In this paper, we introduce a game theoretic framework for studying the problem of minimizing the completion time of instantly decodable network coding (IDNC) for cooperative data exchange (CDE) in decentralized wireless network. In this configuration, clients cooperate with each other to recover the erased packets without a central controller. Game theory is employed herein as a tool for improving the distributed solution by overcoming the need for a central controller or additional signaling in the system. We model the session by self-interested players in a non-cooperative potential game. The utility function is designed such that increasing individual payoff results in a collective behavior achieving both a desirable system performance in a shared network environment and the Pareto optimal solution. We further show that our distributed solution achieves the centralized solution. Through extensive simulations, our approach is compared to the best performance that could be found in the conventional point-to-multipoint (PMP) recovery process. Numerical results show that our formulation largely outperforms the conventional PMP scheme in most practical situations and achieves a lower delay.