User strategy learning when pricing a RED buffer

We study a buffer that implements the Random Early Detect/Discard (RED) mechanism to cope with congestion, and offers service differentiation by proposing a finite number of slopes at different prices for the RED probability. As a characteristic, the smaller the slope, the better the resulting QoS. Users are sensitive to their average throughput and to the price they pay. Since the study of the noncooperative game played is rendered difficult by the discrete nature of the strategy sets, and since it is not likely that users have a perfect knowledge of the game but only know their experienced utility, we introduce a decentralized learning algorithm to progressively reach a Nash equilibrium over time. We examine the effect of prices on the final game outcomes.