# Payment Networks as Creation Games

## TL;DR

This paper introduces a game-theoretic model to analyze how payment channels in blockchain networks form and stabilize, revealing conditions under which certain network structures are stable Nash equilibria.

## Contribution

It is the first to model blockchain payment network formation as a game and analyzes stability conditions for various network topologies.

## Key findings

- Star network is a Nash equilibrium with free fee setting.
- Complete bipartite graph cannot be a Nash equilibrium.
- Network structure stability depends on fee constraints.

## Abstract

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.