Strategic profit sharing leads to collusion in Bertrand oligopolies

One simple way to endogenize the degree of cross ownership in an industry is that rms give away part of their pro ts. We show that this possibility of unilaterally giving pro ts away to the rival previous to Bertrand competition opens the door to multiple equilibria. In the symmetric duopoly with con- stant marginal costs any price between the cost and the monopolistic price can be sustained in a subgame perfect equilibrium. Thus, tacit collusion in the one shot game can be achieved. Further, any market share can also be sustained for any equilibrium price. These results are extended to more than two rms and to asymmetric costs