This paper studies the impact that margin requirements have on both the existence of arbitrage opportunities and the valuation of call options. In the context of the Black-Scholes economy, margin restrictions are shown to exclude continuous-trading arbitrage opportunities and, with two additional hypotheses, still to allow the Black-Scholes call model to apply. The Black-Scholes economy consists of a continuously traded stock with a price process that follows a geometric Brownian motion and a continuously traded bond with a price process that is deterministic.

Models of collusive bidder behavior at single-object second-price and English auctions are provided. The ind ependent private values model is generalized to permit the formulatio n of coalitions and a strategic response by the auctioneer. Cooperati ve strategies are found to be dominant in these models; coalitions of any size are viable, and the payoff to each member increases with th e size of the coalition. In addition, the collusive strategies of the coalition represent a noncooperative equilibrium. The optimal respon se of the auctioneer is to establish a reserve price that is a functi on of the coalition's size. These and other features of the model are found to be consistent with the essential features of actual behavio r. Copyright 1987 by University of Chicago Press.