\section{Asset markets and credit}
\label{sec:markets}

Model C replaces the Walrasian auctioneer of Models A and B with explicit trading, balance sheets, collateralised
credit and defaults. It is where the ``agentic'' part of the title is taken literally: AI agents place orders, borrow
within principal-approved limits and rebalance, and the outcome is a \emph{temporary trading equilibrium} per period
rather than a rational-expectations equilibrium. We never call these outcomes general equilibria; feasibility and
market clearing are verified by assertion, and the Bayesian mean-variance agent is the control against which every
LLM result is read.

\subsection{Assets, balance sheets and the bank}

There are $N$ investors, one bank, one market and a regulator (who sets the margin $m$ and the bank capital ratio
$k_B$). A risky security in fixed supply $S$ pays a dividend
$d_t=\bar d+\rho_d(d_{t-1}-\bar d)+\sigma_du_t$; a safe deposit/loan at rate $r_f$ is intermediated by the bank.
Investor $n$'s balance sheet is deposits $c_n$ plus holdings $p_th_n$ against a loan $b_n$; equity is
$E_n=c_n+p_th_n-b_n$. The bank holds loans and reserves against deposits, an exchange account $F$ (fees) and its equity
$E_B$. Three identities are asserted after every operation: $\sum_nh_n+h_{MM}=S$ (no asset creation; the market
maker's inventory is part of $S$), $\sum_nc_n+F+E_B=\sum_nb_n+\text{reserves}$ (the bank's balance sheet), and
reserves change only through injections (dividends paid by the issuer, interest on reserves). Fees are transfers to the
exchange account; dividends and interest are the only outside flows.

\paragraph{Credit, margin, default and loss allocation.} Loans are collateralised: $b_n\le(1-m)p_th_n$, and the
bank lends only while $E_B\ge k_B(\text{loans}+\text{reserves})$. At the start of each period positions are marked to
market: an investor in breach sells $x=(b_n-(1-m)p_th_n)/(mp_t)$ units to the other investors at a price depressed by
$\lambda_{liq}x/S$ (forced sale), repays, and defaults if a residual loan remains with no cash or negative equity; the
residual is written off against $E_B$. If $E_B<0$ depositors are bailed in pro rata. Every one of these steps has a
payer and a payee (Appendix~\ref{app:replication} lists the tests).

\paragraph{Liquidity provision.} A market maker posts a ladder of limit orders on both sides of its reference price
(depth $\bar h$ shares per level, tick $\varsigma$, $K$ levels), skewed by its inventory and withdrawn on a side when
its inventory limit is reached. Depth is therefore finite and \emph{state-dependent}: a wave of correlated orders
exhausts the ladder, which is the microstructure counterpart of $\lambda_r$ in Proposition~\ref{prop:collateral}.

\subsection{Information and agents}

Each investor receives a forecast of the next dividend innovation, private ($\theta+e_n$) or from model $m$
($\theta+\eta_m$), exactly as in Section~\ref{sec:information}; $D$ and $M$ are treatment variables. Policies map a
structured observation (price, dividend, rate, own expected dividend, own balance sheet, margin capacity, last five
prices) into a proposed action $\{$side, quantity, order type, limit price, borrowing$\}$. Four policy families are
used: (i) the Bayesian mean-variance control, with desired holdings
$h^*=\big(\E[d']+\bar p-(1+r_f)p\big)/(\gamma_a\sigma^2)$ and a limit price part-way toward its valuation;
(ii) rule-based momentum and noise traders; (iii) a deterministic \emph{surrogate} that exposes the LLM interface but
implements rule (i)---it isolates interface effects from language-model behaviour; (iv) live LLM agents
(Section~\ref{sec:llm_design}). Whatever the policy, the proposed action is clipped by deterministic code: borrowing to
the margin and bank-capital capacity, purchases to cash, sales to holdings. LLM output is never accounting truth.

\subsection{Three market designs}

The same orders are cleared under three designs, in separate experiments. The \emph{Walrasian call} finds the price
that minimises absolute excess demand over the submitted limits and rations the long side pro rata; the
\emph{continuous double auction} is a price--time-priority limit order book in which orders arrive in a seeded random
sequence and marketable orders execute at resting prices; \emph{bilateral bargaining} matches buyers and sellers at
random for a few rounds and trades at the Nash-bargaining price when limits cross. We report the execution price,
not an equilibrium price, and we do not conflate the finite price impact of the ladder with price-taking.

\subsection{Timing and metrics}

Within a period: dividend realised and paid; interest accrued; mark-to-market (forced sales, defaults, bail-in);
signals; actions and clipping; trading; settlement. No agent observes anything dated $t+1$ except its own signal about
$t+1$. The pre-registered metrics are return volatility; the average pairwise correlation of order flow across agents
\emph{after residualising each agent's flow on public information} (dividend and price), overall and within the
delegator and human groups; the price-pressure coefficient (returns regressed on the delegators' average model error)
and its $R^2$; Kyle's $\lambda$ (returns on net order flow); spread and depth (order book); price dispersion
(bilateral); defaults, forced sales, loan losses and leverage; and, in stress runs, the return over the two periods
following a common forecast shock.