This chapter considers a two-echelon supply chain where a supplier determines his production quantity and a retailer chooses her order size and retail price for each period in an infinite horizon. Under a price-discount sharing (PDS) scheme, the supplier’s wholesale price linearly depends on the retail price. We develop a stochastic game in which these two supply chain members maximize their discounted profits. We show that a unique Nash equilibrium solution exists for each period, and over the infinite horizon the supplier chooses a stationary base stock policy whereas the retailer’s equilibrium solution could be non-stationary. Next, we investigate the problem of whether or not a wholesale pricing scheme can coordinate the supplier and the retailer, and derive the conditions for supply chain coordination. Moreover, we use Nash arbitration scheme to allocate the system-wide profit between the supplier and the retailer.