\section{Prompts}
\label{app:prompts}

This appendix reproduces verbatim the frozen prompt version \code{v1} of \code{llm/prompting.py}, one rendered example, the JSON schema sent to the providers, and the validation rules of \code{llm/policy.py}. The system prompt is the persona sentence followed by the rules block; the user message is a deterministic rendering of the agent's \code{Observation}. Nothing in either text depends on the latent state.

\lstset{literate={≈}{{$\approx$ }}2}

\subsection*{Personas (\code{ROLE\_PERSONAS})}
The single-prompt design uses \code{generalist} for every LLM slot; the diverse-prompt design assigns the eight personas cyclically in slot order.

\begin{lstlisting}
generalist : You are a professional trader managing your own account in a single-stock electronic market.
value      : You are a value investor: you compare the price to the present value of expected dividends and trade mispricings patiently.
momentum   : You are a momentum trader: you follow recent price trends and cut positions when the trend reverses.
contrarian : You are a contrarian trader: you fade sharp moves that are not justified by dividend news.
liquidity  : You are a liquidity provider: you prefer resting limit orders near the best quotes and keep your inventory small.
risk_averse: You are a risk-averse trader: you keep positions small, avoid market orders and prefer to hold when uncertain.
macro      : You are a news-driven trader: you weigh public announcements and dividend surprises and act when the market has not yet reacted.
quant      : You are a quantitative trader: you reason about expected value per share, spread costs and inventory before each order.
\end{lstlisting}

\subsection*{Rules template (\code{RULES})}
Placeholders in braces are filled from the configuration and the observation (\code{div\_interval}, \code{mu}, \code{r\_pct}, \code{pv\_mean}, \code{rho}, \code{tick}, \code{taker\_bps}, \code{ttl}, \code{max\_qty}, \code{interval}); doubled braces are Python format escapes and render as single braces.

\begin{lstlisting}
Market mechanics (read carefully):
- One risky stock paying a cash dividend every {div_interval} ticks; the long-run mean dividend is {mu:.2f} per share per period and the per-period discount rate is {r_pct:.2f}%, so a share paying the mean dividend forever is worth about {pv_mean:.2f}.
- Dividends deviate persistently from the mean (autocorrelation {rho:.2f} per period). The deviation of the NEXT dividend is not yet announced; public news and, when you have one, your private signal are noisy estimates of it (in cents). The present value of a share rises by about 1/(1+r-rho) ≈ 44 cents per cent of next-dividend deviation.
- Prices are in currency units with a tick of {tick:.2f}. Limit orders rest in the book; market orders execute immediately against the best quotes (taker fee {taker_bps:.1f} bps). Orders may be partially filled. Unfilled limit orders expire after {ttl} ticks.
- You cannot short sell and cannot spend more than your free cash. Maximum order size: {max_qty} shares.
- You decide every {interval} ticks. Between decisions the market keeps trading.

Respond with ONLY a JSON object with exactly these keys:
{{"action": "hold"|"place"|"cancel", "side": "buy"|"sell"|null, "order_type": "limit"|"market"|null, "quantity": integer|null, "limit_price": number|null, "cancel_order_ids": [integers], "confidence": number in [0,1]|null, "rationale": "one sentence, max 200 characters"}}
"place" requires side, order_type and quantity (and limit_price for a limit order). "cancel" requires cancel_order_ids. Anything else is treated as hold.
\end{lstlisting}

\noindent The placeholder \code{interval} is filled with the dividend interval (\code{obs.div\_interval}), not with \code{decision\_interval}; the two coincide (20) in every reported design.

\subsection*{Rendered example}
The following system prompt and user message were produced by running the prompt builder on the observation of an informed LLM slot (agent~9, persona \code{generalist}, tick~110) in a mock run of the baseline configuration with $\varphi=0.25$, seed~1.\footnote{Generated with \code{system\_prompt()} and \code{user\_message()} of \code{llm/prompting.py}; the observation was captured from \code{Simulation.\_observe}. The mid-price history is sub-sampled to every sixth tick of the 61-tick window.}

\begin{lstlisting}
You are a professional trader managing your own account in a single-stock electronic market.

Market mechanics (read carefully):
- One risky stock paying a cash dividend every 20 ticks; the long-run mean dividend is 0.50 per share per period and the per-period discount rate is 0.25%, so a share paying the mean dividend forever is worth about 200.00.
- Dividends deviate persistently from the mean (autocorrelation 0.98 per period). The deviation of the NEXT dividend is not yet announced; public news and, when you have one, your private signal are noisy estimates of it (in cents). The present value of a share rises by about 1/(1+r-rho) ≈ 44 cents per cent of next-dividend deviation.
- Prices are in currency units with a tick of 0.01. Limit orders rest in the book; market orders execute immediately against the best quotes (taker fee 2.0 bps). Orders may be partially filled. Unfilled limit orders expire after 50 ticks.
- You cannot short sell and cannot spend more than your free cash. Maximum order size: 50 shares.
- You decide every 20 ticks. Between decisions the market keeps trading.

