  In PCNs, nodes that forward payments between a source and a receiver are paid
a small fee if the payment is successful. The fee is a compensation for
temporarily committing funds to the payment. However, payments may fail due to
insufficient funds or attacks, often after considerable delays of up to several
days, leaving a node without compensation. Furthermore, attackers can
intentionally cause failed payments, e.g., to infer private information (like
channel balances), without any cost in fees. In this paper, we first use
extensive form games to formally characterize the conditions that lead to
rational intermediaries refusing (or agreeing) to forward payments. A decision
made by an intermediary to forward or not depends on the probability of
failure, which they approximate based on past experience. We then propose and
analyze an alternative fee model that allows the sender to determine and pay a
fraction of the fee to intermediaries in a non refundable manner. A rational
sender chooses the fraction such that the intermediaries' utility for
forwarding the payment exceeds their utility for not forwarding. Our simulation
study, based on real world Lightning snapshots, confirms that our novel
mechanism can increase the probability of successful payments by 12 percent and
decrease routing fees for senders by about 6 percent if all nodes behave
rationally. Furthermore, previously cost free probing attacks now require that
the attacker pays 1500 satoshis for every 1 million satoshis inferred. Finally,
we propose a modification to the Hash Time Locked Contract to enable secure
payments of the non refundable fees.
