  For multi-band wireless ad hoc networks of multiple users, an anti-jamming
game between the users and a jammer is studied. In this game, the users (resp.
jammer) want to maximize (resp. minimize) the expected rewards of the users
taking into account various factors such as communication rate, hopping cost,
and jamming loss. We analyze the arms race of the game and derive an optimal
frequency hopping policy at each stage of the arms race based on the Markov
decision process (MDP). It is analytically shown that the arms race reaches an
equilibrium after a few rounds, and a frequency hopping policy and a jamming
strategy at the equilibrium are characterized. We propose two kinds of
collision avoidance protocols to ensure that at most one user communicates in
each frequency band, and provide various numerical results that show the
effects of the reward parameters and collision avoidance protocols on the
optimal frequency hopping policy and the expected rewards at the equilibrium.
Moreover, we discuss about equilibria for the case where the jammer adopts some
unpredictable jamming strategies.
