  Payment channel networks (PCNs) are a promising solution to the scalability
problem of cryptocurrencies. Any two users connected by a payment channel in
the network can theoretically send an unbounded number of instant, costless
transactions between them. Users who are not directly connected can also
transact with each other in a multi-hop fashion. In this work, we study the
incentive structure behind the creation of payment channel networks,
particularly from the point of view of a single user that wants to join the
network. We define a utility function for a new user in terms of expected
revenue, expected fees, and the cost of creating channels, and then provide
constant factor approximation algorithms that optimise the utility function
given a certain budget. Additionally, we take a step back from a single user to
the whole network and examine the parameter spaces under which simple graph
topologies form a Nash equilibrium.
