An Upper Bound of Node Density in Cooperative Networks with Selfish Behavior

In a wireless network, connectivity is arguably the most critical issue that requires significant study since a network can hardly function well if it is disconnected. On the other hand, there are extraordinary interests in exploiting cooperative techniques in wireless networks in recent years. This paper studies the connectivity problem of large cooperative ad hoc networks. Unlike traditional cooperative networks where all nodes are willing to transmit in a collaborative manner, the cooperative network we considered does not assume that all nodes would like to transmit cooperatively when relaying other nodes´ traffic. In other words, each node exhibits some sense of selfishness. Specifically, we model nodes in such a way that each node cooperatively transmits with $p$-selfishness or location-based $p$-selfishness when relaying other nodes´ traffic. For the considered network, we assume that nodes are generated according to a Poisson Point Process (PPP) and techniques based on stochastic geometry and percolation theory are used to analyze the connectivity in such system. To quantify the performance of the cooperative ad hoc network with selfish behavior, we provides an upper bound of node density for such network to maintain connectivity.