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Heterogeneity and the (de)stabilizing role of rationality

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  • Cavalli, Fausto
  • Naimzada, Ahmad
  • Pireddu, Marina

Abstract

In this paper we study oligopolies of generic size consisting of heterogeneous firms, which adopt best response adjustment mechanisms with either perfect foresight (rational firms) or static expectations (naive firms). Assuming an isoelastic demand function and possibly different marginal costs for the two groups of firms, we focus on the local stability of the Nash equilibrium. We show that, with respect to the oligopoly composition, described in terms of the fraction of rational firms, different scenarios are possible. We find that a high rationality degree may not always guarantee stability, in particular when rational firms have sufficiently larger marginal costs. In fact, in this situation, increasing the fraction of rational firms can even introduce instability. Besides the usual scenarios in which replacing some naive firms with rational ones leads to a stabilization of (or at least keeps unchanged) the dynamics, we provide a family of situations, characterized by costs ratio favorable to naive firms, in which equilibrium loses its stability when naive firms are replaced by rational ones. The results we present are both analytical and simulative.

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  • Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.
    • Handle: RePEc:eee:chsofr:v:79:y:2015:i:c:p:226-244
    DOI: 10.1016/j.chaos.2015.05.017
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    1. Cavalli, Fausto & Naimzada, Ahmad, 2016. "Complex dynamics and multistability with increasing rationality in market games," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 151-161.
    2. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    3. Andrea Caravaggio & Lorenzo Cerboni Baiardi & Mauro Sodini, 2021. "A note on symmetry breaking in a non linear marketing model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 507-531, December.
    4. Fausto Cavalli & Ahmad Naimzada & Mauro Sodini, 2018. "Oligopoly models with different learning and production time scales," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 297-312, November.

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