Cournot equilibrium uniqueness via demi-concavity. (3rd April 2018)

• Record Type: Journal Article
• Authors: von Mouche, P.; Quartieri, F.
• Is Part Of: Optimization. Volume 67:Number 4(2018)
• Page Start: 441
• Page End: 455
• Publication Date: 2018-04-03
• Subjects: Convex analysis -- Cournot oligopoly -- demi-concavity -- equilibrium uniqueness -- quasi-concavity; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1405954
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: A family of oligopolies that possess a unique equilibrium was identified in the second authors doctoral dissertation. For such a family, it is therein specified a class of functions-economically related to the price function of a Cournot oligopoly – that satisfy a particular type of quasi-concavity. The first part of the present article (i) conceptualizes that type of quasi-concavity by introducing the notion of demi-concavity, (ii) considers two possible variants and (iii) provides some calculus properties. The second part, by relying on the results on demi-concavity, proves a Cournot equilibrium uniqueness theorem which is new for the journal literature and subsumes various results thereof. A third part shows an example that illustrates the novelty of the result.