Who wants to break the hockey-stick sales pattern in the supply chain?

The hockey-stick pattern faced by suppliers consists of sales spikes at the end of each period. One of its causes is the information asymmetry that favors the retailer, who has better knowledge about the stochastic consumer demand. Because of delayed purchases, the supplier is induced to offer promotions, allowing the retailer to forward-buy at low prices. We model this situation as an infinitely repeated game, where each stage-game is subject to imperfect information. Drawing from the Nash equilibrium, we express sales and inventories in terms of demand, cost and the strategies players may adopt, and derive the conditions for a cooperative equilibrium.