Paper:

# Mixed Oligopoly: Analysis of Consistent Equilibria

## 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

In this paper, a model of mixed oligopoly with conjectured variations equilibrium (CVE) is examined, in which one of the agents maximizes a convex combination of its net profit with the domestic social surplus. The agents’ conjectures concern the price variations, which depend on the variations in their production outputs. Using the established existence and uniqueness results for the CVE (the *exterior equilibrium*) for any fixed set of feasible conjectures, the notion of the interior equilibrium is introduced by developing a conjecture consistency criterion. Then, the existence theoremfor the interior equilibrium (defined as a CVE state with *consistent conjectures*) is proven. When the convex combination coefficient tends to 1 (thus transforming the model into the mixed oligopoly in its extreme form), two trends are apparent. First, for private companies, the equilibrium with consistent conjectures becomes more proficient than the Cournot-Nash equilibrium. Second, there exists a (unique) value of the convex combination coefficient such that the private agent’s aggregate profit is the same in both the above-mentioned equilibria, which makes subsidies to producers or consumers unnecessary.

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