Equilibrium selection in a nonlinear duopoly game with adaptive expectations

Abstract We analyze a nonlinear discrete time Cournot duopoly game, where players have adaptive expectations. The evolution of expected outputs over time is generated by the iteration of a noninvertible two-dimensional map. The long-run behavior is characterized by multistability, that is, the presence of coexisting stable consistent beliefs, which correspond to Nash equilibria in the quantity space. Hence, a problem of equilibrium selection arises and the long run outcome strongly depends on the choice of the players’ initial beliefs. We analyze the basins of attraction and their qualitative changes as the model parameters vary. We illustrate that the basins might be nonconnected sets and reveal the mechanism which is responsible for this often-neglected kind of complexity. The analysis of the global bifurcations which cause qualitative changes in the topological structure of the basins is carried out by the method of critical curves.

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