Optimal Cross Holding with Externalities and Strategic interactions

We analyze a two period setting where firms first choose equity positions in each other and second engage in operating activities that cause externalities. Firms facing positive externalities optimally choose long equity positions to increase their profits. Firms facing negative externalities encounter a prisoners' dilemma, where each firm optimally chooses short positions in the first period, committing to a more aggressive operating stance that results in lower profits. In contrast to the prior literature, regulation restricting cross holdings reduces consumer surplus and economic welfare when the number of firms is fixed. However, such regulation can increase entry, improving net welfare.