Channel depletion, LN Topology, Cycles and rational behavior of nodes

This scenario is exacerbated when payers exploit the system by releasing payment shards below the maximum milli-satoshi limit and inserting waiting periods between each release, allowing them to bypass controls and accumulate numerous Hashed Time-Locked Contracts (HTLCs) within a payment channel. The exploit becomes more feasible due to a zero fee_base and the practice of rounding down proportional fees, alongside the introduction of Point Time-Locked Contracts (PTLCs) which complicate tracking such strategies due to their non-correlatable nature. This underscores the necessity for robust mechanisms to prevent exploitation and address both technical and economic loopholes in digital payment infrastructures.

Further, the critique of current models used in analyzing payment networks emphasizes the dangers of relying on aesthetically appealing mathematical models without considering their limitations, particularly in dynamic environments like the Lightning Network. The models' assumption of static network topology and fee policies overlooks the nuanced, real-time decision-making of node operators regarding fee adjustments based on various factors. This simplification leads to inaccurate reflections of reality, where dynamic fee management plays a critical role in maintaining channel liquidity. There's an expressed need for incorporating dynamic fees and more sophisticated management tools into these models to better represent actual network behaviors and address channel depletion effectively.

Exploring the management of liquidity in payment channels reveals misconceptions around spanning trees and cycles, indicating that cheaper liquidity paths are preferred over more expensive ones, contrary to initial assumptions. Practical advice for node operators includes adjusting fees to control flow and using caps on pending payments to prevent overload and manipulation by users. This approach aims at maintaining network efficiency and fee fairness. Additionally, the predictability of spanning trees based on wealth distribution and their stability under changing conditions remains uncertain, suggesting areas for further research.

The foundational document "A Mathematical Theory of Payment Channel Networks" offers insights into the economic rationality and network topology contributing to channel depletion. Subsequent investigations into estimating liquidity states and optimizing fees highlight the correlation between circuit rank and depleted channels, suggesting predictability in network behavior driven by fee potential optimization. Despite these advances, challenges such as unknown wealth distributions, static network assumptions, and simplified payment models persist. The research indicates potential privacy concerns from external observations but also points to strategies for effective liquidity management and optimized payment routing. Future explorations are directed towards more accurate datasets to validate predictions against actual network behavior, emphasizing the ongoing evolution of understanding in payment channel networks.