Game Model of a Geographically Distributed Market: the Search for Equilibria

The work aims to analyze a geographically distributed market, composed of some local ones, taking into account limited production capacity. Interaction between producers is seen as Bertrand competition. The producer has both production costs that are the same for all local markets and costs of delivery that vary for different local markets. In the model with two local markets and two producers with limited production capacity all equilibria for every set of parameters for costs and capacity were found. Thereafter, the work analyzed how small changes in production costs and costs of delivery affect the welfare of each of the manufacturers, of each of the consumers of every local market, and how these changes influence public welfare in local markets. Furthermore, the work analyzed how the addition of the third producer or the third local market can affect the welfare. As a result, it was found that in the 2x2 model an equilibrium exists for all sets of parameters. However, it can be either unique or quasi-unique, or non-unique, depending on the model parameters. Changes in costs lead to unpredicted results, such as, for example, an increase in the profit of one producer whilst lowering the costs of another one, or an increase in public welfare from subsidizing which was not used by the manufacturer.