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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
92 lines
2.7 KiB
TeX
92 lines
2.7 KiB
TeX
\section{Simulation Results}
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\label{sec:simulation}
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\subsection{Setup}
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We simulate 500 epochs with 5,000 potential validators, total stake 300M LUX, and 50 appchains growing to 200.
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\begin{table}[H]
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\centering
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\caption{Simulation parameters.}
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\label{tab:simparams}
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\begin{tabular}{lrl}
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\toprule
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\textbf{Parameter} & \textbf{Value} & \textbf{Description} \\
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\midrule
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Potential validators & 5,000 & Maximum validator count \\
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Total stake & 300M LUX & 60\% of supply staked \\
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$s^{\min}_{\text{val}}$ & 2,000 LUX & Min self-stake \\
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$\omega$ & 15 & Delegation multiplier \\
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$c^{\min}$, $c^{\max}$ & 5\%, 25\% & Commission bounds \\
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Hardware cost range & 0.5--5.0 LUX/epoch & Varies by capacity \\
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Opportunity cost $r_{\text{opp}}$ & 5\% annual & Alternative yield \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Validator Count Convergence}
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The number of active validators converges to approximately 2,800 within 50 epochs, determined by the free-entry equilibrium condition.
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\subsection{Commission Rate Distribution}
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\begin{table}[H]
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\centering
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\caption{Commission rate distribution at epoch 500.}
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\label{tab:commission_dist}
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\begin{tabular}{lrr}
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\toprule
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\textbf{Commission Range} & \textbf{Validators (\%)} & \textbf{Stake Share (\%)} \\
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\midrule
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5.0\%--7.5\% & 62 & 71 \\
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7.5\%--10.0\% & 21 & 18 \\
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10.0\%--15.0\% & 12 & 8 \\
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15.0\%--25.0\% & 5 & 3 \\
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\bottomrule
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\end{tabular}
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\end{table}
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As predicted by Theorem~\ref{thm:commission}, most validators converge toward $c^{\min}$, with higher commissions sustained only by validators with superior uptime or exclusive appchain access.
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\subsection{Decentralization Metrics}
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\begin{table}[H]
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\centering
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\caption{Decentralization metrics over simulation epochs.}
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\label{tab:decentralization}
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\begin{tabular}{lrrrr}
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\toprule
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\textbf{Metric} & \textbf{Epoch 1} & \textbf{Epoch 50} & \textbf{Epoch 200} & \textbf{Epoch 500} \\
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\midrule
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Active validators & 500 & 2,800 & 2,750 & 2,700 \\
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Nakamoto coefficient & 5 & 22 & 25 & 28 \\
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Gini coefficient & 0.82 & 0.55 & 0.52 & 0.50 \\
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Top-10 stake share & 45\% & 12\% & 10\% & 9\% \\
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\bottomrule
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\end{tabular}
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\end{table}
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The Nakamoto coefficient exceeds the target of 20 by epoch 50 and continues improving. The Gini coefficient falls well below the 0.60 threshold.
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\subsection{Slashing Impact Analysis}
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We simulate random equivocation events (1\% of validators per 100 epochs):
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\begin{table}[H]
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\centering
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\caption{Slashing statistics over 500 epochs.}
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\label{tab:slashing_stats}
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\begin{tabular}{lr}
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\toprule
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\textbf{Metric} & \textbf{Value} \\
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\midrule
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Total slashing events & 127 \\
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Total LUX slashed & 2,340,000 \\
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Average penalty per event & 18,425 LUX \\
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Validators permanently jailed & 3 \\
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Delegator losses (avg per event) & 0.02\% of delegation \\
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\bottomrule
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\end{tabular}
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\end{table}
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