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

Abstract

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.

Design and Implementation of Smart Phone Games for Linux Clustering

“…The distributed server system usually has more than one server and the servers are divided into two types: one(s) that can share data and one(s) that cannot. The former is called replicated server and the latter, non-replicated server [5][6][7][8][9][10].…”

Common Mistakes in Computing the Nucleolus

“…By defining F 1 = {3, 4}, the value of x 3 is fixed and the second LP gives as solution the allocation x, which is the correct nucleolus for this game. Hasan et al (2011) consider a game where the players represent mobiles which are interested on receiving the same information from a base station. The information could be, for example, the streaming transmission of a sport or cultural event.…”

“…Lemaire cite an even earlier article by Hamlen et al (1977), which presents a single LP model (equivalent to P ) to compute the nucleolus for a 3-player game. Despite the years gone by, these ambiguities appear to still induce errors in recent literature, as SatyaRamesh and Radhakrishna (2009) and Hasan et al (2011) cite Lemaire (1984) as the basis for the allocation methods they use.…”

“…In this note, we discuss these issues and illustrate them in six examples taken from a variety of literature sources. The examples correspond to applications of cooperative game theory in insurances (Lemaire, 1991), joint development of projects (Kruś and Bronisz, 2000), production and transportation planning (Sakawa et al, 2001), electricity markets (SatyaRamesh and Radhakrishna, 2009), mobiles in broadcast transmission (Hasan et al, 2011), and manufacturing (Oh and Shin, 2012). It came to our attention that similar errors have appeared in such a wide range of applications.…”

Green Broadcast Transmission in Cellular Networks: A Game Theoretic Approach

“…In [11], the combined problem of (i) deciding what subset of the mobiles would be assigned to each BS, and then (ii) sharing the BSs' cost of multicast among the mobiles is studied. The subset that is wished to assign to a given BS is said to be its target set of mobiles.…”