Collaborating to compete: A game-theoretical model and experimental investigation of competition among alliances

In collaborating to compete, firms forge different types of strategic alliances: same function alliances (e.g., R & D alliance), cross-function alliances (e.g., marketing and production alliance) and even parallel development of new products. In this research we examine how the type of an alliance and the prescribed profit-sharing arrangement affect the resource commitments of partners in the alliance. We model the interaction within an alliance as a noncooperative variable-sum game, in which each firm invests a part of its resources to increase the utility of a new product offering. Different types of alliances are modeled by varying how the resources committed by partners in an alliance determine the utility of the jointly-developed new product. We then model the inter-alliance competition by nesting two independent intra-alliance games in a super game where the groups compete for a market. The partners of the winning alliance share the profits in one of two ways: equally or in proportion to their investments. The Nash equilibrium solutions for the resulting games are investigated. In the case of same-function alliances, when the market is large the predicted investment patterns under both profit sharing rules are comparable. Partners developing new products in parallel, unlike the partners in a same function alliance, commit fewer resources to their alliance. However, the profit-sharing arrangement matters in such alliances—partners commit more resources when profits are shared proportionally rather than equally. In cross-functional alliances, the partners are playing a coordination game with multiple Nash equilibria. We tested the predictions of the model in a series of laboratory experiments in which subjects played the inter-alliance competition game for a monetary payoff. The experimental results support the theoretical model. We show that reinforcement-based learning, rather than belief-based learning, explains how subjects came to conform to the model. Our analysis of Robertson and Gatignon's survey data on the conduct of corporate partners in technology alliances adds further support to the model for same-function alliances.