Spatial reuse in spectrum sharing: A Matrix Spatial Congestion Games approach

Congestion games, with the nice property that simple dynamics are guaranteed to converge to Nash equilibrium, have been widely used as models for many resource sharing scenarios. However, an obvious limitation of the congestion games is that they fail to capture a key feature of wireless networks: spatial reuse. That is, users separated far away enough can access the same channels without interference. In this paper, in order to take spatial reuse into account, we extend the congestion games to Matrix Spatial Congestion Games (MSCG) where we let the interference level vary from user to user. What´s more, we consider a situation where users are able to access multiple channels at a time. The main aim of this paper is to investigate under what conditions this new model still has the finite improvement property (FIP), which guarantees that a pure Nash Equilibrium (PNE) always exists. In terms of payoff functions we category MSCG into four types. And we have proved that FIP holds for two types, that are MSCG with non-resource-specific and non-user-specific payoff functions and MSCG with non-resource-specific and user-specific payoff functions. For the other two types, we show that FIP does not hold.