Multistability and cyclic attractors in duopoly games

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Equilibrium selection in a nonlinear duopoly game with adaptive expectations (2001, background): “In order to prove Proposition 1, we need the following Lemma, which is a particular case of a more general statement given in Bischi et al. (2000b) If x > 1 then y < 0 and all the images of higher rank are negative and divergent.”
The dynamics of a triopoly Cournot game (2000, background): “In particular, in [10,11] it is shown how the analysis of the only attractors of a Cournot game may not be enough in order to understand the dynamical behaviors, and the role played by the global basins of attraction (which may have complex structure) is evidenced.”
Oligopoly games with Local Monopolistic Approximation (2007, background): “Notice that in the price adjustment process proposed by Tuinstra only the case of linear cost functions gives rise to an explicit dynamical system.”