Equilibrium and inefficiency in multi-product cournot games

Abstract

We consider multi-product (m products) Cournot games played by n firms where products are substitutable goods. Such games can arise in network markets and in general is motivated by markets with differentiated goods and differing producer costs that can be arbitrary, especially due to subsidies. We provide strongly polynomial algorithms for computing the Nash equilibrium for Cournot games with quadratic utility functions. To study the inefficiency, we provide a characterization of Nash equilibrium in multi-product oligopolies with concave utilities and uniform substitutability in terms of games with quadratic utilities. We show that the Price of Anarchy in these games is bounded below by 2/3.