Relay sharing has been recently investigated to increase the performance of coexisting wireless multi–hop networks. We analyze a scenario where two wireless ad hoc networks are willing to share some of their nodes, acting as relays, in order to gain benefits in terms of lower packet delivery delay and reduced loss probability. Bayesian network analysis is exploited to compute the probabilistic relationships between local parameters and overall performance, whereas the selection of the nodes to share is made by means of a game theoretic approach. Our results are then validated through the use of a system level simulator, which shows that an accurate selection of the shared nodes can significantly increase the performance gain with respect to a random selection scheme.