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

Mathematics

María Muñoz-Guillermo¹  Antonio Linero-Bas² 

[1] Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Antiguo Hospital de Marina, 30202 Cartagena, Murcia, Spain;Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain;

关键词: ω-limit set;    Cournot map;    non-empty interior;    Cournot duopoly model;    topological mixing map.;   

DOI  :  10.3390/math9040452

来源: DOAJ

【 摘 要 】

Given a continuous Cournot map $F(x,y)=(f_2\left(y\right),f_1\left(x\right))$ defined from $I^2=[0,1]\times [0,1]$ into itself, we give a full description of its $\omega$-limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the $\omega$-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 $\omega$-limits that appear.

【 授权许可】

Unknown