We study the pricing policy optimization problem for cloud providers while considering three properties of the real-world market:1) providers have only incomplete information about the market; 2) it is in evolution due to the increasing number of users and decreasing marginal cost of providers; 3) it is fully competitive because of providers' and users' revenuedriven nature. As far as we know, there is no existing work investigating the optimal pricing policies under such realistic settings. We first propose a comprehensive model for the real-world cloud market and formulate it as a stochastic game. Then we use the Markov perfect equilibrium (MPE) to describe providers' optimal policies. Next we decompose the problem of computing the MPE into two subtasks:1) dividing the stochastic game into many normal-formal games and calculating their Nash equilibria, for which we develop an algorithm ensuring to converge, and 2) computing the MPE of the original game, which is efficiently solved by an algorithm combining the Nash equilibria based on a mild assumption. Experimental results show that our algorithms are efficient for computing MPE and the MPE strategy leads to much higher profits for providers compared with existing policies.

Key words: cloud computing; Markov perfect equilibrium; game theory; revenue maximization;