Journal of Evolutionary Economics

, Volume 27, Issue 5, pp 905–931 | Cite as

Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers

  • Luca Gori
  • Nicolò Pecora
  • Mauro Sodini
Regular Article


This article tackles the issue of local and global dynamics in a nonlinear duopoly with quantity setting (managerial) firms and horizontal product differentiation. It studies how the dynamics of a two-dimensional discrete time map evolves by focusing on changes either in the degree of product differentiation or the managerial power in the market share bonus. By combining mathematical techniques and numerical experiments, it shows that the Nash equilibrium of the game may not describe the long-term outcomes of the market. This holds because the fixed point of the map may be unstable or because different attractors (simple or chaotic) may capture the long-term dynamics of the model. The article also analyzes market dynamics when a new potential entrant tries to enter or, alternatively, a firm that was already in the market closes down and then tries to re-enter in a context where there is already an incumbent with a strictly positive quantity. The potential entrant may be subject to entry barriers or enters the market depending on the structure of consumers’ preferences and the demands of products of both varieties. In particular, the article analyzes some economic consequences of the non-invertibility of the map in the entry process.


Cournot duopoly Entry barriers Local and global dynamics Managerial firms Market share delegation 

JEL Classification

C61 C62 D43 L13 



The authors gratefully acknowledge two anonymous reviewers for valuable comments and suggestions on an earlier draft. The usual disclaimer applies.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Political ScienceUniversity of GenoaGenoa (GE)Italy
  2. 2.Department of Economics and Social SciencesCatholic UniversityPiacenza (PC)Italy
  3. 3.Department of Economics and Management, University of PisaPisa (PI)Italy

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