论文标题
达到平衡和区块链合并策略的可溶性：一种拓扑方法
Toward Equilibria and Solvability of Blockchain Pooling Strategies: A Topological Approach
论文作者
论文摘要
在2015年，Eyal提出了第一个用于分析区块链平衡的游戏理论模型：当将区块链池抽象为非合作游戏时，两个池可以以封闭形式的配方达到NASH平衡；此外，只要池的矿工数量相等，任意数量的池仍然表现出平衡。然而，是否存在三个或多个不同大小的池的平衡仍然是一个开放的问题。为此，本文研究了任意池的区块链中的平衡。首先，我们表明，可以使用拓扑方法来构建$ q $相同的池之间的平衡，从而通过游戏理论构建了Eyal通过游戏理论所证明的结果。其次，如果池的大小不同，我们表明（i）如果区块链的池表现出两种不同的尺寸，则可以达到平衡，并且（ii）如果区块链具有至少三个不同的池尺寸，则不存在平衡。
In 2015, Eyal proposed the first game-theoretical model for analyzing the equilibrium of blockchain pooling: when the blockchain pools are abstracted as a non-cooperative game, two pools can reach a Nash equilibrium with a closed-form formula; Moreover, an arbitrary number of pools still exhibit an equilibrium as long as the pools have an equal number of miners. Nevertheless, whether an equilibrium exists for three or more pools of distinct sizes remains an open problem. To this end, this paper studies the equilibrium in a blockchain of arbitrary pools. First, we show that the equilibrium among $q$ identical pools, coinciding the result demonstrated by Eyal through game theory, can be constructed using a topological approach. Second, if the pools are of different size, we show that (i) if the blockchain's pools exhibit two distinct sizes, an equilibrium can be reached, and (ii) if the blockchain has at least three distinct pool sizes, there does not exist an equilibrium.
