Agent-Based Analysis of Cryptocurrency Adoption in Transit Systems

Highlights

What are the main findings?

• The agent-based simulation framework demonstrates that population-level technology readiness can rival external market conditions as a dominant driver of cryptocurrency adoption in transit.
• Multi-dimensional scenario analysis reveals significant interaction effects among rider demographics, technology adoption levels, and market conditions—highlighting need for multi-factor evaluations.

What are the implications of the main findings?

• Transit authorities can use the proposed framework as a computational laboratory for “what if” scenario planning, enabling systematic stress-testing of cryptocurrency payment strategies before real-world deployment.
• The methodology underscores the importance of investing in digital literacy and adopting adaptive, multi-scenario policy evaluation rather than optimizing for a single anticipated market condition.

Abstract

As cryptocurrency adoption accelerates globally, cities face a critical question: can digital currencies be adapted by different agencies without compromising financial stability? This paper develops an agent-based modeling framework that enables transit authorities to systematically explore cryptocurrency integration strategies. We simulate 1000 heterogeneous agents with varying risk tolerance, technological proficiency, and social influence susceptibility over 365 days, testing five policy regimes across a comprehensive scenario matrix comprising four risk-attitude compositions, four technology-adoption levels, four social-influence intensities, and three market conditions (bullish, neutral, bearish)—creating 192 distinct population-market configurations evaluated across all five policies with 15 independent replications per configuration (14,400 total simulation runs). The framework produces adoption outcomes ranging from near-zero to over 49% depending on scenario assumptions, with technology familiarity emerging as the dominant driver. The framework provides transit authorities with a practical tool for scenario-based planning: testing policy interventions, stress-testing financial stability under various market conditions, identifying potential vulnerabilities before deployment, and comparing alternative strategies across diverse demographic contexts. This simulation-based approach enables data-driven decision-making in the absence of real-world precedent, offering a structured methodology for evaluating cryptocurrency integration while managing financial stability risks.

1. Introduction

Digital currencies have expanded well beyond Bitcoin to include stablecoins, central bank digital currencies (CBDCs), and Layer-2 payment networks. As their adoption accelerates, city authorities face a practical question: can any of these assets serve as fare payment without putting revenue at risk? The underlying tension is straightforward—digital currencies may reduce transaction costs, but they carry significant price volatility and operate under unclear or evolving regulation.

Three recent cases illustrate the range of outcomes. In 2021, El Salvador incorporated Bitcoin into transit via the Chivo wallet, offering a $30 sign-up bonus to every citizen; after one year, only about 20% of users remained active, with surveys attributing the drop-off to trust problems, technological barriers, and price swings [1]. China’s digital yuan (e-CNY) pilots were more successful. Subway systems in Suzhou, Shenzhen, and Beijing achieved high adoption by integrating the CBDC into existing mobile payment apps, where the near-zero volatility of a state-backed currency removed the price risk that plagued El Salvador’s experiment. Estonia adopted a different approach, deploying blockchain-based digital identity for public services without requiring cryptocurrency transactions at all [2]. The outcomes of crypto adaptation depend not only on the asset but also on how it is deployed and who the target users are.

Despite these mixed outcomes, several potential advantages motivate continued exploration by transit authorities and Mobility-as-a-Service (MaaS) developers. First, credit card interchange fees impose 2–3% costs per transaction on agencies, while blockchain-based payment—particularly stablecoins on high-throughput networks—can reduce settlement costs substantially. Second, tourists and temporary residents can pay fares without currency exchange or international card surcharges, reducing friction for a significant ridership segment. Third, smart contract infrastructure enables automated implementation of dynamic pricing, means-tested subsidies, and multi-modal payment integration without centralized intermediary systems. Whether these advantages outweigh the risks depends on the specific digital asset, population characteristics, and institutional context—precisely the trade-off our framework is designed to evaluate.

In the literature, the barriers to cryptocurrency-based transit payment are well documented. Bitcoin’s annualized price volatility regularly exceeds 50% [3,4], regulatory frameworks differ across jurisdictions and continue to evolve [5,6], older riders frequently lack the digital literacy required to manage wallet-based payments [7], operating dual-currency systems introduces substantial administrative complexity [8], and cryptocurrency is associated with illicit finance [9,10]. We do not argue in this paper that transit authorities should accept cryptocurrency; rather, the accelerating integration of digital wallets into everyday commerce, combined with the pilot programs already underway in multiple cities, makes it timely to develop quantitative tools for evaluating such decisions. Whether the right answer for a given agency turns out to be adoption, rejection, or conditional acceptance of specific asset classes, the decision requires a framework that can account for volatile prices, rider populations, and the network effects that amplify or dampen adoption. Our model provides such a framework, and it is equally useful to an authority that ultimately concludes the risk is unacceptable compared to one that proceeds with integration.

