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A Full Description of ω -Limit Sets of Cournot Maps Having Non-Empty Interior and Some Economic Applications

Author

Listed:
  • Antonio Linero-Bas

    (Departamento de Matemáticas, Campus de Espinardo, Universidad de Murcia, 30100 Murcia, Spain
    These authors contributed equally to this work.)

  • María Muñoz-Guillermo

    (Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Antiguo Hospital de Marina, 30202 Cartagena, Murcia, Spain
    These authors contributed equally to this work.)

Abstract

Given a continuous Cournot map F ( x , y ) = ( f 2 ( y ) , f 1 ( x ) ) defined from I 2 = [ 0 , 1 ] × [ 0 , 1 ] into itself, we give a full description of its ω -limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the ω -limits with non-empty interior gives information about the dynamics and the possible outputs of each firm in a Cournot model. We present some economic models to illustrate, with examples, the type of ω -limits that appear.

Suggested Citation

  • Antonio Linero-Bas & María Muñoz-Guillermo, 2021. "A Full Description of ω -Limit Sets of Cournot Maps Having Non-Empty Interior and Some Economic Applications," Mathematics, MDPI, vol. 9(4), pages 1-33, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:452-:d:504565
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    References listed on IDEAS

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