We study game-theoretic models for capturing participation in blockchain systems. Permissionless blockchains can be naturally viewed as games, where a set of potentially interested users is faced with the dilemma of whether to engage with the protocol or not. Engagement here implies that the user will be asked to complete certain tasks, whenever they are selected to contribute (typically according to some stochastic process) and be rewarded if they choose to do so. Apart from the basic dilemma of engaging or not, even more strategic considerations arise in settings where users may be able to declare participation and then retract before completing their tasks (but are still able to receive rewards) or are rewarded independently of whether they contribute. Such variations occur naturally in the blockchain setting due to the complexity of tracking ``on-chain'' the behavior of the participants. We capture these participation considerations offering a series of models that enable us to reason about the basic dilemma, the case where retraction effects influence the outcome and the case when payments are given universally irrespective of the stochastic process. In all cases we provide characterization results or necessary conditions on the structure of Nash equilibria. Our findings reveal that appropriate reward mechanisms can be used to stimulate participation and avoid negative effects of free riding, results that are in line but also can inform real world blockchain system deployments.

翻译：我们研究了用于刻画区块链系统参与行为的博弈论模型。无需许可的区块链可自然地被视为博弈场景，其中一组潜在感兴趣的用户面临是否参与协议的两难抉择。此处的"参与"意味着：当用户（通常依据某种随机过程）被选中执行任务时，需完成任务并可在选择执行后获得奖励。除了基本的参与与否困境外，更复杂的策略考量出现在以下场景：用户可先声明参与，随后在完成任务前撤回（但仍能获取奖励），或无论是否贡献均能获得奖励。这类变体在区块链环境中自然产生，原因在于难以在链上完整追踪参与者的实际行为。我们通过构建系列模型来刻画这些参与考量，使我们能够分析基本困境、撤回效应影响结果的场景，以及独立于随机过程而普遍支付奖励的情形。针对所有情形，我们给出了纳什均衡结构的刻画结果或必要条件。研究结果表明，恰当的奖励机制可激发参与并规避搭便车的负面影响，这些结论既与现有成果一致，也可为实际区块链系统部署提供参考。