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A nonlinear Cournot duopoly with advertising

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  • Gori, Luca
  • Sodini, Mauro
  • Fanti, Luciano

Abstract

This paper aims at studying local and global dynamics in a nonlinear duopoly with quantity-setting firms and non-cooperative advertising investments that affect the degree of (horizontally) differentiated products. It concentrates on persuasive advertising in a model where each firm has limited information and uses a behavioural rule to set the quantity for the subsequent period. By using some mathematical techniques and numerical simulations, our results show the existence of weak (à la Milnor) attractors, multistability and chaotic dynamics. In the long term, firms may continuously shift from states in which they invest in advertising to states in which advertising investment is absent.

Suggested Citation

  • Gori, Luca & Sodini, Mauro & Fanti, Luciano, 2015. "A nonlinear Cournot duopoly with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 178-190.
    • Handle: RePEc:eee:chsofr:v:79:y:2015:i:c:p:178-190
    DOI: 10.1016/j.chaos.2015.01.022
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    Cited by:

    1. Luca Gori & Nicolò Pecora & Mauro Sodini, 2017. "Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 905-931, November.
    2. Malcolm Brady, 2021. "A Game-Theoretic Model of Strategic Interaction Using Advertising: Simulating the Evolution of the Cournot Nash Equilibrium under Different Competitive Scenarios," Games, MDPI, vol. 12(4), pages 1-16, November.
    3. Malcolm Brady, 2022. "Asymmetric Horizontal Differentiation under Advertising in a Cournot Duopoly," Games, MDPI, vol. 13(3), pages 1-14, May.
    4. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

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