Blockchain Mining Games

Abstract

We study the strategic considerations of miners participating in the bitcoin's protocol. We formulate and study the stochastic game that underlies these strategic considerations. The miners collectively build a tree of blocks, and they are paid when they create a node (mine a block) which will end up in the path of the tree that is adopted by all. Since the miners can hide newly mined nodes, they play a game with incomplete information. Here we consider two simplified forms of this game in which the miners have complete information. In the simplest game the miners release every mined block immediately, but are strategic on which blocks to mine. In the second more complicated game, when a block is mined it is announced immediately, but it may not be released so that other miners cannot continue mining from it. A miner not only decides which blocks to mine, but also when to release blocks to other miners. In both games, we show that when the computational power of each miner is relatively small, their best response matches the expected behavior of the bitcoin designer. However, when the computational power of a miner is large, he deviates from the expected behavior, and other Nash equilibria arise.

Oceanic Games: Centralization Risks and Incentives in Blockchain Mining

“…An integral assumption in the security philosophy of permissionless blockchains is that the network of mining nodes remains "sufficiently" decentralized and distributed. In the extreme case, sufficiently means that no single entity holds 50% or more of the resources but in practice much more fragmentation may be desired to safeguard the safety properties of the underlying protocol [11,22,3].…”

“…Due to continuity properties, there is no difference between using the q = 50% quota or symbolically, the q = 51% quota, as is common in the related literature[28,11,22].…”

An Axiomatic Approach to Block Rewards

“…(5) A deterministic implementation of the proportional rule-with the block reward split fractionally between miners-satisfies all of the desired properties even with risk-averse miners (Corollary 4). The deterministic implementation in (5) can be viewed as a simulation of the functionality of a mining pool inside the blockchain protocol itself, analogous to the "Revelation Principle" from mechanism design theory. 2…”

“…Flaws in the incentives of a blockchain protocol can manifest themselves at multiple timescales. For longest-chain proof-of-work blockchains like Bitcoin, the most well-studied incentive-based attacks, such as selfish mining [4,10,5] and transaction sniping [3], concern miners reasoning strategically over multiple block creation epochs. For example, in selfish mining, a miner relinquishes revenue in the short term to achieve greater revenue (in expectation) in the long run via a type of forking attack.…”

The Framework of Consensus Equilibria for Mining-Pool Games and Related Stability of Gap Games Behaviors in Blockchain Ecosystems

“…We note that mining pool games were extensively studied by Bonneau et al [12], Eyal [26], Eyal and Sirer [27], Kroll et al [40](see also Carlsten et al. [15], Kiayias et al [39], Sapirstein et al [57] and references wherein), smart contracts were discussed by Cong and He [18], and finally move toward blockchain-based accounting and assurance given by Dai and Vasarhelyi [20] and many others. But one critical issue still remaining is: "if it is possible to have a general consensus to lead the Mining-Pool Game stable (see the meaning in details below) in supporting the Blockchain ecosystem running?…”