One of the most important features of blockchain protocols is decentralization, as their main contribution is that they formulate a distributed ledger that will be maintained and extended without the need of a trusted party. Bitcoin has been criticized for its tendency to centralization, as very few pools control the majority of the hashing power. Pass et al. proposed FruitChain [PODC 17] and claimed that this blockchain protocol mitigates the formation of pools by reducing the variance of the rewards in the same way as mining pools, but in a fully decentralized fashion. Many follow up papers consider that the problem of centralization in Proof-of-Work (PoW) blockchain systems can be solved via lower rewards' variance, and that in FruitChain the formation of pools is unnecessary. Contrary to the common perception, in this work, we prove that lower variance of the rewards does not eliminate the tendency of the PoW blockchain protocols to centralization; miners have also other incentives to create large pools, and specifically to share the cost of creating the instance they need to solve the PoW puzzle. We abstract the procedures of FruitChain as oracles and assign to each of them a cost. Then, we provide a formal definition of a pool in a blockchain system, and by utilizing the notion of equilibrium with virtual payoffs (EVP) [AFT 21], we prove that there is a completely centralized EVP, where all the parties form a single pool controlled by one party called the pool leader. The pool leader is responsible for creating the instance used for the PoW procedure. To the best of our knowledge, this is the first work that examines the construction of mining pools in the FruitChain system.

翻译：区块链协议最重要的特征之一是去中心化，其主要贡献在于构建了一个无需可信第三方即可维护和扩展的分布式账本。比特币因其中心化倾向而受到批评，因为极少数矿池控制了绝大部分算力。Pass等人提出了水果链（FruitChain）[PODC 17]，并声称该区块链协议通过像矿池一样降低奖励方差，但以完全去中心化的方式，缓解了矿池的形成。许多后续论文认为，工作量证明（PoW）区块链系统中的中心化问题可以通过降低奖励方差来解决，并且在水果链中矿池的形成是不必要的。与普遍认知相反，本文证明降低奖励方差并不能消除PoW区块链协议的中心化倾向；矿工还有其他动机创建大型矿池，特别是分担创建解决PoW难题所需实例的成本。我们将水果链的流程抽象为预言机，并为每个流程分配成本。然后，我们给出区块链系统中矿池的形式化定义，并利用虚拟收益均衡（EVP）概念[AFT 21]，证明存在一个完全中心化的EVP，其中所有参与方形成一个由称为矿池领导者的单一参与方控制的矿池。矿池领导者负责创建用于PoW流程的实例。据我们所知，这是首次研究水果链系统中矿池构建的工作。