Computation offloading to edge-computing technologies is highly desirable to enable the use of low-latency computation intensive mobile-applications. To meet the desired latency requirements, overloaded cloudlets can further offload the incoming job requests to their under-loaded neighbor cloudlets. A novel economic and non-cooperative continuous-kernel game theoretic model is proposed to analyze the computation offloading strategies between cloudlets of competing service providers, supported by optical access networks. This model achieves a fairness in resource utilization as well as provides incentives to the participants. We investigate the existence and uniqueness conditions of the pure strategy Nash equilibrium for the formulated game. By linearizing the non-linear best response functions, we derive an approximate Nash equilibrium for the formulated game. We explain the dependence of the Nash equilibrium on factors such as computational resources, total incoming job requests, cloudlet to cloudlet transmission latency and corresponding cost factors. Finally, we show improvements in overall latency performance while employing the proposed Nash equilibrium offload strategy.