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.

翻译：二层区块链协议的出现旨在解决链上交易在费用、存储成本和确认延迟方面的可扩展性问题。它们将链下交易聚合为更少的链上交易，从而提供即时结算并降低交易费用。为维护底层账本的安全性，二层协议通常在抵押模型下运行；资源被承诺在链上以支持链下活动。在此设置中出现的一个基本挑战是：如何制定抵押品的建立、承诺和补充策略，以最大化已结算交易的价值。本文中，我们在两种模拟抵押化二层协议的设置下研究此问题。第一种是通用模型，其中一方拥有链上抵押品C，并依据策略决定是结算还是丢弃每笔传入交易。该策略还规定了何时基于剩余抵押品价值补充C。第二种模型考虑离散设置，其中C被分配到k个钱包中，每个钱包大小为C/k，使得当某个钱包已满且无法结算任何传入交易时，将被补充。我们为这些模型设计了多种在线策略，并展示了它们与具有完整交易流信息的（离线）最优策略相比的竞争性能。据我们所知，我们是首个在区块链场景中研究并形式化抵押品与钱包管理的在线竞争性策略的工作。