On the convergence of fictitious play in channel selection games

The channel selection (CS) problem in decentralized parallel multiple access channels considers the mutual interference of the different radio devices, and this interaction can be modeled by strategic-form games. Here, we show that the CS problem is a potential game (PG) and thus the fictitious play (FP) converges to a Nash equilibrium (NE) either in pure or mixed strategies. Using a 2-player 2-channel game, it is shown that convergence in mixed strategies might lead to cycles of action profiles which lead to individual spectral efficiencies (SE) which are worse than the SE at the worst NE in mixed and pure strategies. Finally, taking advantage from the fact that the CS problem is a PG and an aggregation game, we show a method to implement FP with local information and minimum feedback.