Price competition with a stake in your rival

We examine how revenue-sharing and profit-sharing stakes affect price competition intensity under duopoly. Our analysis builds on the price competition framework introduced by Varian (1980) and accounts for fundamental asymmetries in terms of cost and consumer loyalty. A stake exists when a firm appropriates a share of its rival's revenues or profits. For example, a marketplace owner that charges a third-party seller an ad valorem fee on its sales has a revenue-sharing stake, and a firm holding a minority ownership participation in another has a profit-sharing stake. We show that a revenue-sharing stake always has a stronger competition-dampening effect (leads to higher prices) than a profit-sharing stake, and explain how the introduction of a stake affects the intensity of competition between firms. Our analysis generates new insight into how stakes affect competitive interaction in the marketplace.