Additional Fundamental Agents in Financial Markets

• Additional Fundamental Agents (AFAs) are a homogeneous class of agents that use a parameter-controlled, mean-reversion strategy to restore prices to a fixed fundamental value.
• They systematically reduce market volatility by enforcing negative feedback on price deviations, evidenced by decreasing price-level and return volatility in simulations.
• Empirical results show that as more AFAs participate, market stabilization increases while individual trading profits decline due to reduced mean-reversion opportunities.

Additional Fundamental Agents (AFAs) are a homogeneous class of agent-based models introduced to systematically probe the impact of mean-reversion trading on market prices, volatility, and agent profitability. Their role is formulated within an extended agent-based artificial financial market model (ABAFMM), where they are defined by their exclusive adherence to a simple, parameter-controlled, fundamental-value-driven strategy. AFAs are characterized by their stabilizing influence on price dynamics, with their collective presence producing pronounced effects on both the statistical properties of market outcomes and the profit landscape for individual agents (Mizuta et al., 4 Mar 2026).

1. Formal Specification of Additional Fundamental Agents

Each Additional Fundamental Agent (AFA) operates according to a single-parameter excess demand rule designed to restore prices to a fixed fundamental value $P_f=10,\!000$. The fundamental process is static:

$p^*_t = P_f, \quad \forall t$

The excess-demand order of the $i$th AFA at time $t$ is

$D^F_i(t) = \lambda_i(P_f - p_t)$

where $\lambda_i$ is the reaction parameter (set to 1 in all reported simulations), and $p_t$ is the current mid-price. AFAs buy if $p_t < P_f$ and short if $p_t > P_f$, subject to a position constraint: at most one net share long or short per AFA.

This deterministic strategy is independent of technical signals or noise, and AFAs are added as a homogeneous population on top of a baseline of $n=1000$ "normal" heterogeneous agents who trade on a mixed set of strategies.

2. Integration into Market Dynamics

AFAs modify the coarse-grained price-formation rule adopted in the ABAFMM, which under a mean-field approximation updates the mid-price as

$$p_{t+1} = p_t + \kappa \sum_{j=1}^{n+N_{\rm AFA}} D_j(t)$$

with $\kappa$ a small price-impact coefficient, $n$ the number of normal agents, and $N_{\rm AFA}$ the number of AFAs. Each normal agent contributes a potentially model-specific $D_j(t)$; each AFA contributes $D^F_i(t)$ as specified. Increasing $N_{\rm AFA}$ directly amplifies the mean-reversion force, thereby affecting emergent market properties.

3. Profit Calculation and Dynamics

AFA trading profits over a horizon $T$ are calculated as the sum of realized gains due to position change and contemporaneous price movement:

$$\Pi^F_i = \sum_{t=1}^T D^F_i(t)[p_{t+1} - p_t] = \sum_{t=1}^T \lambda_i (P_f - p_t)[p_{t+1} - p_t]$$

Given $\lambda_i = 1$, each AFA exploits the mean reversion of the mid-price toward $P_f$, ideally profiting when the market corrects. However, the magnitude of these profits—and the frequency of profitable trades—depends nontrivially on the aggregate number of AFAs present.

4. Market Stability and Volatility Metrics

A primary metric of AFA impact is price-level volatility around the fundamental:

$$\sigma_p = \sqrt{\frac{1}{T}\sum_{t=1}^T (p_t - P_f)^2}$$

Additionally, return volatility is measured as

$$\sigma_r = \sqrt{\frac{1}{T} \sum_{t=1}^T (r_t - \bar{r})^2}$$

where $r_t = \ln(p_t/p_{t-1})$. Empirically, increases in $N_{\rm AFA}$ lead to monotonic declines in both $\sigma_p$ and $\sigma_r$, a direct manifestation of the negative-feedback stabilization induced by fundamental-value trading. This suppresses deviations from $P_f$ and compresses return fluctuations.

5. Simulation Protocol and Parameterization

The extended ABAFMM is simulated over $T=2 \times 10^7$ time steps for various $N_{\rm AFA}$ (ranging from 0 to 99, added incrementally). All parameters except $N_{\rm AFA}$ are held fixed:

Parameter	Value/Range	Description
$n$	1000	Number of normal agents (NAs)
$P_f$	10,000	Fundamental value
$\lambda_i$ (for AFA)	1	Reaction parameter (order size per price-unit gap)
$w_{1,\max}$	1	Normal agent fundamental-weight
$w_{2,\max}$	100	Normal agent technical-weight
$w_{3,\max}$	1	Normal agent noise-weight
$T_j$	[1,10,000]	Normal agent memory window
$\sigma_{\varepsilon}^2$	0.03	Noise variance
$P_a$	1000	Price scatter parameter

Each $N_{\rm AFA}$ value is typically run once, with observed qualitative trends reported as robust across repeat runs.

6. Empirical Outcomes and Scaling Laws

The systematic introduction of AFAs yields a pronounced stabilization of market prices around $P_f$. Time-series of $p_t$ show tight clustering near the fundamental for $N_{\rm AFA} = 99$, and significant price wandering when $N_{\rm AFA} = 0$. The main quantitative findings are:

• Average per-AFA profit $\langle\Pi^F\rangle$ drops sharply as $N_{\rm AFA}$ increases; for $N_{\rm AFA} \approx 50$, individual AFA profits approach zero.
• The average number of trades per AFA falls rapidly for $N_{\rm AFA} < 20$ before plateauing.
• Observed scaling laws:

$$\sigma_p(N_{\rm AFA}) \propto \frac{1}{\sqrt{N_{\rm AFA}}} \qquad \langle\Pi^F\rangle \propto \sigma_p(N_{\rm AFA})$$

These results indicate that as more fundamentalists participate, they collectively reduce the very volatility and price excursions that enable their profits, exemplifying negative feedback inherent to mean-reversion strategies.

7. Interpretation and Theoretical Implications

AFAs serve as parametric mean-reversion agents whose mechanism inherently links market stabilization and profit erosion. Their presence offers a mathematically controlled way to examine how mechanism design in agent-based financial models affects emergent volatility and strategic incentives. The decline in individual profits with agent population size demonstrates the self-limiting property of such negative-feedback strategies: excess stabilization extinguishes the inefficiencies that make fundamental-based trading lucrative. A plausible implication is that increases in the proportion of fundamental-value traders, all using identical parameters, ultimately suppress the opportunity set for mean-reversion profits (Mizuta et al., 4 Mar 2026).