Interference Games in Wireless Networks

We present a game-theoretic approach to the study of scheduling communications in wireless networks and introduce and study a class of games that we call Interference Games. In our setting, a player can successfully transmit if it “shouts strongly enough”; that is, if its transmission power is sufficiently higher than all other (simultaneous) transmissions plus the environmental noise. This physical phenomenon is commonly known as the Signal-to-Interference-plus-Noise-Ratio (SINR). Specifically, we show that the game has no pure Nash equilibrium and mixed Nash equilibria are either unfair (in the sense that one player has a much larger expected utility than the other players) or have social welfare 0. This state of things calls for the investigation of other notions of equiibrium. We show that there are Sink and Correlated equilibria with value of social welfare close to optimal. We then move to the study of Repeated Interference Games in which two players play possibly infinitely many instances of the Interference Game. We show that there exists a fair Subgame Perfect Equilibrium with maximal social welfare. Notice that such an equilibrium exists in the partial monitoring, that is, when each player only knows whether its previous transmission attempts have been successful. This result cannot be obtained with the well known Folk Theorem which requires full monitoring, that is each player has complete knowledge of the past actions of the other players.