Location-Price Game in a Dual-Circle Market with Different Demand Levels

This paper researches a location-price game in a dual-circle market system, where two circular markets are interconnected with different demand levels. Based on the Bertrand and Salop models, a double intersecting circle model is established for a dual-circle market system in which two players (firms) develop a spatial game under price competition. By a two-stage (location-then-price) structure and backward induction approach, the existence of price and location equilibrium outcomes is obtained for the location game. Furthermore, by Ferrari method for quartic equation, the location equilibrium is presented by algebraic expression, which directly reflects the relationship between the equilibrium position and the proportion factor of demand levels. Finally, an algorithm is designed to simulate the game process of two players in the dual-circle market and simulation results show that two players almost reach the equilibrium positions obtained by theory, wherever their initial positions are.