Mobile Edge computing (MEC) and caching are new forms of computing architecture which brings network functions to the network edge or physical proximity of the users. In MEC, the mobile cloudlets are smart phones which offer computational services to other smart phones available in the physical proximity. Selection of the device for offloading computationally intensive tasks is a very important criterion for end-users Quality of Service. This work focuses on optimal selection of devices which receives offloaded computational tasks. This paper presents a non-cooperative extensive game model where players maximize their pay-offs which leads to minimization of response time. Further, we make our proposed model to implicitly depend upon the battery life of the computational task receivers. The game model achieves Nash Equilibrium by using backward induction technique. This work also takes care of the device availability by clustering the previous availability data. Finally, we evaluate the performance of the proposed model upon response time, end-users utility and memory utilizations. We also see that the proposed work out performs the different schemes which we used for comparisons.