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On Cournot-Nash-Walras Equilibria and Their Computation

Abstract

This paper concerns a model of Cournot-Nash-Walras (CNW) equilibrium where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/firms who share a certain amount of a so-called rare resource needed for their production, and the Walras equilibrium determines the price of that rare resource. We prove the existence of CNW equilibria under reasonable conditions and examine their local stability with respect to small perturbations of problem data. In this way we show the uniqueness of CNW equilibria under mild additional requirements. Finally, we suggest some efficient numerical approaches and compute several instances of an illustrative test example.

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Correspondence to Jiří V. Outrata.

Additional information

This work was partially supported by the Grant Agency of the Czech Republic under Grant P402/12/1309 and 15-00735S, by the Grant Agency of the Charles University by Grant SFG 2567, by the Australian Research Council under grant DP-110102011 and in part by a grant from the Department of Energy and funding from the USDA.

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Outrata, J.V., Ferris, M.C., Červinka, M. et al. On Cournot-Nash-Walras Equilibria and Their Computation. Set-Valued Var. Anal 24, 387–402 (2016). https://doi.org/10.1007/s11228-016-0377-4

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  • DOI: https://doi.org/10.1007/s11228-016-0377-4

Keywords

  • Cournot-Nash-Walras equilibrium
  • Existence
  • Stationarity conditions
  • Stability
  • MOPEC

Mathematics Subject Classification (2010)

  • 90C33
  • 91B52
  • 49J40
  • 90C31