Abstract: The continuing growth of modern big cities leads to their spatial expansion and the emergence of new road connections and urban areas. Areas where large transportation flows of pedestrians, passengers, and drivers come together create demand points, which attract business companies that strive to allocate their resources in the most sought-after places. However, the law of supply and demand restrains companies from allocating all their resources solely in the most popular congestion areas since the more valuable an urban area, the higher the cost to be paid for a resource unit allocation there. As a result, companies act in a non-cooperative manner and try to minimize their own overall costs when allocating resources across available commercial areas in a big city. Non-cooperative behavior of companies leads to the problem of Nash equilibrium search in the game of competing entrepreneurs. In this paper, we study the corresponding resource allocation game under affine cost functions and obtain Nash equilibrium strategies in explicit form. These findings allow us to develop a simple procedure for computing Nash equilibria in the game of companies allocating their resources among urban congestion areas. The computational study demonstrates the dependence of the average price for resource allocation on the number of players and their resource volumes. The outcome of the paper contributes to flow theory and seems to be fresh and useful for managers.

Key words: Resource allocation, Nash equilibrium, Affine costs