Respond with ONLY a JSON object with exactly these keys:
{"action": "hold"|"place"|"cancel", "side": "buy"|"sell"|null, "order_type": "limit"|"market"|null, "quantity": integer|null, "limit_price": number|null, "cancel_order_ids": [integers], "confidence": number in [0,1]|null, "rationale": "one sentence, max 200 characters"}
"place" requires side, order_type and quantity (and limit_price for a limit order). "cancel" requires cancel_order_ids. Anything else is treated as hold.
\end{lstlisting}

\begin{lstlisting}
Time: tick 110. Next dividend in 10 ticks.
Best bid 200.80 / best ask 201.12 / mid 200.96 / last trade 201.12.
Bid depth (price x shares): 200.80x14, 200.70x28, 200.69x13, 200.68x14, 200.65x12. Ask depth: 201.12x14, 201.15x4, 201.19x8, 201.20x14, 201.23x4.
Mid-price history (oldest to newest, 61 ticks sampled): 200.20, 200.29, 200.48, 200.09, 200.54, 200.66, 200.64, 200.64, 200.60, 200.73, 200.96.
Change over the window: +0.38%. Recent volatility (std of tick returns): 0.042%.
Last 30 trades: volume 168 shares, 57% buyer-initiated.
Last dividend paid: 0.55 per share. Public estimate of the next dividend's deviation from its mean: public estimate +5.0 cents. Present value of expected dividends using only public information: 202.23.
Your private signal: next dividend deviation estimated at +3.6 cents (signal precision 2.0; higher is more reliable).
Your account: cash 18634.09 (free 18634.09), holdings 92 shares, equity 37122.41.
You have no open orders.
Decide now. Reply with the JSON object only.
\end{lstlisting}

\noindent\sloppy Optional lines, in the order in which they are inserted when the corresponding treatment is active: \code{TRADING IS HALTED on this stock (orders will be rejected).} after the first line; up to three \code{Public news (tick $t$): \dots} lines after the public-value line; \code{Your open orders: id \dots: buy/sell remaining/qty @ price (age)} (at most six) instead of \code{You have no open orders.}; \code{Feedback: your equity changed by $\pm x$\% since your last decision (cumulative $\pm y$\%).} (adaptive feedback); \code{Your recent decisions and outcomes:} followed by up to five bullet lines (memory); \code{Messages from other traders in your group (unverified opinions):} followed by up to five bullet lines (communication channel).

\subsection*{JSON schema (\code{DECISION\_JSON\_SCHEMA})}
Sent as \code{text.format} (OpenAI, \code{strict: true}) and \code{output\_config.format} (Anthropic). Every key is required; \code{null} is allowed where indicated; no additional properties.

\begin{lstlisting}
{
  "type": "object",
  "properties": {
    "action":           {"type": "string", "enum": ["hold", "place", "cancel"]},
    "side":             {"type": ["string", "null"], "enum": ["buy", "sell", null]},
    "order_type":       {"type": ["string", "null"], "enum": ["limit", "market", null]},
    "quantity":         {"type": ["integer", "null"]},
    "limit_price":      {"type": ["number", "null"]},
    "cancel_order_ids": {"type": "array", "items": {"type": "integer"}},
    "confidence":       {"type": ["number", "null"]},
    "rationale":        {"type": "string"}
  },
  "required": ["action", "side", "order_type", "quantity", "limit_price",
               "cancel_order_ids", "confidence", "rationale"],
  "additionalProperties": false
}
\end{lstlisting}

\subsection*{Parsing and validation rules}
The reply is first parsed, then validated against the pydantic model \code{Decision}, then checked for feasibility by \code{LLMPolicy.to\_action}. Any failure yields a hold action with \code{valid = False} and the reason string below; a provider error or a budget halt yields a hold with the error string as reason.

\begin{enumerate}\sloppy
\item \textbf{Parsing} (\code{parse\_decision}): whitespace and a surrounding \code{```}/\code{```json} fence are stripped; if the text is not valid JSON, the first \code{\{\dots\}} block is tried; failure $\to$ reason \code{json: <message>}.
\item \textbf{Schema} (\code{Decision}): \code{action} $\in$ \{hold, place, cancel\}; \code{side} $\in$ \{buy, sell, null\}; \code{order\_type} $\in$ \{limit, market, null\}; \code{quantity} integer $\ge 0$ or null; \code{limit\_price} number $>0$ or null (currency units); \code{cancel\_order\_ids} list of integers; \code{confidence} in $[0,1]$ or null; \code{rationale} trimmed to 400 characters; failure $\to$ reason \code{schema: <field>: <message>} (first three errors).
\item \textbf{hold}: always valid; no intent.
\item \textbf{cancel}: the ids are intersected with the agent's open orders (resting and in flight); empty intersection $\to$ \code{cancel: no valid order ids}; otherwise one cancel intent per surviving id.
\item \textbf{place}, in this order:
  \begin{enumerate}
  \item side, order type and quantity must all be present (\code{place: missing side/order\_type/quantity});
  \item quantity $>0$ (\code{place: quantity <= 0}) and $\le$ \code{max\_order\_qty} $=50$ (\code{place: quantity q > max 50});
  \item the asset must not be halted (\code{place: market halted});
  \item limit orders need a price (\code{place: limit without price}); the price is converted to ticks by $\operatorname{round}(100\,\text{price}/\text{tick\_cents})$ and must be positive and within $\pm20\%$ of the midpoint (\code{place: limit price outside ±20\% of mid});
  \item market orders need a non-empty opposite side (\code{place: market order with empty opposite side});
  \item buys: $\lfloor \text{ref}\times\text{tick\_cents}\times q\times1.001\rfloor \le$ free cash, where ref is the limit price or else the best ask or midpoint (\code{place: cost c > free cash f});
  \item sells: $q$ is clipped to holdings minus the remaining quantity of the agent's resting sells; if nothing is free the decision is invalid (\code{place: no free shares to sell}); a clipped sell is recorded as valid.
  \end{enumerate}
\item The surviving intent is tagged \code{llm} and submitted to the exchange, which applies its own checks (price band, cash reservation, position limit, leverage); an exchange rejection is logged in the event log, not in the decision log.
\end{enumerate}