Competition with exclusive contracts in vertically related markets: An equilibrium non-existence result
研究两个上游企业通过排他性两部收费合同向两个下游企业供应同质投入品的博弈，发现在很一般条件下该博弈不存在纯策略子博弈完美均衡，原因在于可变部分需成对稳定但无法内化下游竞争外部性。
I study a model in which two upstream firms compete to supply a homogeneous input to two downstream firms selling differentiated products. Upstream firms offer exclusive, discriminatory, public, two-part tariff contracts to the downstream firms. I show that, under very general conditions, this game does not have a pure-strategy subgame-perfect equilibrium. The intuition is that variable parts in such an equilibrium would have to be pairwise-stable; however, with pairwise-stable variable parts, downstream competitive externalities are not internalized, implying that upstream firms can profitably deviate. I contrast this non-existence result with earlier papers that found equilibria in related models.