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.

中文翻译：

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内生的公共和私人领导，社会和私人边际成本各不相同

我们研究了混合双头垄断中的内生时机，价格竞争以及不同的社会和私人边际成本。我们发现，出现了任何均衡时机模式-贝特朗，斯塔克尔伯格和私人领导，斯塔克尔伯格和公共领导以及多个斯塔克尔伯格均衡。当外资在私人公司中的份额少于50％时，公共领导比私人领导更有可能出现。相反，当私人公司中的外国所有权份额很大时，私人领导才能以独特的平衡出现。这些结果可能解释了日本公共金融机构最近的政策变化。我们还发现，公共和私人领导的福利优势与私人公司的社会和私人边际成本之差之间存在非单调的关系。非单调关系不会出现在利润排名中。尽管一些属性不同，但在数量竞争下也可获得相似的结果。