In this paper, we consider a market with potential entrants and incumbents. We characterize the whole set of equilibrium or equilibria in Cournot- and Bertrand models . To describe entry and exit decisions of firms, we relax the assumption of positive outputs and provide some algorithms to find the firms which actively produce in these models. Our results show that there is a unique pure strategy Cournot equilibrium, where only the firms survived from an efficient iteration algorithm produce under two different models: 1-) High-degree heterogenous goods, linear demand, different constant costs 2-) Low-degree heterogeneous goods, declining marginal revenues, convex or not too concave costs.
Additionally, we study Bertrand model and argue why an established firm can decrease its price in equilibrium when it is faced with a low threat potential entrant firm. Further, we show several examples in which pure strategies lead multiple undominated Bertrand equilibria. Moreover, Bertrand best replies might be negatively sloped (i.e, the game is not supermodular) on some part of the domain when the number of firms is more than two. These results are very different from the existing literature on Bertrand models, where uniqueness usually holds and best reply functions slope upwards under a linear demand assumption. Finally, we apply these models to a merger-setting and show that exit-inducing Cournot and Bertrand horizontal mergers should be allowed from both a consumer welfare and total welfare point of view, which contradicts the conventional wisdom.
P.S.: The seminar will be held in English.