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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 394810, 13 pages
Research Article

Market Share Delegation in a Bertrand Duopoly: Synchronisation and Multistability

1Department of Economics and Management, University of Pisa, Via Cosimo Ridolfi 10, 56124 Pisa, Italy
2Department of Law, University of Genoa, Via Balbi 30/19, 16126 Genoa, Italy
3Department of Economics and Law, University of Macerata, Via Crescimbeni 20, 62100 Macerata, Italy

Received 21 October 2014; Revised 2 March 2015; Accepted 9 March 2015

Academic Editor: Jinde Cao

Copyright © 2015 Luciano Fanti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper tackles the issue of local and global analyses of a duopoly game with price competition and market share delegation. The dynamics of the economy is characterised by a differentiable two-dimensional discrete time system. The paper stresses the importance of complementarity between products as a source of synchronisation in the long term, in contrast to the case of their substitutability. This means that when products are complements, players may coordinate their behaviour even if initial conditions are different. In addition, there exist multiple attractors so that even starting with similar conditions may end up generating very different dynamic patterns.