Strategic Behavior and the Environment, 2014, 4: 187–211 Energy-constrained Mean Field Games in Wireless Networks ∗ Hamidou Tembine Ecole Sup´ erieure d’Electricit´ e, Supelec, France; tembine@ieee.org ABSTRACT In this paper, we study anti-jamming problems in energy-aware wireless networks using mean field stochastic games. We consider three types of users: jammers, primary users and secondary users. When active, each secondary transmitter–receiver uses carrier sensing and is subject to a long-term energy constraint. We formulate the interaction between primary and large number of secondary users as a hierarchical mean field game. The proposed mean field framework allows one to describe the evolution of the remaining energy distribution and the location of the secondary users. We provide explicit optimal strategies for both primary and secondary users based on attackers strategies. Each sec- ondary user reacts to the aggregative behavior of the others and man- ages its battery based on the anticipated complete characterization of the optimal distribution of energy. Keywords: Stochastic optimization; game theory; environmental economics; telecommunications; mean-field type game; energy-efficiency. ∗ This work has been partially supported by the European Research Council (ERC) Start- ing Grant number 305123 MORE (Advanced Mathematical Tools for Complex Network Engineering). ISSN 1944-012X; DOI 10.1561/102.00000040 c  2014 H. Tembine