  Payment channels networks drastically increase the throughput and hence
scalability of blockchains by performing transactions \emph{off-chain}. In an
off-chain payment, parties deposit coins in a channel and then perform
transactions without invoking the global consensus mechanism of the blockchain.
However, the transaction value is limited by the capacity of the channel, i.e.,
the amount of funds available on a channel. These funds decrease when a
transaction is sent and increase when a transaction is received on the channel.
Recent research indicates that there is an imbalance between sending and
receiving transactions, which leads to channel depletion in the sense that one
of these operations becomes impossible over time due to the lack of available
funds.
  We incentivize the balanced use of payment channels through fees. Whereas the
current fee model depends solely on the transaction value, our fee policies
encourage transactions that have a positive effect on the balance in a channel
and discourage those that have a negative effect. This paper first defines
necessary properties of fee strategies. Then, it introduces two novel fees
strategies that provably satisfy all necessary properties. Our extensive
simulation study reveals that these incentives increase the effectiveness of
payments by $8\%$ to $19\%$.
