China’s financial market exhibits a dual structure characterized by “retail investor dominance (80% of trading volume) - foreign capital technological monopoly (0.3% of institutions controlling 43.6% of order flow)”. Traditional models (e.g., VaR, GARCH) struggle to capture such asymmetric features due to their assumptions of homogeneous agents and static distributions [8, 9]. Agent-based modeling (ABM) accurately replicates three localized risks through a hierarchical agent design (embedding an emotion contagion module in the retail investor layer, implanting parameters for technological latency disparities and strategy homogenization coefficients in the foreign capital layer, and setting policy transmission time delays in the regulatory layer) [6, 10]: herding effects triggered by retail investor sentiment (e.g., a 47% sharp decline in order book thickness during the 2024 futures flash crash), order capture rates exceeding 82% due to technological stratification (consistent with Pagnotta’s S-shaped curve) [11, 12], and cross-border regulatory arbitrage (27% of high-frequency trading evading scrutiny) [13]. Compared to traditional methods (e.g., the failure of historical simulation in testing individual stocks on the Shenzhen Stock Exchange, GARCH models' inability to capture microstructural dynamics) [14], “The ABM incorporates a millisecond-level order book protocol (with a 100 ms step size) to dynamically simulate processes such as strategy disguise (e.g., ID changes every 2.1 h) and liquidity collapse [15]. This allows the model to reproduce the risk transmission chain: when the strategy homogenization coefficient exceeds 0.65, the percolation probability P surges, leading to a market crash of approximately 9% within 5 min [11]. This capability addresses a significant limitation of international models, which exhibit prediction errors of up to 32% [14].”

Beyond its accuracy in replicating market phenomena, the application of this ABM complex network model is necessitated by pressing regulatory challenges and enable policy sandbox simulations. The governance of high-frequency risks in China requires simultaneously tackling algorithmic black boxes, data sovereignty barriers (Article 31 of the Data Security Law), and lagging policy tools (regulatory delays leading to a 58% increase in loss rates). The value of the complex network ABM model is demonstrated in three aspects: First, it quantifies risk thresholds using a percolation phase transition algorithm: λ i = 1 − 1 − p k i · I s e n t i m e n t I b a s e , where the risk probability P surges from 0.2 to 0.8 when the strategy homogenization coefficient exceeds 0.65, providing a 3.2-h earlier warning of flash crashes compared to traditional volatility models [11]. Second, it supports the compilation of regulatory rules into machine-executable formats, such as translating fair trading provisions into dynamic tax rates based on technological latency disparities (a 0.2% tax increase for every 50 ms delay) to tax technological hegemony [11], and encoding circuit breaker rules as exponential functions of aggregation coefficients to curb monopolies (triggering scrutiny when the aggregation coefficient exceeds 0.3) [11]. Third, it resolves data silos while ensuring compliance with both GDPR and the Data Security Law [16, 17]. These functionalities make the ABM model a powerful tool for simulating the feedback loop between the regulatory and market layers, whereas traditional simulations fail to evaluate the effectiveness of regulatory interventions due to their neglect of policy intervention nodes.

Based on the dynamic Granger causality analysis framework, regulatory nodes are equipped with real-time monitoring capabilities to detect changes in causal relationships among market nodes. The regulatory node employs an overlapping window method to segment market trading data, quantifying causal influence intensity between nodes through vector autoregressive models. The monitoring mechanism includes: preprocessing market trading data for stationarity to remove non-stationary biases; computing lagged cross-covariance sequences to establish VAR models; estimating coefficient matrices through Yule-Walker equations; and calculating conditional Granger causality values to identify key risk transmission paths.

Drawing from the causality-driven node selection algorithm, regulatory nodes select optimal intervention timing based on dynamic causality graphs. Specific implementations include: calculating the out-degree of each market node to identify 'driving hub' nodes with maximum causal influence; automatically triggering regulatory intervention when key nodes' causal out-degree exceeds preset thresholds; and adopting a segmented learning-execution strategy to periodically update the causality network, ensuring policy trigger mechanisms adapt to market structure changes.

Adopting a local information-based pinning control strategy, the regulatory feedback mechanism is designed as follows: each regulatory node manages only a subset of market nodes within its causal influence domain; extracting feedback information based on local causal relationships and control influence regions; employing sign control functions to dynamically adjust control direction based on error states; and ensuring control coverage spans the entire market network, i.e., Ω 1 ∪ Ω 2 ∪ . . . ∪ Ω m = Ω .

At the topological center, “Regulatory Node A” (orange dot) connects directly to “Core Node B (foreign capital/licensed institutions)” (yellow dot) via “policy transmission” links. Core Nodes B interconnect through internal cycles of “strategy homogenization” links and extend downward to “Sub-core Node C (market makers)” (blue dot) via “order flow control” links. Market makers further connect to the outermost “Peripheral Nodes (retail investors)” (green dot) through “latency advantage” links, while retail investors relay information back to Regulatory Node A via “risk feedback” links, forming a complete closed-loop system. The regulatory control input can be designed as: u p t = s p t ∑ ᵣ   ∈ Ω p   h e ᵣ t , ė ᵣ t where s p t is the control function related to error states, and Ω p represents the influence domain of the pth regulatory node [20, 21].

Therefore, this diagram serves as an intuitive representation of the theoretical innovation of the model. Placing the “regulatory node” at the topological center constitutes a visual practice of Qian Xuesen’s methodology of “open complex giant systems”, emphasizing that policy intervention is a key endogenous variable shaping market structure in the Chinese context. This design reflects the characteristic of “strong policy intervention” in China’s financial market. The closed loop formed by “policy transmission” and “risk feedback” depicted in the figure accurately simulates the operational logic of regulatory cycles with Chinese characteristics—policies are transmitted top-down, while market risks are fed back bottom-up. The “strategy homogenization” links among core nodes lay the groundwork for subsequent simulations of systemic risk. This topological structure forms the foundational framework for all subsequent dynamic evolution.

