Abstract
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.
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Notes
However, it is not uncommon to observe bargaining owners-managers in designing mechanisms of managerial pay (Bebchuk and Fried 2004).
See Fanti et al. (2016) for a critique on this result when the owner bargains the executive pay with his manager.
See Agliari et al. (2006) for a critique of the rational expectations paradigm in economic dynamic models.
A contract that is publicly available implies that firms know the kind of contract agreed upon with the manager as well as the type of manager behavior. In contrast, under private information, there should be problems of signaling and uncertainty related to the available information.
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The authors gratefully acknowledge two anonymous reviewers for valuable comments and suggestions on an earlier draft. The usual disclaimer applies.
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Gori, L., Pecora, N. & Sodini, M. Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers. J Evol Econ 27, 905–931 (2017). https://doi.org/10.1007/s00191-017-0503-y
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DOI: https://doi.org/10.1007/s00191-017-0503-y