Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior

Sarah Mignot, Fabio Tramontana and Frank Westerhoff
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Sarah Mignot: University of Bamberg

Annals of Operations Research, 2024, vol. 337, issue 3, No 4, 809-834

Abstract: Abstract We develop a nonlinear duopoly model in which the heuristic expectation formation and learning behavior of two boundedly rational firms may engender complex dynamics. Most importantly, we assume that the firms employ different forecasting models to predict the behavior of their opponent. Moreover, the firms learn by leaning more strongly on forecasting models that yield more precise predictions. An eight-dimensional nonlinear map drives the dynamics of our approach. We analytically derive the conditions under which its unique steady state is locally stable and numerically study its out-of-equilibrium behavior. In doing so, we detect multiple scenarios with coexisting attractors at which the firms’ behavior yields distinctively different market outcomes.

Keywords: Duopoly model; Heuristic expectation formation; Learning behavior; Nonlinear dynamics; Stability and bifurcation analysis; Coexisting attractors (search for similar items in EconPapers)
JEL-codes: C73 D43 L12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05497-x

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