In an oligopoly, prior to choosing quantities/prices, each firm has an opportunity to form pair-wise collaborative links with other firms. These pair-wise links lower costs of production of the firms which form a link. The collection of pair-wise links defines a collaboration network. We study stable and efficient networks under different types of market competition. We find that except under extreme competition, a la Bertrand, firms have an incentive to collaborate wit their competitors to lower costs of production. We find that two simple architectures, the complete network, where every firm has a collaboration link with every other firm, and the network with a dominant group, which contains a large number of completely connected firms and several isolated firms, are stable under different market conditions. We also observe that stable networks are often efficient from a social point of view.