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Hashpower allocation in Pay-per-Share blockchain mining pools

Pierre-Olivier Goffard, Hansjoerg Albrecher, Jean-Pierre Fouque

TL;DR

The paper addresses how miners should allocate hashpower across Pay-per-Share pools under risk and fee constraints, modeling wealth with $X_t$ for solo and $X_t^{PPS}$ for PPS. It derives a simple horizon-independent rule $k^* = argmax_k lambda_k (b_k - gamma b_k^2)$ in a mean-variance setting and develops a dividend-maximization framework using barrier strategies and scale functions $W^{(q)}$ and $Z^{(q)}$ to compute the value $V(x;a^*_w)$ for a given hashpower distribution. The analysis employs a bottom-up numerical approach to identify the optimal hashpower allocation across multiple PPS pools and demonstrates implications for network decentralization. The results provide actionable guidance for miners and pool operators on balancing profitability and risk, and highlight how PPS parameters influence the concentration of mining power across the network.

Abstract

Mining blocks in a blockchain using the \textit{Proof-of-Work} consensus protocol involves significant risk, as network participants face continuous operational costs while earning infrequent capital gains upon successfully mining a block. A common risk mitigation strategy is to join a mining pool, which combines the computing resources of multiple miners to provide a more stable income. This article examines a Pay-per-Share (PPS) reward system, where the pool manager can adjust both the share difficulty and the management fee. Using a simplified wealth model for miners, we explore how miners should allocate their computing resources among different mining pools, considering the trade-off between risk transfer to the manager and management fees.

Hashpower allocation in Pay-per-Share blockchain mining pools

TL;DR

The paper addresses how miners should allocate hashpower across Pay-per-Share pools under risk and fee constraints, modeling wealth with for solo and for PPS. It derives a simple horizon-independent rule in a mean-variance setting and develops a dividend-maximization framework using barrier strategies and scale functions and to compute the value for a given hashpower distribution. The analysis employs a bottom-up numerical approach to identify the optimal hashpower allocation across multiple PPS pools and demonstrates implications for network decentralization. The results provide actionable guidance for miners and pool operators on balancing profitability and risk, and highlight how PPS parameters influence the concentration of mining power across the network.

Abstract

Mining blocks in a blockchain using the \textit{Proof-of-Work} consensus protocol involves significant risk, as network participants face continuous operational costs while earning infrequent capital gains upon successfully mining a block. A common risk mitigation strategy is to join a mining pool, which combines the computing resources of multiple miners to provide a more stable income. This article examines a Pay-per-Share (PPS) reward system, where the pool manager can adjust both the share difficulty and the management fee. Using a simplified wealth model for miners, we explore how miners should allocate their computing resources among different mining pools, considering the trade-off between risk transfer to the manager and management fees.

Paper Structure

This paper contains 11 sections, 1 theorem, 68 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Blockchain and mining pool
  3. Blockchain mining process
  4. Mining pools
  5. Miner's wealth process
  6. Mean-variance trade-offs
  7. Mean-variance optimization accounting for risk aversion
  8. Mean-Variance efficient frontier approach
  9. Expected discounted dividend maximization
  10. Numerical illustrations and decentralization of mining network
  11. Conclusion

Key Result

Proposition 1

Denote by $b^\ast = \underset{k = 0,\ldots, n}{\min} b_k.$ We have and where the functions $g, G$ and $\bar{G}$ are given by with $H(\cdot)$ the Heaviside step function.

Figures (5)

  • Figure 1: A block that has not been mined yet.
  • Figure 2: A mined block with a hash value having one leading zero.
  • Figure 3: Mean-variance tradeoff depending on the risk aversion parameter in the presence of $n = 3$ pools.
  • Figure 4: Efficient frontier for $n = 4$ pools.
  • Figure 5: Hashpower distribution among mining pools depending on the selected criterion.

Theorems & Definitions (13)

  • Remark 1
  • Example 1
  • Remark 2
  • Remark 3
  • Example 2
  • Remark 4
  • Example 3
  • Example 4
  • Remark 5
  • Proposition 1
  • ...and 3 more