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In this paper, we study the problem of optimal data transfer over multiple overlay paths. Instead of solving the problem from the single controller point of view, we adopt the game theory perspective to consider the problem from a more realistic view where multiple traffic controllers competing for the shared bandwidth. We formulate the problem as a general- sum stochastic game, and a reinforcement learning technique namely Correlated-Q Learning is implemented to derive the best- possible strategy, i.e. the strategy to play correlated equilibrium (CE) for each controller. Through a proof-of-concept simulation scenario with 2 overlay paths and 2 controllers, we show that by playing cooperative strategies, e.g. CE, the controllers can achieve superior performance compared to acting selfishly. The result emphasizes that considering the problem of optimal multipath data transfer from the single controller perspective is inadequate.