Lightning Network Economics: Cost-Minimal Channels and their Implications for Network Structure
summary
Model treats each channel as two independent Poisson flows with Poisson arrival rates λ_ij, on‑chain reopen costing cost b for two on‑chain tx, and locked collateral earning rate r. Closed‑form and asymptotic formulas show optimal deposit scales differently: unidirectional vs symmetric bidirectional differ by an order of magnitude as r → 0, so bidirectional channels stay open much longer. Local moves (mutations, hermetization by a new hub) eliminate 3‑ and 4‑cycles and directed length‑2 paths; if all edge weights equal, average degree above ~5.66 creates profitable hubbing (bound ~12.7 for larger weight ratios). Open problems: asymmetric optimal sizes, fees, and rebalancing.
AI-written summary · about
chapters (18)
- 0:00Start
- 1:03THE DEVIL IS IN THE DEFAULTS
- 2:06AGENDA
- 2:28LIGHTNING NETWORK - CHANNELS
- 5:28LIGHTNING-LINKS
- 6:49MAIN QUESTIONS
- 7:32PREVIOUS WORKS
- 8:38CHANNEL MODEL
- 11:51CHANNEL COST
- 13:26SHOULD WE OPEN A CHANNEL?
- 16:23COST OF A LIGHTNING CHANNEL
- 18:10OPTIMAL CHANNEL SIZE
- 24:05STRUCTURE OF THE LIGHTNING NETWORK
- 26:51CHANGES TO THE LIGHTNING NETWORK
- 28:54DON'T MAKE SHORT CYCLES
- 33:21LIMIT YOUR DEGREES
- 36:39DISCUSSION
- 38:22OPEN PROBLEMS
