Cross-ownership and stability in a Cournot duopoly

This paper analyses the dynamics of a Cournot duopoly under cross-ownership participation when players have heterogeneous, i.e. bounded rational and naïve, expectations. We find that when the shareholder that owns firm also holds a percentage of firm , the parametric stability region of the unique Cournot-Nash equilibrium is larger than when every firm is owned by a unique shareholder, and an increase in the fraction of shares that the shareholder that owns firm has in firm tends to stabilise the market equilibrium. Moreover, when products are (horizontally) differentiated, a rise in the fraction of shares of firm held by the shareholder that owns firm acts as an economic (de)stabiliser when products of variety and are (complements) substitutes between each other. The policy implication is that, despite on the one hand, cross-ownership acts as an anti-competitive device that indeed tends to reduce social welfare with the corresponding anti-trust consequences, on the other hand, it acts as an economic stabiliser (except when products are complements).