Blockchain Mining Games (1607.02420v1)

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.

• The paper’s main contribution is modeling Bitcoin mining as a stochastic game, identifying Nash equilibrium thresholds in both immediate-release and strategic-release settings.
• It demonstrates that miners with over approximately 36.1% or 30.8% computational power can deviate from the standard protocol to achieve higher rewards.
• The rigorous analysis informs potential protocol redesigns to mitigate vulnerabilities and improve the robustness of decentralized ledger technologies.

Strategic Implications of Blockchain Mining Games

The paper "Blockchain Mining Games" authored by Kiayias et al. explores the strategic interactions engaged by miners within the Bitcoin protocol, specifically focusing on mining activities. This work focuses on the modeling of such strategic considerations as stochastic gaming interactions, an approach that sheds light on the incentives and actions of miners in a decentralized context.

Bitcoin, the most notable decentralized digital currency to date, operates based on a blockchain protocol—an innovation intended to maintain an immutable and peer-to-peer verified ledger of transactions. Understanding the game-theoretic principles that mediate miner behavior is crucial not only for assessing the robustness of Bitcoin but also for elucidating the broader decentralized ledger technologies (DLTs).

Problem Formulation and Game Variants

Miners in the Bitcoin protocol collectively develop a tree of blocks. They are remunerated after successfully adding a new node (block) which is ultimately adopted within the network. Given the possibility of concealing newly mined nodes, miners engage in what is effectively a game with incomplete information, where strategic behavior deviates from simple block releases.

The paper investigates two simplified variants of this mining game: the immediate-release game and the strategic-release game. In the immediate-release model, any newly mined block is released instantaneously; miners select which block to mine but without strategic withholding of mining results. Contrastingly, the strategic-release game allows miners to mine from any announced block but introduces complexity through the choice of withholding newly mined blocks.

Main Contributions and Analytical Outcomes

The authors provide a comprehensive analysis within these two frameworks, illustrating scenarios where miners’ strategic decisions lead away from the behavior intended by the Bitcoin protocol designer.

1. Immediate-Release Game: Here, the authors determine thresholds for miner computational power under which the suggested "Frontier" strategy—following the longest chain—is a Nash equilibrium. The threshold for a Nash equilibrium being maintained is calculated to lie within the range $0.361 \leq p \leq 0.455$. This finding implies that if any miner's relative computational power exceeds 36.1%, other Nash equilibria arise due to potential strategic deviations that can lead to better individual outcomes.
2. Strategic-Release Game: This variant presents more intricate dynamics. The paper provides rigorous bounds, indicating that a threshold computational power of approximately 30.8% suffices for the honest strategy to hold as a Nash equilibrium. Above this computational threshold, miners can engage in profitable block withholding or strategic block release decisions.

The exhaustive mathematical derivations supporting these findings contribute significantly to both theoretical understanding and practical implications regarding strategic mining behavior. The results indicate that block withholding strategies become advantageous for miners wielding substantial computational resources, which deviates from behavior presumed in the Bitcoin design, thereby introducing a vector for potential protocol vulnerabilities.

Implications and Future Perspectives

Practically, understanding the exact scenarios under which miners deviate from expected behaviors in Bitcoin mining provides insight into the possible redesign and enforcement of incentivization schemes to ensure protocol robustness. From a theoretical standpoint, these insights extend well into more general blockchain and distributed network designs where game-theoretic paradigms dictate system behavior.

Future research can extrapolate these rewarding game-theoretic hypotheses to consider more complex models such as those incorporating network latency, further decentralization parameters, and emergent consensus algorithms. Furthermore, these models could offer a template to investigate evolving DLTs beyond Bitcoin, particularly with emerging challenges in scalability and decentralization.

In summary, this paper provides critical groundwork for understanding the strategic landscape miners operate within, revealing potential systemic weaknesses while also guiding future protocol modifications to mitigate adversarial strategies inherent to blockchain systems.