Journal of Global Optimization

, Volume 57, Issue 3, pp 707-718

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility

  • Pierre von MoucheAffiliated withWageningen University Email author 
  • , Federico QuartieriAffiliated withIULM University


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.


Equilibrium (semi-)uniqueness Generalized convexity Log-concavity Oligopoly Price flexibility Price function