as a buyback cost. The buyback cost represents the cost of revoking a request that had been accepted. Additionally, matroid set systems and knapsack systems may use buyback techniques.