Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers
- 155 Downloads
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.
KeywordsCournot duopoly Entry barriers Local and global dynamics Managerial firms Market share delegation
JEL ClassificationC61 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.
- Agliari A, Bignami F (2010) Synchronization and on-off intermittency phenomena in a market model with complementary goods and adaptive expectations. Stud Nonlinear Dyn E 14(2):1–15Google Scholar
- Bebchuk L, Fried J (2004) Pay without performance. The unfulfilled promise of executive compensation. Harvard University Press, Cambridge (MA)Google Scholar
- Fanti L, Gori L, Sodini M (2016) Managerial delegation theory revisited. Manage Decis Econ, forthcomingGoogle Scholar
- Fershtman C, Judd K (1987) Equilibrium incentives in oligopoly. Am Econ Rev 77(5):927–940Google Scholar
- Jansen T, van Lier A, van Witteloostuijn A (2007) A note on strategic delegation: the market share case. Int J Ind Organ 25(3):531–539Google Scholar
- Jansen T, van Lier A, van Witteloostuijn A (2009) On the impact of managerial bonus systems on firm profit and market competition: the cases of pure profit, sales, market share and relative profits compared. Manage Decis Econ 30(3):141–153Google Scholar