Paper:

# Analysis of Consistent Equilibria in a Mixed Duopoly

## Vyacheslav V. Kalashnikov^{*1, *2, *3}, Vladimir A. Bulavsky^{*2},

Nataliya I. Kalashnykova^{*3, *4}, Junzo Watada^{*5},

and Diego de Jesús Hernández-Rodríguez^{*4}

^{*1}Tecnológico de Monterrey (ITESM), Campus Monterrey, 64849, Mexico

^{*2}Central Economics & Mathematics Institute (CEMI), Russian Academy of Sciences (RAS), Moscow 117418, Russia

^{*3}Sumy State University, Sumy, 40007, Ukraine

^{*4}Department of Physics & Maths (FCFM), Universidad Autónoma de Nuevo León (UANL), San Nicolás de los Garza 66450, Mexico

^{*5}Graduate School of Information, Production and Systems, Waseda University, 2-7 Hibikino, Wakamatsuku, Kitakyushu, Fukuoka 808-0135, Japan

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.

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