A game-theoretic model for co-promotions: Choosing a complementary versus an independent product ally

This paper studies the optimal choice of promotional partners in a three-firm market where two firms sell complementary products and a third firm sells an independent product. Game-theoretic models are developed to investigate the following scenarios: no promotional partnership, partnership between the two complementary products, partnership between a complementary product and the independent product, and partnership between the three products. Equilibrium Nash solutions are obtained and conditions under which each of the four scenarios above can be implemented are identified. Results show that these conditions depend on various parameters, mainly the degree of product complementarity, the effectiveness of individual promotion, the effectiveness of joint promotion, and the base demand for each product. Commonly, a partnership between a complementary product and the independent product is optimal when the price effect of the complementary product is large, while the partnership between the two complementary products is more appealing when the effect of individual promotion is large enough. When feasible, a promotional partnership between the three products is preferred, except in some specified conditions.