On the Convergence of Fictitious Play in Channel Selection Games

Samir M. Perlaza (1) , Victor Quintero Florez (2) , Hamidou Tembine (3) , Samson Lasaulce (4)

1 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec
2 Universidad del Cauca [Popayán]
3 E3S - Supélec Sciences des Systèmes
4 L2S - Laboratoire des signaux et systèmes

Considering the interaction through mutual interference of the different radio devices, the channel selection (CS) problem in decentralized parallel multiple access channels 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 a 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, exploiting the fact that the CS problem is a PG and an aggregation game, we present a method to implement FP with milder information conditions than those required in its original version.

Domaines: Informatique et théorie des jeux [cs.GT]

Samir M. Perlaza, Victor Quintero Florez, Hamidou Tembine, Samson Lasaulce. On the Convergence of Fictitious Play in Channel Selection Games. IEEE Latin America Transactions, 2011, 9 (4), pp.470 - 476. ⟨10.1109/TLA.2011.5993730⟩. ⟨hal-00657518⟩