Mixed Duopoly Stochastic Sales Model with Advertising and Experience Gains for the Public and Foreign Competitors
Vitaliy Kalashnikov*,, Natalyia Kalashnykova**, and Petr Kuzmin***
*Facultad de Economía (FAECO), Universidad Autónoma de Nuevo León (UANL)
Monterrey, Nuevo León, Mexico
**Facultad de Ciencias Físico Matemáticas (FCFM), Universidad Autónoma de Nuevo León (UANL)
Monterrey, Nuevo León, Mexico
***Department of International Institute of Economics, Management and Information Systems, Altai State University
68 Socialist Street, Barnaul 656049, Russia
In this research, we propose a stochastic model with the finite horizon of time for sales competition between the state-owned company and private (foreign) competitor. We assume that the foreign company objective function is to maximize revenues and the state-owned agent is concerned about welfare maximization. There are many stochastic models for sales, but what is new in our case is that we assume mixed oligopoly and have different types of firms: private and state owned. They have somewhat different objective functions. As a control variable, we take the advertisement expenses of the private firm. Sale bursts rate depends and the advertisement expenditure and experience stock gained. For the public firm, we assume that advertising efforts are fixed. It means that the optimal control is to maximize private firm revenues taking into account possible uncertainties of stochastic profit flow using Bellman’s optimality condition. We can find out that the Advertisement-Experience (AE) efforts of the private firm are increasing if sales are increasing. Next, the AE might decrease if the experience level of the private firm increases and we have a sales burst. To optimize the governmental policies, we check for optimal AE effort of the public firm so the social welfare achieves the maximum value.
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