Technology Category
Multiagent Systems: Mechanism DesignGame Theory and Economic Paradigms: Mechanism DesignSearch and Optimization: Distributed Search
A Mathematical Theory of Payment Channel Networks
🤖 AI Summary
This work addresses the scalability and liquidity limitations of pairwise payment channels in payment channel networks by proposing an efficient solution based on multi-party structures such as coinpools. It develops a geometric framework centered on the polytope of feasible wealth distributions $W_G$, mapping liquidity states to this polytope via strict circulations and characterizing payment feasibility through cut-set intervals. The study demonstrates that multi-party channels can linearly increase the wealth accessible to a single node—scaling with $k/n$—thereby substantially improving capital efficiency. It derives a sustainable off-chain throughput formula $S = \zeta / \rho$ and introduces three effective strategies to mitigate channel exhaustion. The analysis integrates tools from convex geometry, graph cut theory, hypergraph modeling, and flow optimization to systematically examine how fee structures and coordination mechanisms influence network dynamics.
Technology Category
Application Category
📝 Abstract
We introduce a geometric theory of payment channel networks that centers the polytope $W_G$ of feasible wealth distributions; liquidity states $L_G$ project onto $W_G$ via strict circulations. A payment is feasible iff the post-transfer wealth stays in $W_G$. This yields a simple throughput law: if $\zeta$ is on-chain settlement bandwidth and $\rho$ the expected fraction of infeasible payments, the sustainable off-chain bandwidth satisfies $S = \zeta / \rho$. Feasibility admits a cut-interval view: for any node set S, the wealth of S must lie in an interval whose width equals the cut capacity $C(\delta(S))$. Using this, we show how multi-party channels (coinpools / channel factories) expand $W_G$. Modeling a k-party channel as a k-uniform hyperedge widens every cut in expectation, so $W_G$ grows monotonically with k; for single nodes the expected accessible wealth scales linearly with $k/n$. We also analyze depletion. Under linear, asymmetric fees, cost-minimizing flow within a wealth fiber pushes cycles to the boundary, generically depleting channels except for a residual spanning forest. Three mitigation levers follow: (i) symmetric fees per direction, (ii) convex/tiered fees (effective flow control but at odds with source routing without liquidity disclosure), and (iii) coordinated replenishment (choose an optimal circulation within a fiber). Together, these results explain why two-party meshes struggle to scale and why multi-party primitives are more capital-efficient, yielding higher expected payment bandwidth. They also show how fee design and coordination keep operation inside the feasible region, improving reliability.
Problem
Research questions and friction points this paper is trying to address.
payment channel networks
scalability
capital efficiency
throughput
feasibility
Innovation
Methods, ideas, or system contributions that make the work stand out.
payment channel networks
feasible wealth polytope
multi-party channels
channel depletion
throughput law
🔎 Similar Papers
No similar papers found.
💼 Related Jobs
