A frequently cited proposition in industrial organization is that vertical integration of bilateral monopolists improves economic efficiency in the case of fixed-proportions production. The traditional argument shows that rivalrous firms implementing a Stackelberg solution charge a higher price for the final good than they would if they were vertically integrated. This paper shows that if rivalrous firms make pricing decisions simultaneously and reach a Nash equilibrium instead of the usual Stackelberg solution, the price of the final good still exceeds that under vertical integration. Thus, the social advantage of cooperation between bilateral monopolists continues to hold under new behavioral assumptions. Copyright 1991 by Blackwell Publishing Ltd.