As illustrated in Figure 2, the node distribution state after network initialization is presented. The figure should reveal a dense concentration of nodes representing “retail investors,” forming the foundational layer of the network; a smaller number of “core nodes” with numerous connections are scattered throughout, serving as network hubs, while “market maker” nodes occupy an intermediate position between the two. The annotated example nodes (ID: 235, Degree: 9) and (ID: 3326, Degree: 9) are two typical retail investor nodes.

Therefore, this figure serves as a successful validation of the model’s “localization adaptation.” The visualization results are highly consistent with the parameters set in Table 1 (80% retail investors, 0.3% core nodes), demonstrating that the model initialization effectively generates a digital mirror of a “retail investor-dominated market” aligned with China’s reality (as documented in the CSRC’s White Paper on Investor Structure). Nodes 235 and 3326, each with a degree of 9, indicate that an average retail investor typically connects with 9 other nodes, whereas a core node may possess hundreds or thousands of connections. This visually corroborates the scale-free nature of the network, wherein a minority of nodes hold extensive linkages, providing a structural basis for rapid risk transmission through these hub nodes. The corresponding formula is expressed as below. P k ∼ k − γ where k denotes the degree (number of connections) of a node or the scale of an event; P(k) represents the probability of an event having a scale k; and γ is the power-law exponent, a constant greater than 0.

At the moment of completing market structure initialization, we simultaneously introduce the Strategic Homogeneity Coefficient ρ , a core metric quantifying the degree of behavioral convergence among participants in financial markets. This coefficient fundamentally captures the similarity of trading strategies at the group level and the lack of diversity. Rooted in strategic convergence analysis from game theory and discrete choice theory, it reflects the gradual contraction of the strategy space toward local consensus when market participants act on limited information or similar decision-making frameworks (e.g., quantitative models) [28]. The coefficient is measured by calculating the variance or entropy of the strategy distribution: if participants widely adopt similar algorithms (such as trend-following or mean-reversion strategies), the coefficient approaches 1, indicating high homogeneity; if strategies exhibit a diverse distribution, the coefficient nears 0. In dynamic environments, strategic homogeneity is driven by the speed of information dissemination, technological constraints (e.g., algorithmic black boxes), and institutional factors (e.g., cross-border data barriers), collectively trapping participants in a “minority game” dilemma—where the marginal benefit of deviating from mainstream strategies diminishes sharply, further reinforcing convergence [29].

Percolation theory serves as a fundamental framework for studying critical phase transitions in disordered systems, initially proposed by Broadbent and Hammersley in 1957. Its core concept focuses on abrupt changes in long-range connectivity within random geometric structures. By simulating fluid flow behavior in porous media [18], this theory reveals that when system components (such as pore occupancy or bond connection probability) reach a critical threshold (the percolation threshold p c ), the system undergoes a sharp phase transition from “local connectivity” to “global percolation” (or conversely, blockage). This transition fundamentally involves the emergence or disappearance of a percolating cluster in disordered media, manifesting as stepwise changes in conductivity, permeability, or risk contagivity [30].

In financial risk modeling, the core value of percolation theory lies in its critical threshold scaling laws and cluster dynamics. When the critical threshold p c is mapped to the tipping point of systemic risk (e.g., when the strategy homogenization coefficient exceeds a certain value within its range), breaching this threshold allows minor local disturbances (such as a single institution’s default) to trigger a global liquidity collapse through connected clusters, replicating the phase transition logic of pore blockage  →  fluid flow interruption

The cluster formation mechanism, in turn, corresponds to the path of risk contagion: highly connected nodes in the core institutional layer (e.g., foreign market makers) act as hubs for risk transmission, with their betweenness centrality positively correlated with order capture rates. When strategy homogenization drives the connection probability p between nodes toward p c , sentiment factors in the retail investor layer accelerate risk diffusion within clusters, ultimately inducing a percolation phase transition.

As shown in Figure 3‐1, before risk propagation, the network nodes exhibit uniform coloration (e.g., all in blue) with a stable connection structure; after risk propagation, as depicted in Figure 3‐2, it is clearly observable that starting from a few “core nodes” with altered colors (e.g., turned red), the color change rapidly diffuses through connecting edges to “market maker” nodes (turning yellow), eventually affecting a large number of “retail investor” nodes (turning red), forming a chain reaction. Thus, Figure 3 serves as a vivid demonstration of the application of percolation theory in financial risk transmission and within this model. It intuitively reveals that the propagation of systemic risk is not uniform but rather proceeds along network connection paths, particularly through high-degree core hub nodes in a leap-like manner. This process also aligns with the logic described by the percolation theory formula, as presented below. λ i = 1 − 1 − p k i

Where λ i represents the probability of a certain event occurring (typically the probability of “occurring at least once”); p denotes the probability of the event occurring in a single attempt (which remains constant), thus 1 − p is the probability of the event not occurring in a single attempt; and k i signifies the number of independent attempts. It follows that nodes with higher connectivity k i exhibit a greater probability λ i of transmitting and receiving risk [31, 32].

Therefore, the introduction of percolation theory enables this study to transform the abstract concept of “risk transmission” into a visualizable “digital pandemic” [33], powerfully demonstrating why sell-offs by individual institutions can trigger panic across the entire market.