The academic literature in this specific area is limited. Most cryptocurrency research treats digital assets as investment options rather than payment instruments for public services, while existing financial stability frameworks were built for traditional payment systems and do not account for the extreme price swings, fragile liquidity, and absent institutional backstops that are common in cryptocurrency markets. At the same time, we know little about how individuals actually choose between payment methods in a dual-currency environment, particularly when social influence and volatile prices exist simultaneously.

This paper addresses three objectives that together fill this gap. First, we study how cryptocurrency price volatility—modeled through geometric Brownian motion (GBM) with regime switching and stress-tested against extreme tail events—shapes payment behavior across different rider demographics. Second, we examine how peer influence propagates through social networks to accelerate or inhibit adoption. Third, we test policy interventions—including dynamic fees and reserve requirements—that might manage financial risk.

We employ agent-based modeling because it can represent heterogeneous individuals with different risk preferences, technological skills, and social connections, capturing bounded rationality and behavioral biases. We simulate 1000 transit users across a scenario matrix of 4 risk-attitude compositions × 4 technology levels × 4 social-influence intensities × 3 market conditions, yielding 192 configurations per policy. Income distributions shift with scenario axes, producing median incomes ranging from $52k to $95k. The overarching goal is to identify under what conditions cryptocurrency payments enhance rather than erode financial stability for the transit authority.

The remainder of the paper is organized as follows. Section 2 reviews the relevant literature and presents the model architecture, including the GBM-based price diffusion process, agent specifications, and the policy framework. Section 3 reports simulation results across all scenario and policy configurations. Section 4 discusses implications, limitations, and directions for future research. Section 5 concludes the paper.

2. Literature Review

Understanding how cryptocurrency payments might function within public transportation systems requires drawing on several interconnected research areas spanning cryptocurrency market dynamics, agent-based modeling, behavioral economics, financial stability, and social network effects. Since Bitcoin’s introduction [11], the cryptocurrency ecosystem has experienced dramatic growth, yet adoption remains uneven and heavily concentrated among technology-forward users. A critical barrier is extreme price volatility—Baur et al. [3] and Yermack [4] refer to annualized volatility frequently exceeding fifty percent, fundamentally challenging the use of cryptocurrencies as a stable currency for exchange. Speculation that price dynamics are shaped by market manipulation and fragmented liquidity compounds the difficulty of relying on these assets for routine transactions such as transit fares [10,12]. The regulatory landscape adds another layer of complexity: Zetzsche et al. [5] argue that existing regulations struggle to accommodate peer-to-peer cryptocurrency transactions, while Blandin et al. [6] document significant cross-jurisdictional fragmentation. These risks must be weighed against potential benefits including reduced interchange fees [13] and technological innovation [14], but evaluating this trade-off requires analytical tools capable of capturing the interplay between heterogeneous users, volatile markets, and institutional constraints. Farmer and Foley [15] argue that macroeconomic events emerge from micro-level interactions among diverse agents following adaptive rules, and that equilibrium models miss critical dynamics including emergent patterns and heterogeneous responses to shocks, suggesting the importance and applicability of simulation-based analysis for these types of questions. Applied to financial markets, LeBaron [16] shows that simple agent-based frameworks reproduce stylized facts—fat tails, volatility clustering—through interaction of heterogeneous strategies, while Hommes [17] demonstrates that fundamentalist–chartist interactions generate complex price dynamics resembling actual markets. Tesfatsion [18] establishes methodological standards emphasizing empirically grounded behavioral rules. Lux [19] shows that herding among heterogeneous agents generates endogenous crashes without external shocks; Brock and Hommes [20] demonstrate strategy-switching dynamics paralleling payment method adoption; and Thurner et al. [21] reveal how individual financial decisions create network externalities amplifying system-wide fragility—a mechanism analogous to individual payment choices aggregating into revenue volatility for transit authorities.

