On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility
P von Mouche, F Quartieri - Journal of Global Optimization, 2013 - Springer
Journal of Global Optimization, 2013•Springer
We consider a class of homogeneous Cournot oligopolies with concave integrated price
flexibility and convex cost functions. We provide new results about the semi-uniqueness and
uniqueness of (Cournot) equilibria for the oligopolies that satisfy these conditions. The
condition of concave integrated price flexibility is implied by (but does not imply) the log-
concavity of a continuous decreasing price function. So, our results generalize previous
results for decreasing log-concave price functions and convex cost functions. We also …
flexibility and convex cost functions. We provide new results about the semi-uniqueness and
uniqueness of (Cournot) equilibria for the oligopolies that satisfy these conditions. The
condition of concave integrated price flexibility is implied by (but does not imply) the log-
concavity of a continuous decreasing price function. So, our results generalize previous
results for decreasing log-concave price functions and convex cost functions. We also …
Abstract
We consider a class of homogeneous Cournot oligopolies with concave integrated price flexibility and convex cost functions. We provide new results about the semi-uniqueness and uniqueness of (Cournot) equilibria for the oligopolies that satisfy these conditions. The condition of concave integrated price flexibility is implied by (but does not imply) the log-concavity of a continuous decreasing price function. So, our results generalize previous results for decreasing log-concave price functions and convex cost functions. We also discuss the particular type of quasi-concavity that characterizes the conditional revenue and profit functions of the firms in these oligopolies and we point out an error of the literature on the equilibrium uniqueness in oligopolies with log-concave price functions. Finally, we explain how the condition of concave integrated price flexibility relates to other conditions on the price and aggregate revenue functions usually considered in the literature, e.g., their concavity.
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