On the dynamics of games with product differentiation: a multimarket setting

Villena, Marcelo J.; Araneda, Axel A.

Keywords: stability, chaos, Economies of scale, Multi-market oligopoly, Cournot–Nash competition, Bertrand–Nash competition, Differentiated goods


In this paper we generalize Matsumoto and Szidarovszky’s work of differentiated oligopoly for a multimarket setting, considering n markets and m players. In particular, we analyze quantity and price competition when firms present joint economies of scale in different markets. This analysis enriches the current literature, capturing an empirical regularity of modern markets. We explicitly obtain the Nash equilibrium solutions of every game under certain conditions, and in turn a stability analysis is carried out for each singular point. Some numerical simulations are developed, confirming the chaotic behavior of these games, by bifurcations and Lyapunov exponent. Finally, it is shown that the dynamic of one player in one particular market depends crucially on the competition configuration of the other market and the level of complementarity of the products.

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Fecha de publicación: 2018
Año de Inicio/Término: September 6–8, 2018
URL: http://www.mdef.it/meetings/mdef-2018/