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Necessary Conditions for Concave and Cournot Oligopoly Games

  • Ferenc ForgóEmail author
  • Zoltán Kánnai
Chapter
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Abstract

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.

Keywords

Concave games Cournot oligopoly Necessary conditions 

JEL-code:

L13 

Notes

Acknowledgements

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

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

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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