Coalitional Game Framework for Multicast in Wireless Networks

TL;DR

The paper investigates stable coalition formation for multicast in wireless networks using coalitional game theory. It derives analytical conditions for when the grand coalition is stable (non-empty core) and when it is not (empty core), including symmetric-rate and rate-bounded scenarios. It also establishes sufficient conditions for Dc-stability, determining how users should partition into coalitions under various parameter regimes, and validates findings with numerical results across multiple network settings. The work provides a principled framework for designing stable cooperative multicast strategies and reveals how data rates, power, file size, and bandwidth costs influence coalition stability.

Abstract

We consider a wireless network in which there is a transmitter and a set of users, all of whom want to download a popular file from the transmitter. Using the framework of cooperative game theory, we investigate conditions under which users have incentives to cooperate among themselves to form coalitions for the purpose of receiving the file via multicast from the transmitter. First, using the solution concept of core, we investigate conditions under which it is beneficial for all users to cooperate, i.e., the grand coalition is stable. We provide several sets of sufficient conditions under which the core is non-empty as well as those under which the core is empty. Next, we use the concept of $\mathbb{D}_c$-stability to identify a set of sufficient conditions under which the users in the network form a certain fixed number of coalitions such that all the users within each coalition cooperate among themselves. Our analytical results show how the values of different system parameters, e.g., data rates of different users, transmit and receive power, file size, bandwidth cost, etc., influence stability properties of coalitions, and provide a systematic approach to evaluating cooperation of users for multicast. We also study cooperation among different users using numerical computations. The problem of coalition formation in the context of multicast addressed in this paper is fundamental, and our analysis provides new insights into the feasibility of stable cooperative multicast strategies, contributing to a deeper understanding of cooperation in wireless networks.

Figures (7)

• Figure 1: The figure shows an example network with $N = 6$ users.
• Figure 2: The figure shows the sum of utilities of all users versus the rate, $R_6$, of the minimum rate user for a scenario in which there are $N=15$ users with rates $R_6, R_7, \ldots,R_{20}$. The rates $R_7, \ldots, R_{20}$ remain fixed at their respective values specified in the first paragraph of Section \ref{['SC:numerical:results']}.
• Figure 3: The figure shows the sum of utilities of all users versus the receive power, $P_{Rx}$. Here, we have considered a scenario in which $P_{Rx,i} = P_{Rx}$ for all $i$.
• Figure 4: The figure shows the sum of utilities of all users versus the transmit power, $P_{Tx}$.
• Figure 5: The figure shows the sum of utilities of all users versus the rate $R_{20}$.

Theorems & Definitions (15)

• Definition 1
• Definition 2
• Theorem 1
• Definition 3
• Theorem 2
• Remark 1
• Theorem 3
• Proposition 1
• Theorem 4
• Theorem 5