Two-Player Location-Price Game in a Spoke Market with Linear Transportation Cost

This paper investigates the location game of two players in a spoke market with linear transportation cost. A spoke market model has been proposed, which is inspired by the Hotelling model and develops two-player games in price competition. Using two-stage (position and price) patterns and the backward guidance method, the existence of price and location equilibrium results for the position games is proved.

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.

Cournot and Bertrand Competition in a Model of Spatial Price Discrimination with Differentiated Products

This study investigates spatial price discrimination with two types of market competition – price competition and quantity competition – and two kinds of cross-relations between goods – substitutes and complements – with endogenous location choices in a barbell model. The results herein present that the maximum differentiation (end point agglomeration) is the unique location equilibrium with substitutes (complements), irrespective of what type of competition. We demonstrate that if the unit transportation rate is sufficiently high, then consumer surplus, profits, and social welfare are higher under price competition than under quantity competition for both substitutes and complements. This means that introducing a spatial barrier to competition generated through transportation costs may solve the problem of inconsistency from the conflict interests between consumers, firms, and a social planner.

Price and location equilibria in a circular market: a pure vs a mixed duopsony with a co-operative

The objective of the present paper is to analyze the location-price competition in circular markets where the power lies with the buyers. To this end, it considers two alternative market structures. Namely, the pure ones, where the buyers of a primary commodity are private firms, and mixed ones, where a private firm competes against a producer’s co-operative. According to the results, the pure-strategy location equilibrium in both cases involves a distance between the two players larger or equal to 1/4. Nevertheless, the equilibriums are qualitatively different. In the pure duopsony, a large distance is required to prevent a price war while in the mixed duopsony, the private firm tries to stay away from the co-op in order to ensure a strictly positive profit.