Selfish mining: majority is not enough (Eyal and Sirer 2014)

Bitcoin was thought incentive-compatible: a miner earns its share of blocks by publishing them. Eyal and Sirer showed a pool can earn more by keeping blocks secret and releasing them only to overtake or tie the honest chain, wasting honest work. Above a threshold hashrate, between 0 and 1/3 depending on how ties break, selfish mining pays.

What to look for

The simulated state machine matches the closed-form revenue. With gamma = 0 (ties go to honest blocks) the threshold is 1/3; when the pool wins every tie, any pool profits.

The history behind this experiment: Breakthroughs in Consensus.

Revenue against hashrate

import matplotlib.pyplot as plt
import numpy as np

import blockchainkit as bk

alphas = np.linspace(0.02, 0.48, 24)
fig, ax = plt.subplots(figsize=(7, 4.5))
ax.plot(alphas, alphas, "--", color="black", label="honest mining: revenue = alpha")
for gamma, color in ((0.0, "#2563eb"), (0.5, "#16a34a"), (1.0, "#ea580c")):
    exact = [bk.consensus.selfish_mining_revenue(a, gamma) for a in alphas]
    ax.plot(alphas, exact, color=color, label=f"selfish, gamma = {gamma}")
    sims = [
        bk.consensus.simulate_selfish_mining(a, gamma, blocks=40_000, seed=7).revenue
        for a in alphas[::4]
    ]
    ax.plot(alphas[::4], sims, "o", color=color)
    threshold = bk.consensus.selfish_mining_threshold(gamma)
    ax.axvline(threshold, color=color, linestyle=":", alpha=0.7)
ax.set(
    xlabel="pool hashrate alpha",
    ylabel="pool share of blocks",
    title="Selfish mining pays above (1 - gamma)/(3 - 2 gamma)",
)
ax.legend(fontsize=8)
fig.tight_layout()

result = bk.consensus.simulate_selfish_mining(0.4, 0.0, blocks=200_000, seed=1)
assert result.revenue > 0.4
print(f"a 40% pool gets {result.revenue:.1%} of the blocks")

a 40% pool gets 48.0% of the blocks

Exercise

Selfish mining lowers the total rate of blocks on the main chain. Explain why difficulty retargeting (the next experiment) turns that into profit for the pool in absolute terms, not just as a share.