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In downlink orthogonal frequency division multiple access (OFDMA) networks, an effective way of using the limited wireless spectrum resources can significantly improve network response. This paper presents a game-theoretic scheme with anticoordinated players by incorporating adaptation of femto base station (FBS) transmit power, attenuation of interference and utility function for open access mode and closed access mode respectively. The deployment of femtocells in the networks is to produce improved energy efficiency (EE) and optimized reponse of payoff function. In open access mode, each user belongs to the operator’s network can connect to the FBS and in closed access case, only a specified set of users can privately couple to the FBS whereas in the early access scenario it only allows authentic subscribers to take the advantage of femtocell networks. Additionally, the operating principle of spectrum sharing scheme has been discussed in which FBS as a player acquire knowledge from utility responses of their strategic communications and revise their strategies at each level of the game process. Here, an FBS is regarded as a player in the game to select the users who are satisfied to a greatest extent and an FBS plays a role of mentor. Thereafter, the equilibrium concept has been invoked to aid the anti-coordinated players for the strategies. Besides, a femtocell power adaptation algorithm has also been introduced based upon the set of enabled femtocells who can be used to retain its blocking probability that guarantees convergence to the stable strategy of the game, where the FBS monitors the subscribers’ actions and gives only limited data exchange. The simulations demonstrate that the proposed algorithm attains a high quality performance such as rapid convergence, interference attenuation to a greatest extent, noticeable EE improvement etc. Finally, validate the simulation results with its rarely studied extension in cognitive femtocell networks.