Nash equilibria and dominant strategies are two of the major approaches to deal with selfishness in an automated system (AS), where each agent is a selfish entity.
In this paper, we consider the scenario when the receiver(s) and the relay links are both selfish, which generalizes the previous scenario in which either the relay links are selfish or the receivers are selfish. This also advances all previous studying in routing by taking into account the budget balance ratio. We prove that no mechanism can achieve budget balance ratio greater than
when truthful revealing is a dominant strategy for each of the relay links and receivers. Here,
is the number of vertices in the network. In the meanwhile, we also present a mechanism that achieves the budget balance ratio
and is truthful for both the receivers and relay links, which closes the bounds. When we relax the truthful revealing requirement to Nash Equilibrium for relay links, we present a mechanism that achieves an asymptotically optimal budget balance ratio.