均衡中的共识：一个人对所有人能做出公平的决定吗？
Consensus in Equilibrium: Can One Against All Decide Fairly?
摘要：
当除了一个代理之外的所有代理合谋将决策值引导到他们的偏好时，分布式共识是否存在均衡？如果存在均衡，则$n-1$大小联盟不能通过偏离算法来做得更好，即使它更喜欢不同的决策值。我们表明，在这种条件下，只有当网络中的代理数量是奇数和决策是二进制（两个可能的输入值之间）的平衡存在。也就是说，在这个框架中，我们提供了二元和多值共识之间的分离。此外，输入和输出分布必须是均匀的，而不管通信模型（同步或异步）。此外，我们定义了一个新的问题-弹性输入共享（RIS），并使用它找到了一个{ \em iff}条件的$(n-1)$ -弹性平衡的确定性二元共识，实质上表明，平衡的确定性共识是等价于每个代理学习所有其他的输入在某种强意义上。最后，我们注意到，$(n-2)$弹性平衡的二元共识是可能的任何$n$。对于\emph{multi-valued}共识的$(n-2)$ -弹性均衡的情况是开放的。
英文摘要：
Is there an equilibrium for distributed consensus when all agents except one collude to steer the decision value towards their preference? If an equilibrium exists, then an $n-1$ size coalition cannot do better by deviating from the algorithm, even if it prefers a different decision value. We show that an equilibrium exists under this condition only if the number of agents in the network is odd and the decision is binary (among two possible input values). That is, in this framework we provide a separation between binary and multi-valued consensus. Moreover, the input and output distribution must be uniform, regardless of the communication model (synchronous or asynchronous). Furthermore, we define a new problem - Resilient Input Sharing (RIS), and use it to find an {\em iff} condition for the $(n-1)$-resilient equilibrium for deterministic binary consensus, essentially showing that an equilibrium for deterministic consensus is equivalent to each agent learning all the other inputs in some strong sense. Finally, we note that $(n-2)$-resilient equilibrium for binary consensus is possible for any $n$. The case of $(n-2)$-resilient equilibrium for \emph{multi-valued} consensus is left open.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
