The RAND Journal of Economics
We develop a model in which a main product (called product A) provides a performance quality z by itself, whereas a complementary product (called product B) is useless by itself but enhances the main product's performance quality to q > z. This asymmetric complementarity gives rise to the following results. First, if z is relatively small, then firms A and B behave as if the products are symmetrically complementary with the usual double marginalization problem. Second, if z is sufficiently large, then firms A and B price their products as if they are independent. Third, over a certain range of intermediate z, no pure-strategy Nash equilibrium exists.
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Accepted Author Manuscript
Cheng, L. K., & Nahm, J. (2007). Product boundary, vertical competition, and the double mark-up problem. The RAND Journal of Economics, 38(2), 447-466. doi: 10.1111/j.1756-2171.2007.tb00077.x