Who Should Pay for Forwarding Packets?

Abstract

We present a game-theoretic study of hybrid communication networks in which mobile devices can connect to a base station, The maximal number of allowed hops might be bounded in order to guarantee small latency. We introduce hybrid connectivity games to study the impact of selfishness on this kind of infrastructure.

Mobile devices are represented by selfish players, each of which aims at establishing an uplink path to the base station minimizing its individual cost. Our model assumes that intermediate nodes on an uplink path are reimbursed for transmitting the packets of other devices. Depending on the model, the reimbursements can be paid either by a benevolent network operator or by the senders of the packets using micropayments via a clearing agency that possibly collects a small percentage as commission.

Our main findings are these: If there is no constraint on the number of allowed hops on the path to the base station, then the existence of equilibria is guaranteed regardless of whether the network operator or the senders pay for forwarding packets. If there is an upper bound on the number of allowed hops on the uplink path, then the existence of equilibria depends on who pays for forwarding packets. If the network operator pays, then the existence of equilibria is guaranteed only if at most one intermediate node is allowed. If the senders pay for forwarding their packets, then equilibria are guaranteed to exist given any upper bound on the number of allowed hops.

Our equilibrium analysis gives a first game-theoretic motivation for the implementation of micropayment schemes in which senders pay for forwarding their packets. We further support this evidence by giving an upper bound on the “price of anarchy” for this kind of hybrid connectivity game that is independent of the number of nodes but depends only on the number of hops and the power gradient.