Coalition Games with Cooperative Transmission: A Cure for the Curse of   Boundary Nodes in Selfish Packet-Forwarding Wireless Networks
  In wireless packet-forwarding networks with selfish nodes, application of a repeated game can induce the nodes to forward each others' packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the other nodes do not depend on them. This problem is sometimes known as {\em the curse of the boundary nodes}. To overcome this problem, an approach based on coalition games is proposed, in which the boundary nodes can use cooperative transmission to help the backbone nodes in the middle of the network. In return, the backbone nodes are willing to forward the boundary nodes' packets. Here, the concept of core is used to study the stability of the coalitions in such games. Then three types of fairness are investigated, namely, min-max fairness using nucleolus, average fairness using the Shapley function, and a newly proposed market fairness. Based on the specific problem addressed in this paper, market fairness is a new fairness concept involving fairness between multiple backbone nodes and multiple boundary nodes. Finally, a protocol is designed using both repeated games and coalition games. Simulation results show how boundary nodes and backbone nodes form coalitions according to different fairness criteria. The proposed protocol can improve the network connectivity by about 50%, compared with pure repeated game schemes. 
Zhu Han and Vincent Poor