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

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.