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In this paper we describe an effective new technique by which to guarantee cooperativeness in Hybrid Radio-Frequency/Free Space Optics (RF/FSO) networks. Our approach is based on a novel Bayesian game-theoretic model, and uses a pricing scheme in which each destination node pays some amount of virtual money to the source node in order to acquire a reliable connection. We describe both single-stage and multi-stage solutions for the game in terms of its Nash and Perfect Bayesian Equilibriums. Pure strategies are found when the required conditions are met; otherwise the game is played as a mixed-strategy. Our numerical results quantify the inherent tradeoffs involved in changing the game's parameters vis-a-vis the equilibrium player strategies and game's outcomes.