  Payment networks were introduced to address the limitation on the transaction
throughput of popular blockchains. To open a payment channel one has to publish
a transaction on-chain and pay the appropriate transaction fee. A transaction
can be routed in the network, as long as there is a path of channels with the
necessary capital. The intermediate nodes on this path can ask for a fee to
forward the transaction. Hence, opening channels, although costly, can benefit
a party, both by reducing the cost of the party for sending a transaction and
by collecting the fees from forwarding transactions of other parties.
  This trade-off spawns a network creation game between the channel parties. In
this work, we introduce the first game theoretic model for analyzing the
network creation game on blockchain payment channels. Further, we examine
various network structures (path, star, complete bipartite graph and clique)
and determine for each one of them the constraints (fee value) under which they
constitute a Nash equilibrium, given a fixed fee policy. Last, we show that the
star is a Nash equilibrium when each channel party can freely decide the
channel fee. On the other hand, we prove the complete bipartite graph can never
be a Nash equilibrium, given a free fee policy.
