\section{Numerical algorithms}
\label{app:algorithms}

\paragraph{A.1 Steady state of Model A.} Given $(K_Q,D)$: $L=1-\tau_sD$, $Q^P=\max(K_Q-\bar qD,0)$,
$\iota=\iota^*(Q^P/L)$ from (\ref{eq:threshold}) by Brent's method on $(0,1)$, $T$ from (\ref{eq:bundle}),
$R^K=1/\beta-1+\delta$, $K=T(\alpha_K/R^K)^{1/(1-\alpha_K)}$, prices from the marginal products, $C$ from the goods
identity. Implemented in \texttt{age.equilibrium.lq\_map.steady\_state}.

\paragraph{A.2 Linearised household in sequence space (savings mapping).} Unknowns $\hat c_{0..T}$ and
$\hat a_{1..T+1}$; equations: budget $\bar c\hat c_t+\bar a\hat a_{t+1}=\bar wL\hat w_t+\bar R\bar a(\hat R_t+\hat a_t)$
for $t=0..T$, Euler $\hat c_t=\hat c_{t+1}-\gamma^{-1}\hat R_{t+1}$ for $t=0..T-1$, and terminal
$\hat a_{T+1}=\hat a_T$. Partial equilibrium: price paths from $z_s=\rho_z^{s-1}\theta$ with the aggregate capital
path fixed. General equilibrium: $\hat Y_t=z_t+\alpha_K\hat a_t$, $\hat w_t=\hat Y_t$,
$\hat R_t=(\bar R^K/\bar R)(z_t-(1-\alpha_K)\hat a_t)$ substituted into the same linear system. Then
$\kappa_0=\hat a_1^{PE}/\theta$, $\kappa_{full}=\hat a_1^{GE}/\theta$, $\alpha=1-\kappa_0/\kappa_{full}$, and
$|U_{xx}|=\bar a^2[-u''(\bar c)-\beta u''(\bar c)\bar R\,\mathrm{MPC}]$ with the MPC from a windfall solve.

\paragraph{A.3 Delegation share and compute market.} $D=F_\kappa(\PV_{goods}(D)-\phi-\tau_s\bar w)$ by Brent's method;
short-run compute market by Brent's method on the monotone excess demand in $Q^P$ (Proposition~\ref{prop:compute}).

\paragraph{A.4 Model B.} Cash-on-hand grid of 160 points (cubic spacing) on $[\underline a,1.2\,a_{max}]$, earnings on
7 Rouwenhorst states normalised to unit mean efficiency, return term on 5 Gauss--Hermite nodes. Value-function
iteration: for each $(x,\epsilon)$ and each $d$, grid search over $a'$ on the asset grid with linear interpolation of
$\E V$; Howard improvement with 20 policy steps; tolerance $10^{-6}$. Invariant distribution by non-stochastic
simulation (lotteries) to tolerance $10^{-11}$. General equilibrium: coarse scan of excess assets over 8 values of
$r$ on $[-0.02,1/\beta-1)$, Brent's method on the bracketing interval (tolerance $2\times10^{-4}$), inner fixed point on
$D$ (5 iterations). Concentrated ownership: the owner class is appended to the wealth distribution as a point mass
of size $n_K$ holding the capitalised rents.

\paragraph{A.5 Model C.} Common random numbers: $u_{0..T}$, $e_{0..T,n}$, $\eta_{0..T,m}$ drawn from the seed before
the loop. Walrasian call: price among submitted limits minimising $|$demand $-$ supply$|$, ties toward the previous
price, pro-rata rationing. Continuous double auction: price--time priority book; marketable orders execute at resting
prices; metrics from the book after each arrival. Bilateral: random matching for three rounds, Nash price with equal
weights. Order-flow correlation: residualise each agent's signed quantity on $[1,d_t,p_t]$, average pairwise
correlation. Kyle's $\lambda$: OLS slope of returns on net flow. Price pressure: OLS slope and $R^2$ of returns on the
delegators' average model error.

\paragraph{A.6 Validation of the zero-AI limits.} Model A with $\delta=1,\gamma=1$ reproduces $K=\alpha_K\beta Y$
(Brock--Mirman); Model B with no compute and no return noise reproduces a standard Aiyagari economy
($r=4.0\%$, Gini $0.64$ at $\beta=0.95$, $\sigma_e=0.17$, $\rho_e=0.96$).