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Cournot games with biconcave demand. (English) Zbl 1290.91115
Summary: Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for the uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either “nearly linear” or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.

MSC:
91B54 Special types of economic markets (including Cournot, Bertrand)
91A40 Other game-theoretic models
91A10 Noncooperative games
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