On proportional power sharing mechanisms for secondary spectrum markets

We consider a proportional sharing mechanism for allocating spectrum to secondary users. Each user bids for a portion of the received power at a measurement point and receives a share that is proportional to its bid while paying a charge equal to the bid. The users then transmit over a common band treating all interference as noise. Under this mechanism, we model the secondary users as players is a bidding game. The players' interaction in this game is complicated due to the interference among them.We characterize the existence of a Nash equilibrium for both price taking and price anticipating users.