Abstract
The Lightning Network is a decentralized payment network built on top of a block-chain, in which intermediary nodes provide a trust-less routing service for end users. We provide an overview of the current state of the network and show that it can be well approximated by a scale free generative model with a fitness parameter, which suggests that nodes behave strategically on the network. Those strategic interactions between nodes can be described by a Bertrand competition model with capacity constraints. We show that there is a unique equilibrium in which a centralized network is never optimal, and the routing fee is strictly greater than the marginal cost. When nodes are heterogeneous in their opportunity cost of capital only, the equilibrium network structure can match the current state of the network.
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