Mixed strategy Nash equilibrium in two-user resource allocation games

The problem of power allocation/channel selection in two-user games is considered. Unlike most of the game theoretic studies on resource allocation problems which consider pure strategies, this work investigates mixed strategies and mixed strategy Nash equilibrium (MSNE) that enables users to adopt more subtle strategies to improve their utilities. The necessary and sufficient conditions for the existence/uniqueness of MSNE are derived, first in a two-channel case and then in a more practical N channel case. In the two-channel game, the MSNE which maximizes the utilities of both users is found. In the N-channel game, a channel selection algorithm for the users, the outputs of which can be used to check the existence/uniqueness of MSNE, is proposed.