The performance of wireless networks suffers from collisions. These occur when multiplewireless nodes transmit simultaneously, and their signals interfere with each other. To reduce collisions, nodes may use a randomized protocol to regulate their behavior. An example of such a protocol is slotted ALOHA, in which at the beginning of each time slot all nodes have a fixed probability to start a transmission for the duration of that slot. In this paper we consider a wireless network where all nodes use slotted ALOHA, and we investigate the impact of cooperation among nodes. Full cooperation eliminates collisions between nodes, which clearly has a positive impact on the network performance, measured by the aggregate node throughput. We are interested in how to allocate the corresponding performance gains obtained from cooperation among the nodes. In order to study this allocation problem, we define and analyze a corresponding cooperative ALOHA game. We show that this type of game is convex and we consider three solution concepts: the core, the Shapley value, and the compromise value. Further, we introduce the set of Weighted Gain Splitting (WGS) allocation rules, and show that this set coincides with the core of the game. These WGS rules can be used to provide an alternative characterization of the Shapley value. Finally, we analyze how the cooperative solution concepts change with the parameters of the wireless network.
