Cooperation among nodes is essential for the reliable routing of packets in large scale wireless sensor networks from nodes to base station. Most of the previous works have assumed a single governing authority with full cooperation among nodes. The assumption of node cooperation, however, cannot be applied to wireless sensor networks (WSNs) with more than one governing authority. In this paper, we introduce the concept of multi-class wireless sensor networks where each class is governed by a different authority. We study the evolution of cooperation in static and mobile multi-class wireless sensor networks using Evolutionary Game Theory which has, to the best of our knowledge, never been attempted before. We then propose a novel localized distributive algorithm we call the Patient Grim Strategy (PGS), and demonstrate that it provides a Nash equilibrium solution to the game theoretic problem of cooperation in multi-class static wireless sensor networks. Our simulation results show that in static multi-class WSNs populations playing the prisoner?s dilemma, significant propensities to cooperate can evolve.