Major cryptocurrency networks have relied on random peering choice rules for making connections in their peer-to-peer networks. Generally, these choices have good properties, particularly for open, permissionless networks. Random peering choices however do not take into account that some actors may choose to optimize who they connect to such that they are quicker to hear about information being propagated in the network. In this paper, we explore the dynamics of such greedy strategies. We study a model in which nodes select peers with the objective of minimizing their average distance to a designated subset of nodes in the network, and consider the impact of several factors including the peer selection process, degree constraints, and the size of the designated subset. The latter is particularly interesting in the context of blockchain networks as generally only a subset of nodes are the propagation source for content. We first analyze an idealized version of the game where each node has full knowledge of the current network and aims to select the $d$ best connections, and prove the existence of equilibria under various model assumptions. Since in reality nodes only have local knowledge based on their peers' behavior, we also study a greedy protocol which runs in rounds, with each node replacing its worst-performing edge with a new random edge. We exactly characterize stability properties of networks that evolve with this peering rule and derive regimes where stability is possible and even inevitable. We also run extensive simulations with this peering rule examining both how the network evolves and how different network parameters affect the stability properties of the network. Our findings generally show that the only stable networks that arise from greedy peering choices are low-diameter and result in disparate performance for nodes in the network.

翻译：主流加密货币网络依赖于随机连接选择规则来建立其点对点网络中的连接。通常，这些选择具有良好的性质，特别是对于开放的无许可网络而言。然而，随机连接选择并未考虑到某些参与者可能会优化其连接对象，以便更快地获知网络中传播的信息。本文探讨了此类贪婪策略的动态特性。我们研究了一个模型，其中节点选择对等节点以最小化其到网络中指定子集的平均距离，并考虑了节点选择过程、度数约束以及指定子集大小等若干因素的影响。后者在区块链网络背景下尤为有趣，因为通常只有一部分节点是内容的传播源。我们首先分析了该博弈的理想化版本，其中每个节点完全了解当前网络，并旨在选择最佳的 $d$ 个连接，证明了在各种模型假设下均衡的存在性。由于现实中的节点仅基于其邻居行为拥有局部知识，我们还研究了一种轮次运行的贪婪协议，每个节点用一条新的随机边替换其表现最差的边。我们精确刻画了依此连接规则演化的网络的稳定性性质，并推导了稳定性可能甚至必然出现的条件。我们还利用该连接规则进行了大量模拟，考察了网络的演化过程以及不同网络参数对网络稳定性的影响。我们的发现总体上表明，由贪婪连接选择产生的唯一稳定网络具有低直径，并导致网络中节点性能的差异。