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

Antonio Linero-Bas and María Muñoz-Guillermo
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Antonio Linero-Bas: Departamento de Matemáticas, Campus de Espinardo, Universidad de Murcia, 30100 Murcia, Spain
María Muñoz-Guillermo: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Antiguo Hospital de Marina, 30202 Cartagena, Murcia, Spain

Mathematics, 2021, vol. 9, issue 4, 1-33

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 ? -limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the ? -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 ? -limits that appear.

Keywords: ?-limit set; Cournot map; non-empty interior; Cournot duopoly model; topological mixing map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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