### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 962-970 |

Number of pages | 9 |

Journal | Journal of Advanced Computational Intelligence and Intelligent Informatics |

Volume | 18 |

Issue number | 6 |

Publication status | Published - 2014 Nov 1 |

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### Keywords

- Equilibrium theory
- Game theory
- Management engineering

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Vision and Pattern Recognition
- Human-Computer Interaction

### Cite this

*Journal of Advanced Computational Intelligence and Intelligent Informatics*,

*18*(6), 962-970.

**Analysis of consistent equilibria in a mixed duopoly.** / Kalashnikov, Vyacheslav V.; Bulavsky, Vladimir A.; Kalashnykova, Nataliya I.; Watada, Junzo; Hernández-Rodríguez, Diego De Jesús.

Research output: Contribution to journal › Article

*Journal of Advanced Computational Intelligence and Intelligent Informatics*, vol. 18, no. 6, pp. 962-970.

}

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

UR - http://www.scopus.com/inward/record.url?scp=84912104765&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84912104765&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84912104765

VL - 18

SP - 962

EP - 970

JO - Journal of Advanced Computational Intelligence and Intelligent Informatics

JF - Journal of Advanced Computational Intelligence and Intelligent Informatics

SN - 1343-0130

IS - 6

ER -