Abstract
Game theory, and its specific area – spatial games, deal with the behavior of competitors. Spatial games focus on analyzing imperfect competition from a spatial point of view and the competitors represent companies operating in the market with the aim to attract customers and find the best location for their branch. Each company applies its own pricing policy, which affects its market share. In this article we present formulation and solution of a specific spatial game of two players who decide on the locations of their branches in space and want to maximize their revenues. The space is characterized by a graph, where location of customers and possible places of service represent its nodes. Customers choose one of the companies based on their total costs, consisting of the price of the product and shipping costs. The service in each of the nodes must be performed by either one or the other player. Such a situation can be analyzed using zero-sum games. The article presents the issue of determining the price of one player, based on a predetermined price of the opponent, to have player's revenues as high as possible. The game considers limited offer of the first player and different demands in each of the nodes.
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