In this article, we investigate the local and global dynamics of a nonlinear duopoly model with price-setting firms and managerial delegation contracts (relative profits). Our study aims at clarifying the effects of the interaction between the degree of product differentiation and the weight of manager's bonus on long-term outcomes in two different states: managers behave more aggressively with the rival (competition) under product complementarity and less aggressively with the rival (cooperation) under product substitutability. We combine analytical tools and numerical techniques to reach interesting results such as synchronisation and on-off intermittency of the state variables (in the case of homogeneous attitude of managers) and the existence of chaotic attractors, complex basins of attraction, and multistability (in the case of heterogeneous attitudes of managers). We also give policy insights.
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Multistability and complex basins in a nonlinear duopoly with price competition and relative profit delegation
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September 2016
Research Article|
September 20 2016
Multistability and complex basins in a nonlinear duopoly with price competition and relative profit delegation
Luciano Fanti;
Luciano Fanti
a)
1Department of Economics and Management,
University of Pisa
, Via Cosimo Ridolfi, 10, I–56124 Pisa (PI), Italy
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Luca Gori;
Luca Gori
b)
2Department of Political Science,
University of Genoa
, Piazzale E. Brignole, 3a, I–16125 Genoa (GE), Italy
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Cristiana Mammana;
Cristiana Mammana
c)
3Department of Economics and Law,
University of Macerata
, Via Crescimbeni, 20, I–62100 Macerata (MC), Italy
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Elisabetta Michetti
Elisabetta Michetti
d)
3Department of Economics and Law,
University of Macerata
, Via Crescimbeni, 20, I–62100 Macerata (MC), Italy
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a)
E-mail: luciano.fanti@unipi.it. Tel.: +39 050 22 16 369. FAX: +39 050 22 10 603.
b)
Electronic addresses: luca.gori@unige.it and dr.luca.gori@gmail.com. Tel.: +39 010 209 95 03. FAX: +39 010 209 55 36.
c)
E-mail: cristiana.mammana@unimc.it
d)
Author to whom correspondence should be addressed. Electronic mail: elisabetta.michetti@unimc.it
Chaos 26, 093110 (2016)
Article history
Received:
January 15 2016
Accepted:
August 22 2016
Citation
Luciano Fanti, Luca Gori, Cristiana Mammana, Elisabetta Michetti; Multistability and complex basins in a nonlinear duopoly with price competition and relative profit delegation. Chaos 1 September 2016; 26 (9): 093110. https://doi.org/10.1063/1.4962296
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