The Impact Of Cross-shareholding On Corporate Collusion Under The Cournot Model

Partial cross ownership(PCO)among firms is common around the world.By holding shares in each other,firms establish a connection of interests through which the decisions of competition,collaboration,and collusion are affected.We take the tacit collusion among firms as the research subject and make a theoretical analysis of the effects of PCO on firms' anti-competitive behaviors.We analyze the market equilibrium of an n-firm industry which allows asymmetric cross ownership and establish a general framework to analyze the collusion behavior,under Cournot competition.We find that increasing PCO always increases equilibrium price and weakens market competition but is more complicated in affecting tacit collusion.Specifically,increasing PCO to some extent hinders tacit collusion under traditional uniform output distribution scheme.According to the shareholding structure,a complex interest network will be formed among firms.If firm A increases the shares of another firm,the incentive for those firms that do not directly or indirectly hold shares of firm A to participate in tacit collusion will be weakened.From this perspective,increasing PCO may hinder tacit collusion.However,this scheme is not always feasible for collusion:collusion needs to benefit every firm.Under the strategy of splitting the market uniformly,because of the existence of asymmetric shareholding structure,the interests of some firms may be damaged.For a greater variety of situations,we find that increasing PCO are more likely to facilitate collusion.Firstly,if we take the Nash--Cournot equilibrium as the benchmark and reconsider the feasible collusion schemes,we find that there exists a critical level of PCO,and before reaching this level,increasing PCO always facilitate collusion.Secondly,we examine different subgame perfect equilibriums including stick-and-carrot strategy and strongly renegotiation-proof(SRP)strategy.Taking the SRP strategy as an example,for the firm increasing its shares,the incentive to participate in collusion is strengthened,while for the firm with increased shares,the incentive to participate in collusion is unaffected.Further,we can obtain the necessary and sufficient conditions for increasing PCO to promote collusion.To sum up,we conducted a relatively comprehensive study on the influence of increasing PCO on tacit collusion,which can provide a reference for antitrust policy,and also provide a new theoretical basis for empirical research.