Dynamic competitive newsvendors with service-sensitive demands

When two firms compete for service-sensitive demands based on their product availability, their actions will affect the future market share reallocation. This problem was first studied by Hall and Porteus (2000) using a dynamic game model. We extend their work by incorporating a general demand model, which enables us to obtain properties that reveal the dynamics of the game and the behavior of the players. In particular, we provide conditions under which the market share of a firm has a positive value and give it an upper bound. We further extend the game competition model to an infinite-horizon setting. We prove that there exists a stationary equilibrium policy and that the dynamic equilibrium policy always converges to a stationary equilibrium policy. We demonstrate that demand patterns will dictate how firms compete rationally and show the likely outcomes of the competition.