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

Abstract

Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[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.

Keywords

• ω-limit set
• Cournot map
• non-empty interior
• Cournot duopoly model
• topological mixing map