Product differentiation in successive vertical oligopolies

This is a successive oligopoly model with two varieties of a final product. Downstream firms choose one variety to sell on a final market. Upstream firms specialize in the production of one input specifically designed for one variety, but they also produce the input for the other variety at an extra cost. We show that as more downstream firms choose one particular variety, more upstream firms specialize in the input specific to that variety, and vice-versa. Multiple equilibria may result, and the softening effect of product differentiation on competition might not be strong enough to induce maximal differentiation.