On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies

This paper takes a novel approach to studying the existence and stability of Nash equilibria in N-firm Cournot–Bertrand oligopolies. First, we show that such games can be monotonically embedded into a game of strategic heterogeneity, so that each firm best responds to the choices of all other firms in a monotonic way. We then show that this monotonicity can be exploited to derive conditions which guarantee the existence of a unique, dominance solvable Nash equilibrium which is stable under all adaptive dynamics. These conditions constitute a strict improvement over existing results in the literature. Finally, we examine the effect on these conditions resulting from additional firms entering the market.