Endogenous public and private leadership with diverging social and private marginal costs

We investigate endogenous timing in a mixed duopoly with price competition and different social versus private marginal costs. We find that any equilibrium timing patterns-Bertrand, Stackelberg with private leadership, Stackelberg with public leadership, and multiple Stackelberg equilibria-emerge. When the foreign ownership share in a private firm is less than 50%, public leadership is more likely to emerge than private leadership. Conversely, private leadership can emerge in a unique equilibrium when the foreign ownership share in a private firm is large. These results may explain recent policy changes in public financial institutions in Japan. We also find there is a nonmonotonic relationship between the welfare advantage of public and private leadership and the difference between social and private marginal costs for a private firm. A nonmonotonic relationship does not emerge in profit ranking. Similar results are obtained under quantity competition, although some properties are different.