Consider a set of parties invited to execute a protocol $\Pi$. The protocol will incur some cost to run while in the end (or at regular intervals), it will populate and update local tables that assign (virtual) rewards to participants. Each participant aspires to offset the costs of participation by these virtual payoffs that are provided in the course of the protocol. In this setting, we introduce and study a notion of coalition-safe equilibrium. In particular, we consider a strategic coalition of participants that is centrally coordinated and potentially deviates from $\Pi$ with the objective to increase its utility with respect to the view of {\em at least one} of the other participants. The protocol $\Pi$ is called a coalition-safe equilibrium with virtual payoffs (EVP) if no such protocol deviation exists. We apply our notion to study incentives in blockchain protocols. We proceed to use our framework to provide a unified picture of incentives in the Bitcoin blockchain, for absolute and relative rewards based utility functions, as well as prove novel results regarding incentives of the Fruitchain blockchain protocol [PODC 2017] showing that the equilibrium condition holds for collusions up to $n-1$ players for absolute rewards based utility functions and less than $n/2$ for relative rewards based utility functions, with the latter result holding for any "weakly fair" blockchain protocol, a new property that we introduce and may be of independent interest.

中文翻译：

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具有虚拟收益的联盟安全均衡

考虑一组受邀执行协议 $\Pi$ 的各方。该协议将在最后（或定期）运行时产生一些成本，它将填充和更新为参与者分配（虚拟）奖励的本地表。每个参与者都希望通过协议过程中提供的这些虚拟收益来抵消参与成本。在这种情况下，我们引入并研究了联盟安全均衡的概念。特别是，我们考虑了一个参与者的战略联盟，该联盟是集中协调的并且可能偏离 $\Pi$，目的是增加其相对于其他参与者 {\em 至少一个} 的观点的效用。如果不存在这样的协议偏差，则协议 $\Pi$ 被称为具有虚拟收益 (EVP) 的联盟安全均衡。我们应用我们的概念来研究区块链协议中的激励机制。我们继续使用我们的框架为基于绝对和相对奖励的效用函数提供比特币区块链中激励的统一图，并证明有关 Fruitchain 区块链协议 [PODC 2017] 激励的新结果表明均衡条件成立对于基于绝对奖励的效用函数的高达 $n-1$ 玩家的串通，基于相对奖励的效用函数小于 $n/2$，后者的结果适用于任何“弱公平”区块链协议，这是我们的一个新属性介绍并可能具有独立兴趣。