Economic lot-sizing game with price-dependent demand

We study the economic lot-sizing (ELS) game with price-dependent demand, whereby several retailers form a coalition to jointly place orders to a single supplier and determine their sale prices over a multi-period finite time horizon for profit maximization. We show that the game is balanced and has a non-empty core in general. We also show that the game is convex in two special cases where the retailers' demand functions are the same and where the time horizon consists of two periods. We give a counter-example to demonstrate that the game is non-convex in general. We perform numerical experiments to show the benefits of cooperating on inventory replenishment.