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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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I study the endogenous choice of a price or quantity contract in a mixed duopoly with a socially concerned firm, which maximizes a combination of profit and consumer welfare. Equilibria with price and quantity contracts might co‐exist; welfare under price competition might be lower than under quantity competition; the firms' profit ranking might be different from that of a private duopoly or mixed duopoly with a public firm. Hence, if a firm follows a social strategy, the optimal market strategy crucially depends on the levels of social concern and competition in the market. The presence of socially concerned firms may change the mode of competition. Copyright © 2014 John Wiley & Sons, Ltd.

First mover advantage, Strategic delegation, Research and development, L13, L2, O31,