A coalition game approach to the association problem of mobiles in broadcast transmission

We consider a common object (data) that each mobile in the medium is interested to receive, and which can be obtained from any base station transmitting the data. For example, the broadcast object could be streaming transmission of a sport or cultural event, or it could be some signaling such as a beacon for time synchronization or for power control purposes. This problem can be conceived as a coalition game played by mobiles which we call as association game of mobiles. This game has an incentive to form grand coalition where all players join to the game. We prove that using Bondareva-Shapley theorem, this coalition game has a non-empty core which means that grand coalition is stable. Then, we examine the cost allocation policy for different methods such as egalitarian allocation, proportional repartition of total cost, the Shapley value and the nucleolus. We also conclude that if the nucleolus is used as the cost allocation algorithm, the players maintain the grand coalition satisfying the minimization of total cost for broadcast transmission.