Profit formulation and equilibrium strategy of firms with cross-shareholding

A profit formulation of cross-shareholding among firms was presented based on feedback control principle. Constructing a two-stage game, we focused on the equilibrium strategy and market performance of two firms in Cournot duopoly with cross-shareholding. The equilibrium strategy, which consists of two firms' equilibrium equities and equilibrium outputs, was solved by backward induction. The results show that the equilibrium strategy under cross-shareholding always increases each firm's profit, so as to realize a win-win situation between two rivals, no matter the products are substitutes or complements. However, in the case of substitute products, cross-shareholding reduces consumer surplus and economic welfare.