On the subject of user behavior, the behavioral economics literature explains why individual choices systematically deviate from rational cost minimization. Kahneman and Tversky [22] demonstrated that individuals evaluate outcomes relative to reference points, exhibit loss aversion, and display nonlinear probability weighting—implying that transit users will be disproportionately sensitive to cryptocurrency price drops and may overweight extreme price movements. Tversky and Kahneman [23] further suggest that repeated decisions shift reference points over time, creating path-dependent adoption dynamics. Beyond risk preferences, Thaler [24] shows that mental accounting creates distinct spending rules across payment categories, while Soman [25] finds that transparency and perceived control drive payment preferences—particularly relevant given that many users find blockchain technology opaque. Simon [26] and Gigerenzer and Gaissmaier [27] argue that cognitive limitations lead decision-makers to rely on heuristics rather than optimization, and Frederick et al. [28] document present bias creating tension between the immediate costs of learning new payment systems and the delayed benefits of adoption. Individual payment decisions are also fundamentally social. Granovetter [29] shows that weak ties transmit novel information more effectively than strong ties, implying that cryptocurrency awareness may spread most effectively through acquaintances bridging disconnected groups. Jackson [30] demonstrates that network structure critically determines diffusion speed, while the Watts–Strogatz model [31] captures both local clustering and long-range connections characteristic of real social networks. Banerjee [32] and Bikhchandani et al. [33] show that information cascades can lock populations into choices driven by early randomness, suggesting that initial cryptocurrency adoption rates may be highly path-dependent. Empirically, Hong et al. [34] and Brown et al. [35] provide evidence that peer behavior significantly affects financial participation decisions, while Bursztyn et al. [36] decompose peer effects into social learning and social utility—suggesting that cryptocurrency adoption may be driven both by genuine learning and by desire to signal technological sophistication. Katz and Shapiro [37] show that network externalities generate multiple equilibria and coordination failures, implying that transit systems may face tipping-point dynamics where small interventions trigger disproportionate adoption shifts. These individual-level dynamics operate within institutional contexts where financial stability is paramount. Bernanke and Gertler [38] show that payment system disruptions can trigger broader crises through liquidity spirals, positioning stability as a public good. When transit authorities accept cryptocurrency, they assume responsibilities traditionally managed by central banks—without corresponding institutional backstops. Rochet and Tirole [39] and Rysman [40] analyze the two-sided market structures inherent in payment systems, revealing coordination problems that are particularly acute for novel payment technologies, while Upper [41] develops stress-testing frameworks demonstrating that resilience depends on the interaction of network topology, liquidity distribution, and contagion mechanisms.

Although blockchain and crypto payment is slowly taking off, the research in the area is not rich. Several gaps exist: (a) cryptocurrency research focuses on investment rather than payment applications [42]; (b) financial stability frameworks do not account for cryptocurrency-specific risks [43]; (c) social network models of adoption have not been applied to payment systems where individual choices aggregate into system-level financial exposure [44]. Our framework addresses these gaps by combining volatility dynamics, behavioral heterogeneity, social learning networks, and stability analysis in a single agent-based model.

2.1. Model Architecture

The model has three components (Figure 1): (1) heterogeneous transit users who learn and adapt, (2) a transit authority managing dual-currency revenue, and (3) a market environment that drives cryptocurrency prices.

2.1.1. Market Environment

The market environment generates the cryptocurrency price that agents observe when making their decisions. We model this price as a continuous-time diffusion process—specifically, geometric Brownian motion (GBM):

$$d{P}_t=\mu P_{t}dt+\sigma P_{t}d{W}_t.$$

(1)

$P_t$ is the cryptocurrency price at time t, $\mu$ is the drift (expected annual return), $\sigma >0$ is the annualized volatility, and $d{W}_t$ is a standard Wiener process increment representing continuous random fluctuations. For simulation, we discretize this diffusion at a daily time step of $\Delta t=1/365$:

$$P_{t+\Delta t}=P_t\exp \left[\left(\mu -{\displaystyle \frac{{\sigma }^2}{2}}\right)\Delta t+\sigma \sqrt{\Delta t}{ϵ}_t\right],$$

(2)

where ${ϵ}_t\sim \mathcal{N}(0,1)$. This GBM diffusion process serves as the baseline price engine for all 14,400 simulation runs reported in Section 3. It drives the volatility signal ${\sigma }_t$ that enters agents’ risk utility (Equation (4)), the Value-at-Risk (VaR) calculation (Equation (13)), and the stability score (Equation (12)). Parameters are calibrated from historical cryptocurrency data (Section 3.1) and can be re-calibrated when real transaction data become available. Note that the following assumptions were made in the simulation process, which may not accurately reflect real-world scenarios.

