In the present paper, we propose an extension of Spengler's (1950) analysis of successive oligopolies, to study the effects of entry in the downstream and upstream markets. Free entry is analyzed using replica economies à la Debreu and Scarf (1963). We find that free entry may have different effects in the upstream and in the downstream market. Namely, the usual convergence of the price to the corresponding marginal cost only occurs in the downstream market.
Jaskold Gabszewicz, J., & Zanaj, S. (2011). Free entry in successive oligopolies. International Journal of Economic Theory. https://doi.org/10.1111/j.1742-7363.2011.00157.x