Why Riding the Lightning? Equilibrium Analysis for Payment Hub Pricing

Payment Channel Network (PCN) is an auspicious solution to the scalability issue of the blockchain, improving transaction throughput without relying on on-chain transactions. In a PCN, nodes can set prices for forwarding payments on behalf of other nodes, which motivates participation and improves network stability. Analyzing the price setting behaviors of PCN nodes plays a key role in understanding the economic properties of PCNs, but has been under-studied in the literature. In this paper, we apply equilibrium analysis to the price-setting game between two payment hubs in the PCN with limited channel capacities and partial overlap demand. We analyze existence of pure Nash Equilibriums (NEs) and bounds on the equilibrium revenue under various cases, and propose an algorithm to find all pure NEs. Using real data, we show bounds on the price of anarchy/stability and average transaction fee under realistic network conditions, and draw conclusions on the economic advantage of the PCN for making payment transfers by cryptocurrency users.