Competitive Policies for Online Collateral Maintenance
Ghada Almashaqbeh, Sixia Chen, Alexander Russell
TL;DR
This paper addresses online collateral management for layer-two blockchain protocols under distribution-independent competitive analysis. It introduces two canonical models—the discrete $k$-Wallet model and the general collateral model—and analyzes online policies against an offline oracle with full future knowledge. Key results include explicit competitive ratios for the main algorithms: $\textsc{FlushAll}$ achieves $\frac{2 - r}{1 - r}$-competitiveness and $\textsc{FlushWhenFull}$ achieves $\frac{k+1}{k(1 - r)}$-competitiveness in the $k$-wallet setting, with an optimal wallet count $k^* \approx \sqrt{1 + C/T} - 1$; in the $r=1$ regime, deterministic strategies have limitations and pairing wallets improves performance. In the general collateral model, the threshold policy $\mathrm{A}_\eta$ attains a provable bound with optimum $\eta^* = \sqrt{(1 - T/C)\cdot \beta}$ and $\beta = \tau/(pC)$, yielding a ratio $\frac{1 - \beta}{(\sqrt{1 - T/C} - \sqrt{\beta})^2}$; the corollary shows competitive performance for $\textsc{FlushWhenFull}$ in the Gen model. Overall, the work lays a foundation for robust, distribution-insensitive wallet management in layer-two systems such as payment channels, probabilistic micropayments, DeFi collateral pools, and AMMs, guiding practical choices for wallet counts and replenishment policies and suggesting directions for adaptive, transaction-aware extensions.
Abstract
Layer-two blockchain protocols emerged to address scalability issues related to fees, storage cost, and confirmation delay of on-chain transactions. They aggregate off-chain transactions into a fewer on-chain ones, thus offering immediate settlement and reduced transaction fees. To preserve security of the underlying ledger, layer-two protocols often work in a collateralized model; resources are committed on-chain to backup off-chain activities. A fundamental challenge that arises in this setup is determining a policy for establishing, committing, and replenishing the collateral in a way that maximizes the value of settled transactions. In this paper, we study this problem under two settings that model collateralized layer-two protocols. The first is a general model in which a party has an on-chain collateral C with a policy to decide on whether to settle or discard each incoming transaction. The policy also specifies when to replenish C based on the remaining collateral value. The second model considers a discrete setup in which C is divided among k wallets, each of which is of size C/k, such that when a wallet is full, and so cannot settle any incoming transactions, it will be replenished. We devise several online policies for these models, and show how competitive they are compared to optimal (offline) policies that have full knowledge of the incoming transaction stream. To the best of our knowledge, we are the first to study and formulate online competitive policies for collateral and wallet management in the blockchain setting.