In peer-to-peer applications, we need to encourage selfish users to share and contribute local resources to the global resource pool that all peers may benefit from, by providing adequate incentives. If we assume that all users are non-cooperative and always attempt to maximize their own net gains, at the first glance, we could model such behavior as a non-cooperative game and derive the equilibrium that no users deviate from. However, two observations complicate the case. (1) In such a game, user valuation on the contribution amount fluctuates, due to the dynamic supply-demand relationship of the shared resources; and (2) desirable global system properties require payoff functions to be reasonably designed. In this paper, we model the peer-to-peer system as a Cournot Oligopoly game with dynamic payoff functions that incorporate system performance requirements, and propose a control-theoretic solution to the problem. Throughout the paper, we use a peer-to-peer global storage system as a running example and case study. Simulation results have shown that the control-theoretic solution may effectively adapt the user contributions to track system dynamics, maximize the local net gain, and achieve satisfactory global properties.