On price stability and the nature of product differentiation
- 188 Downloads
In a spatial competition model, we analyze the stability of the Nash-price equilibrium under horizontal and vertical product differentiation, considering both homogenous and heterogeneous expectations. Regardless of the nature of product differentiation, assuming that firms behave according to an adaptive expectations rule, it is found that the Nash-price equilibrium is asymptotically stable. If at least one firm follows the gradient rule based on marginal profit, an increase in the adjustment speed turns out to be a source of complexity. Moreover, the influence of the locations on price stability depends on the nature of product differentiation and on the expectations scheme.
KeywordsHorizontal product differentiation Vertical product differentiation Bounded rationality Dynamic stability
JEL classificationC62 D43 L13
This study was funded by the Spanish Ministry of Economics and Competitiveness (ECO2016–74940-P) and the Government of Aragon and FEDER (S10/2016 and S13/2016 Consolidated Groups) and S40-17R Reference Group.
Compliance with ethical standards
This paper benefited from comments made by two anonymous referees of this journal.
Conflict of interest
The authors declare that they have no conflict of interest.
- Agiza HN, Elsadany AA (2004) Chaotic dynamics in nonlinear duopoly game with heterogenous players. Appl Math Comput 149:843–860Google Scholar
- Bischi GI, Naimzada A (2000) Global analysis of a dynamic duopoly game with bounded rationalit. In: Filar JA, Gaitsgory V, Mizukami K (eds) Advances in Dynamic Games and Applications, vol 5, BirkhauserGoogle Scholar
- Chamberlin E, 1933. The theory of monopolistic competition. Harvard University press. Cambridge (MA)Google Scholar
- Elsadany AA, Agiza HN, Elabbasy EM (2013) Complex dynamics and chaos control of heterogeneous quadropoly game. Appl Math Comput 219:11110–11118.Google Scholar
- Fudenberg D, Tirole J (1984) The fat-cat effect, the puppy-dog ploy, and the lean and hungry look. Am Econ Rev 74(2):361–366Google Scholar
- Gandolfo G (2010) Economic dynamics. Forth. Springer, HeidelbergGoogle Scholar
- Kopel M (1996) Simple and complex adjustment dynamics in Cournot duopoly models. Chaos Soliton. Fract. (12):2031–2048Google Scholar
- Sandri M (1996) Numerical calculation of Lyapunov exponents. Math J 6(3):78–84Google Scholar