Game-theoretic analysis among competing retailers: Extensions of multi-newsvendor model

The paper presents the game-theoretic analysis among multiple competing retailers under deterministic price-sensitive customer demand, which in each retail market arrives continuously at a constant rate that is the function decreasing in his own retail price, but increasing in other retail prices. We consider two kinds of games, i.e. the competitive game and the cooperative game. We show that competition leads to lower equilibrium profit for each retailer than that in the cooperative game, and the cooperative equilibrium is not stable while competitive equilibrium is stable when retailers operate independently, and illustrate that a competitive approach is certainly more appropriate to determine the set of equilibrium points that can be reached in independent trade conditions. Numerical examples illustrate the importance of the cooperation. The special emphasis is placed on two important aspects of games: profit allocation and stability.