In the framework of symmetric Cournot oligopoly, this paper provides two minimal sets of assumptions on the demand and cost functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to (i) decreasing industry price and increasing or decreasing per-firm output; and (ii) increasing industry price (and decreasing per firm output.) In both cases, per-firm profits are decreasing.The analysis relies crucially on lattice-theoretic methods and yields general, unambiguous and easily interpretable conclusions of a global nature. As a byproduct of independent interest, new insight into the existence of Cournot equilibrium is developed.
We consider the issue of first versus second-mover advantage in differentiated-product Bertrand duopoly with general demand and asymmetric linear costs. We generalize existing results for the cases where prices are either strategic substitutes and/or complements, dispensing with common extraneous assumptions. We show that a firm with a sufficiently cost lead over its rival has a first mover advantage. For the linear version of the model, we invoke a natural endogenous timing scheme coupled with equilibrium selection according to riskdominance. This yields sequential play with the low-cost firm as leader as the unique equilibrium outcome.
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