Consistent Conjectural Variations Equilibrium in a Mixed Duopoly
Nataliya I. Kalashnykova*1,*2, Vladimir A. Bulavsky*3, Vyacheslav V. Kalashnikov*2,*3,*4, and Felipe J. Castillo Pérez*1
*1FCFM, UANL, San Nicolás de los Garza, N.L. 66450, Mexico
*2Sumy State University, Sumy, Ukraine 40007
*3Central Economics & Mathematics Institute (CEMI), Moscow 117418, Russia
*4ITESM, Campus Monterrey, Monterrey, N.L. 64849, Mexico
In this paper, we consider a model of mixed duopoly with Conjectured Variations Equilibrium (CVE). The agents’ conjectures concern the price variations depending on the increase or decrease in their production outputs. We establish existence and uniqueness results for the conjectured variations equilibrium (called an exterior equilibrium) for any set of feasible conjectures. To introduce the notion of an interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as a CVE with consistent conjectures). To prepare the base for the extension of our results to the case of non-differentiable demand functions, we also investigate the behavior of the consistent conjectures in dependence upon a parameter representing the demand function derivative with respect to the market price.
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