On the Nash Equilibria in Decentralized Parallel Interference Channels

Luca Rose (1, 2) , Samir M. Perlaza (3) , Merouane Debbah (2)

1 Thales Research and Technology [Palaiseau]
2 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec
3 FT R&D - France Télécom Recherche & Développement

In this paper, the 2-dimensional decentralized parallel interference channel (IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static game. Eachtransmitter is assumed to be a fully rational entity with complete information on the game, aiming to maximize its own individual spectral efficiency by tuning its own power allocation (PA) vector. Two scenarios are analysed. First, we consider that transmitters can split their transmit power between both dimensions (PA game). Second, we consider that each transmitter is limited to use only one dimension (channel selection CS game). In the first scenario, the game might have either one or three NE in pure strategies (PS). However, two or infinitely many NE in PS might also be observed with zero probability. In the second scenario, there always exists either one or two NE in PS. Using Monte-Carlo simulations, we show that in both games there always exists a non-zero probability of observing more than one NE. More interestingly, we show that the highest and lowest network spectral efficiency at any of the NE in the CS game are always higher than the ones in the PA.

Domaines: Réseaux et télécommunications [cs.NI]

Luca Rose, Samir M. Perlaza, Merouane Debbah. On the Nash Equilibria in Decentralized Parallel Interference Channels. IEEE International Conference on Communications ICC2011, Jun 2011, Japan. pp.ICC-2011 Rose. ⟨hal-00553531⟩