Fog computing promises to support many emerging classes of applications that can't be rely on a cloud-only backend. Fog-to-Fog (F2F) cooperation is suggested in the openFog's Fog computing Reference Architecture, now adopted as an IEEE standard, as a way to improve the computation service provided by this computing delivery model.In this paper, we propose DFR-Distributed Fair Randomized, a distributed F2F cooperation algorithm that allows for sharing computation resources among fog providers that agree on a (reasonable) measure of fairness. We adopt an analytical approach to study the cooperation problem of providers subject to different load conditions. We initially put the cooperation problem in the light of a simple game-theory framework to capture the selfish behavior of providers without any fairness criteria and its consequence in limiting cooperation. Then, we cast the problem as an optimization problem that incorporates fairness. Preliminary simulations results show how DFR converges to the predicted optimal value.