We consider two firms that compete against each other jointly in upstream and downstream markets under two pricing games: Purchasing to stock (PTS), in which firms select input prices prior to setting consumer prices; and purchasing to order (PTO), in which firms sell forward contracts to consumers prior to selecting input prices. The antitrust implications of the model depend on the relative degree of oligopoly rivalry in the upstream and down- stream markets. Firms strategically precommit to setting prices in the less rivalrous market, which serves to soft- en competition in the more rivalrous market, resulting in anticompetitive effects. Bertrand prices emerge in equilibrium when the markets are equally rivalrous, while Cournot outcomes arise with upstream monopsony or downstream monopoly markets. The slope of firm reaction functions depends on relative rivalry, a feature we use to derive testable hypotheses for antitrust analysis of a wide variety of industry practices.