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.