We consider a three-tier architecture for mobile and pervasive computing scenarios, consisting of a local tier (mobile nodes), a middle tier (cloudlets) of nearby computing nodes, typically located at the mobile nodes access points (APs) but characterized by a limited amount of resources, and a remote tier of distant cloud servers, which have practically infinite resources. This architecture has been proposed to get the benefits of computation offloading from mobile nodes to external servers without resorting to distant servers in case of delay sensitive applications, which could negatively impact the performance. In this paper, we consider a scenario where no central authority exists and multiple non-cooperative mobile users share the limited computing resources of a close-by cloudlet and can decide to compute on each of the three tiers of the envisioned architecture. We define a model to capture the users interaction and to investigate its dynamics, formulate the problem as a Generalized Nash Equilibrium Problem and show existence of an equilibrium. We present an algorithm for the computation of an equilibrium which is amenable to distributed implementation. Through numerical examples, we illustrate its behavior and the characteristic of the achieved equilibria.