The Miner's Dilemma (1411.7099v2)

Abstract: An open distributed system can be secured by requiring participants to present proof of work and rewarding them for participation. The Bitcoin digital currency introduced this mechanism, which is adopted by almost all contemporary digital currencies and related services. A natural process leads participants of such systems to form pools, where members aggregate their power and share the rewards. Experience with Bitcoin shows that the largest pools are often open, allowing anyone to join. It has long been known that a member can sabotage an open pool by seemingly joining it but never sharing its proofs of work. The pool shares its revenue with the attacker, and so each of its participants earns less. We define and analyze a game where pools use some of their participants to infiltrate other pools and perform such an attack. With any number of pools, no-pool-attacks is not a Nash equilibrium. With two pools, or any number of identical pools, there exists an equilibrium that constitutes a tragedy of the commons where the pools attack one another and all earn less than they would have if none had attacked. For two pools, the decision whether or not to attack is the miner's dilemma, an instance of the iterative prisoner's dilemma. The game is played daily by the active Bitcoin pools, which apparently choose not to attack. If this balance breaks, the revenue of open pools might diminish, making them unattractive to participants.

• The paper introduces a game-theoretic model showing that non-attack strategies fail to achieve equilibrium when pools can benefit from block withholding.
• The analysis reveals that two mining pools engage in dynamics akin to the iterative prisoner’s dilemma, where attacking becomes a dominant strategy despite mutual losses.
• The study finds that in scenarios with multiple pools, a symmetric Nash equilibrium emerges with all pools attacking, leading to diminished revenue density and decentralization challenges.

An Analytical Exploration of Strategic Dynamics in Bitcoin Mining Pools

Ittay Eyal's paper, "The Miner's Dilemma," offers an intricate examination of strategic interactions, particularly focusing on the phenomenon of block withholding among Bitcoin mining pools. This exploration contributes to a deeper understanding of economic behaviors in distributed systems secured by proof-of-work mechanics, such as Bitcoin and other digital currencies.

Summary and Findings

Eyal defines a block withholding attack whereby mining pools sabotage one another by infiltrating opponents and withholding blocks, thereby redistributing rewards and influencing revenue outcomes. Through a rigorous analytical framework, Eyal constructs a game-theoretic model where pools actively decide whether to launch block withholding attacks against other pools.

The paper establishes several critical insights:

1. Non-Equilibrium of No-Attack: Attacks never bring about a Nash equilibrium where non-attack strategies can be persistent if not universally upheld, indicating that at least one pool will find a unilateral incentive to engage in attacks if undisturbed by others.
2. Two-Pool Dynamics and Miner’s Dilemma: When just two pools are considered, an equilibrium resembling the iterative prisoner's dilemma arises. Both pools may prefer no attacks for optimal long-term revenues; yet, the dominant strategy in each iterative round is to attack, showing the depiction of a tragedy of the commons scenario where rational strategies can lead to mutual detriment.
3. Multiple Pools Equilibrium: With several pools of identical sizes, a symmetric Nash equilibrium emerges where all pools attack each other, confirming that the revenue density is less than unity, pointing to diminished returns for all involved.
4. Implications for System Structure: These findings imply that persistent block withholding might promote the emergence of small, closed mining pools by deteriorating revenue prospects in larger, open pools, indirectly driving distribution of mining power that aligns better with the inherent decentralization goals of blockchain technologies.

Implications and Future Directions

The noted potential for widespread adoption of block withholding as pools grapple with strategic decisions highlights broader implications for digital currency economics. Despite implicit cooperation among pools, any deviation by a pool instigating block withholding for short-term gains might trigger a cycle of mutual attacks, diminishing resources for all over time. Eyal's observations are crucial for understanding not just how mining operations might evolve in practice but also for designing more robust systems that maintain equitable distribution of resources and stability.

Additionally, the introduction of deeply-rooted game-theoretic constructs like the prisoner's dilemma juxtaposes well with distributed computing environments, offering a practical cross-discipline analysis that could inspire future research. The strategic landscape could shift if modifications to the protocol are developed to mitigate against block withholding or if alternative economic incentives are structured to dissuade such behaviors conclusively.

Overall, Eyal’s work provides a comprehensive look into the intra-network competitive behaviors of mining pools in Bitcoin, informing both theoretical models and practical solutions within the cryptoeconomic paradigm. Implementing policies or technological changes to maintain cooperation will require continued vigilance and adaptive strategies as these mechanisms naturally evolve. This paper may serve as both a caution and a guidepost for those developing decentralizing tools and markets in blockchain-based systems.