Coalition formation games for relay transmission: Stability analysis under uncertainty

Relay transmission or cooperative communication is an advanced technique that can improve the performance of data transmission among wireless nodes. However, while the performance (e.g., throughput) of a source node can be improved through cooperation with a number of relays, this improvement comes at the expense of a degraded performance for the relay nodes due to the resources that they dedicate for helping the source node in its transmission. In this paper, we formulate a coalitional game among the wireless nodes that seek to improve their performance by relaying each other's data. The game is classified as a coalition formation game in which the nodes can take individual and distributed decisions to join or split from a given coalition while ensuring that their individual throughput is maximized. A Markov chain model is proposed to investigate the stability of the resulting coalitional structures. Further, we consider the practical case in which the wireless nodes do not have an exact and perfect knowledge of the parameters (e.g., channel quality) in coalition formation. For this scenario, we analyze the stability of the partitions resulting from the proposed coalition formation game under uncertainty. We also define the conditions needed for obtaining the stable and unstable coalitional structures among the nodes that are performing cooperative transmission.