Anything goes with heterogeneous, but not always with homogeneous oligopoly
Corchón and Mas-Colell [1996. On the stability of best reply and gradient systems with applications to imperfectly competitive models. Economics Letters 51, 59-65] showed that in heterogeneous oligopoly (almost) everything is possible. In order to obtain a similar result for homogeneous oligopoly, either one needs an externality in the cost function, or the reaction correspondences should fulfill a special condition.
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