Collective Sensitivity, Collective Accessibility, and Collective Kato’s Chaos in Duopoly Games

Hongqing Wang, Tianxiu Lu (), Risong Li (), Yuanlin Chen, Yongjiang Li and Weizhen Quan
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Hongqing Wang: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
Tianxiu Lu: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Risong Li: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
Yuanlin Chen: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Yongjiang Li: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
Weizhen Quan: Department of Mathematics, Zhanjiang Preschool Education College, Zhanjiang 524037, China

Mathematics, 2022, vol. 10, issue 22, 1-15

Abstract: By using the uniform continuity of two onto maps, this paper further explores stronger forms of Kato’s chaos, sensitivity, and accessibility of Cournot maps. In particular, the sensitivity, the collective sensitivity, the accessibility, and the collective accessibility of the compositions of two reaction functions are studied. It is observed that a Cournot onto map H on a product space is sensitive (collectively sensitive, collectively accessible, accessible, or collectively Kato chaotic) if and only if the restriction of the map H 2 to the MPE-set is sensitive as well. Several examples are given to show the necessity of the reaction functions being continuous onto maps.

Keywords: sensitivity; accessibility; Kato’s chaos; duopoly game (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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