Necessary Conditions for Concave and Cournot Oligopoly Games

  • Ferenc ForgóEmail author
  • Zoltán Kánnai


Necessary conditions for the existence of pure Nash equilibria introduced by Joó (A note on minimax theorems, Annales Univ. Sci. Budapest, 39(1996), 175–179) for concave non-cooperative games are generalized and then applied to Cournot oligopoly games. If for a specified class of games there always exists a pure Nash equilibrium, then cost functions of the firms must be convex. Analogously, if for another specified class of games there always exists a pure Nash equilibrium, then revenue functions of the firms must be concave in their respective variables.


Concave games Cournot oligopoly Necessary conditions 





Research was done in the framework of Grant NKFI K-1 119930.


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Authors and Affiliations

  1. 1.Department of Operations Research and Actuarial SciencesCorvinus University of BudapestBudapestHungary
  2. 2.Department of MathematicsCorvinus University of BudapestBudapestHungary

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