On Pairwise Stability and Anti-Competitiveness of Cross-Holdings in Oligopoly

This paper considers a model of endogenous bilateral cross-holdings. A notion of pairwise stability is applied to analyze firms' incentives for cross-holdings. Under certain conditions and Cournot competition on the output market, it is shown that monopoly is the only outcome of pairwise stable cross-holdings when there are two firms; a wide range of outcomes is possible when there are three firms, including as special cases the triopoly and the duopoly Cournot equilibria without any cross-holding; and the Cournot equilibrium is an outcome of pairwise stable cross-holdings when there are four or more firms. Competitive implications of the results are also briefly discussed.