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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.
100 lines
3.7 KiB
TeX
100 lines
3.7 KiB
TeX
\section{Simulation Results}
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\label{sec:simulation}
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\subsection{Simulation Setup}
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We simulate the Lux token economy over 500 epochs (approximately 10 years) under the following assumptions:
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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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$S_0$ & 500M LUX & Genesis supply \\
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$R_0$ & 5M LUX/epoch & Initial reward \\
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$\alpha$ & 0.97 & Reward decay factor \\
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$\sigma^*$ & 0.67 & Target staking ratio \\
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Transaction growth & 15\%/year & Compound growth rate \\
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Initial TPS & 50 & Transactions per second \\
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Avg gas per tx & 50,000 & Gas units \\
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Validators & 1,000 & Initial validator count \\
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Appchains & 10 $\to$ 200 & Growing over simulation \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Supply Trajectory}
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\begin{algorithm}[H]
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\caption{Token Supply Simulation}
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\label{alg:simulation}
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\begin{algorithmic}[1]
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\Require Parameters from Table~\ref{tab:simparams}
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\State $S \gets S_0$; $\sigma \gets 0.40$; $\text{BaseFee} \gets 25 \text{ gwei}$
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\For{$t = 0$ to $T$}
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\State $R_t \gets R_0 \cdot \alpha^t \cdot f(\sigma)$
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\State $\text{TPS}_t \gets 50 \cdot 1.15^{t/52}$
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\State $G_t \gets \text{TPS}_t \cdot 50000 \cdot 12$ \Comment{Gas per block (12s blocks)}
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\State Update $\text{BaseFee}$ via Equation~\eqref{eq:basefee}
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\State $\phi_t \gets \phi_{\min} + (\phi_{\max} - \phi_{\min}) \cdot \min(1, G_t / G_{\text{cap}})$
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\State $B_t \gets \phi_t \cdot \text{BaseFee} \cdot G_t \cdot N_b$
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\State $V_t \gets$ scheduled vesting
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\State $S \gets S + R_t + V_t - B_t$
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\State Update $\sigma$ based on yield vs opportunity cost
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\EndFor
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\end{algorithmic}
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\end{algorithm}
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The simulation reveals three distinct phases:
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\begin{enumerate}
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\item \textbf{Inflationary phase} (epochs 0--80): Vesting releases and rewards exceed burns. Peak supply reaches approximately 680M LUX.
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\item \textbf{Equilibrium phase} (epochs 80--200): Burns catch up to emissions as transaction volume grows. Supply oscillates around 620M LUX.
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\item \textbf{Deflationary phase} (epochs 200+): Burns consistently exceed rewards as the exponential decay of $R_t$ continues while transaction volume grows. Supply decreases toward the long-run target.
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\end{enumerate}
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\subsection{Staking Yield Analysis}
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\begin{table}[H]
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\centering
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\caption{Projected annualized staking yields by epoch range.}
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\label{tab:yields}
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\begin{tabular}{lrrr}
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\toprule
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\textbf{Epoch Range} & \textbf{Staking Ratio} & \textbf{Gross Yield} & \textbf{Net Yield (post-inflation)} \\
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\midrule
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0--50 & 0.45 $\to$ 0.60 & 12.5\% & 8.2\% \\
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50--100 & 0.60 $\to$ 0.67 & 8.3\% & 5.1\% \\
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100--200 & 0.67 & 5.8\% & 4.9\% \\
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200--500 & 0.67 & 3.2\% & 4.1\% \\
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\bottomrule
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\end{tabular}
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\end{table}
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Notably, the net yield in the deflationary phase (epochs 200+) exceeds the gross yield because deflation increases the purchasing power of staked tokens. This creates a positive feedback loop that sustains validator participation even as nominal rewards decline.
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\subsection{Sensitivity Analysis}
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We analyze sensitivity to transaction volume growth rate $g$:
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\begin{table}[H]
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\centering
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\caption{Supply at epoch 500 under varying transaction growth rates.}
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\label{tab:sensitivity}
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\begin{tabular}{rrrr}
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\toprule
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\textbf{Growth Rate $g$} & \textbf{Supply at $t=500$} & \textbf{Net Emission} & \textbf{Phase at $t=500$} \\
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\midrule
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5\% & 640M & $+0.3\%$ & Mild inflation \\
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10\% & 580M & $-0.8\%$ & Mild deflation \\
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15\% (base) & 510M & $-1.5\%$ & Deflation \\
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20\% & 430M & $-2.2\%$ & Strong deflation \\
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\bottomrule
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\end{tabular}
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\end{table}
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The model is robust: even under pessimistic growth (5\%), supply remains bounded. Under realistic growth (10--15\%), the network achieves sustainable deflation.
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