TY - JOUR

T1 - Analysis of consistent equilibria in a mixed duopoly

AU - Kalashnikov, Vyacheslav V.

AU - Bulavsky, Vladimir A.

AU - Kalashnykova, Nataliya I.

AU - Watada, Junzo

AU - Hernández-Rodríguez, Diego De Jesús

PY - 2014/11/1

Y1 - 2014/11/1

N2 - This paper examines a model of a mixed duopoly with conjectural variations equilibrium (CVE), in which one of the agents maximizes a convex combination of his/her net profit and domestic social surplus. The agents' conjectures concern the price variations, which depend on their production output variations. Based on the already established existence and uniqueness results for the CVE (called the exterior equilibrium) for any set of feasible conjectures, the notion of interior equilibrium is introduced by developing a consistency criterion for the conjectures (referred to as influence coefficients), and the existence theorem for the interior equilibrium (understood as a CVE state with consistent conjectures ) is proven. When the convex combination coefficient tends to 1, thus transforming the model into the mixed duopoly in its extreme form, two trends are apparent. First, for the private company, the equilibrium with consistent conjectures becomes more proficient than the Cournot-Nash equilibrium. Second, there exists a (unique) value of the combination coefficient such that the private agent's profit is the same in both of the above-mentioned equilibria, which makes subsidies to the producer or to consumers unnecessary.

AB - This paper examines a model of a mixed duopoly with conjectural variations equilibrium (CVE), in which one of the agents maximizes a convex combination of his/her net profit and domestic social surplus. The agents' conjectures concern the price variations, which depend on their production output variations. Based on the already established existence and uniqueness results for the CVE (called the exterior equilibrium) for any set of feasible conjectures, the notion of interior equilibrium is introduced by developing a consistency criterion for the conjectures (referred to as influence coefficients), and the existence theorem for the interior equilibrium (understood as a CVE state with consistent conjectures ) is proven. When the convex combination coefficient tends to 1, thus transforming the model into the mixed duopoly in its extreme form, two trends are apparent. First, for the private company, the equilibrium with consistent conjectures becomes more proficient than the Cournot-Nash equilibrium. Second, there exists a (unique) value of the combination coefficient such that the private agent's profit is the same in both of the above-mentioned equilibria, which makes subsidies to the producer or to consumers unnecessary.

KW - Equilibrium theory

KW - Game theory

KW - Management engineering

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M3 - Article

AN - SCOPUS:84912104765

SN - 1343-0130

VL - 18

SP - 962

EP - 970

JO - Journal of Advanced Computational Intelligence and Intelligent Informatics

JF - Journal of Advanced Computational Intelligence and Intelligent Informatics

IS - 6

ER -