A percolation model for the emergence of the Bitcoin Lightning Network

The distributed ledger system known as blockchain has triggered a revolution in the payments industry, and is the technological infrastructure underlying cryptocurrencies such as Bitcoin. Even so, the blockchain concept itself faces some limitations which may hinder its future growth and adoption. One problem, in particular, is the issue of scalability. While validated blockchain platforms can typically process between 3 and 7 transactions per second, the Visa system handles many thousands. The lack of blockchain scalability stems mainly from constraints on transaction throughput, with the block size fixed at 1MB, and by the fact that new blocks are only created on average only every ten minutes. These limitations safeguard the platform against malicious attacks, and so cannot easily be relaxed without major changes in the protocol.

One alternative to modifying the core protocol is to use sidechains or second-layer solutions, which let parties keep some of their transactions separate from the main blockchain system. For example, the idea of a “Lightning channel” is that two parties, offering up collateral and opening a channel, can then exchange money back and forth rapidly over some period of time. They only eventually validate and store the netted transaction on the main blockchain. If one party fails to correctly update the balance, the other can keep the posted collateral, which acts as a form of insurance. The scalability problem could be solved if enough channels were opened, such that the Lightning Network spans across the whole pool of blockchain users. In a new paper, LML External Fellow Fabio Caccioli and colleagues Silvia Bartolucci (Imperial College London) and Pierpaolo Vivo (King’s College London) investigate under which conditions a Lightning Network emerges which spans a large fraction of Bitcoin users, the outcome depending on blockchain and Lightning fees, and the average wealth and volume of transactions per user.

They model the emergence of the Lightning Network as a (bond) percolation process, and explore how the distributional properties of the volume and size of transactions per user may impact its feasibility. In the model, all agents can transfer Bitcoins using the main blockchain and also, if convenient, open a channel on the Lightning Network and transact “off chain.” The authors study the emergence of a connected component both numerically and analytically as a function of the parameters, and identify a phase transition separating regions in the phase space where the Lightning Network is sustainable or not. As they show, a phase diagram clarifies the minimal volume of transactions that would make the Lightning Network sustainable for a given level of fees.

The paper is available at https://www.nature.com/articles/s41598-020-61137-5

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