• Volatility Assumptions: The baseline GBM specification assumes constant $\sigma$ within each regime period, generating price paths through continuous diffusion alone—without discrete jumps. This simplification is intentional to isolate the effect of smooth volatility on agent behavior and produce tractable VaR estimates under the normality assumption. Real cryptocurrency markets exhibit fat tails, volatility, and sudden price jumps that requires complicated models such as the Merton jump-diffusion variant of the model:

  $$d{P}_t=\mu P_{t}dt+\sigma P_{t}d{W}_t+J_t{P}_{t}d{N}_t$$

  (3)

  where $N_t\sim \mathrm{Poisson}\left({\lambda }_{\mathrm{jump}}\right)$ with ${\lambda }_{\mathrm{jump}}=0.05$ jumps per day governs jump arrivals and $J_t\sim \mathcal{N}({\mu }_J=-0.15,{\sigma }_J=0.10)$ gives jump magnitudes (negative mean reflecting crash asymmetry). Under this specification, the daily return variance becomes ${\sigma }_{\mathrm{daily}}^2+{\lambda }_{\mathrm{jump}}({\sigma }_J^2+{\mu }_J^2)$, increasing VaR₉₅ by approximately 40–55% relative to the pure GBM baseline. However, because our framework uses VaR as a comparative metric across policies and scenarios, the relative ranking of all reported results is preserved—only the absolute dollar magnitudes increase. Transit authorities requiring conservative absolute risk bounds should apply the jump-diffusion multiplier to our reported VaR values.
• Market Liquidity Assumptions: we make three simplifying assumptions about market structure. First, the transit authority can convert cryptocurrency to USD instantly at the market price (perfect liquidity). Second, transit-scale transactions do not move market prices—a reasonable assumption given how small they are relative to global cryptocurrency trading volumes. Third, markets operate continuously, consistent with the 24/7 nature of cryptocurrency exchanges.
• Alternative Cryptocurrencies: The baseline calibration uses Bitcoin-equivalent parameters for simulation. The framework can accommodate any digital asset simply by adjusting $\mu$ and $\sigma$. Stablecoins ($\sigma \approx 0.05$), Ethereum ($\sigma \approx 0.60$), and CBDCs ($\sigma \approx 0.01$) can all be evaluated within the same diffusion-based architecture.

2.1.2. Transit Users

Each agent $i\in \{1,2,\dots ,N\}$ has a parameter vector defined by ${\mathsf{\theta }}_{\mathit{i}}=(r_i,a_i,y_i,s_i,w_i,{\lambda }_i,m_i)$, representing seven attributes. We chose these seven based on common practice in relevance studies: risk tolerance [22]; age and income, following standard demographic studies; technology proficiency, estimated as perceived ease-of-use [45]; social influence susceptibility, which follows the existing literature; and learning rate and memory length for bounded rationality [34,36].

Risk tolerance $r_i\in [0,1]$ measures willingness to accept price volatility (0 = fully averse, 1 = risk-seeking). Age $a_i$ and income $y_i$ are in years and dollars. Tech proficiency $s_i\in [0,1]$ captures comfort with digital payments. Social influence susceptibility $w_i\in [0,1]$ is how much peer behavior affects the agent. Learning rate ${\lambda }_i\in [0,1]$ controls how fast preferences adapt, and memory length $m_i\in \mathbb{N}$ is how many past experiences the agent retains. Parameters are drawn from truncated normal distributions centered at the midpoint of each type’s range, with $\sigma =(\mathrm{hi}-\mathrm{lo})/4$, so about 95% of draws fall within bounds. For income we use scenario-conditioned log-normal distribution.

With the market diffusion process generating daily price signals and the transit authority setting fee policy in response, individual agents process these inputs to make payment decisions. In our defined setting in this paper, each agent chooses between cryptocurrency and dollar payments based on four factors: cost, risk, technological convenience, and past experience. For payment method j, agent i’s utility at time t combines four components additively:

$$U_{i,j,t}=U_{i,j,t}^{cost}+U_{i,j,t}^{risk}+U_{i,j,t}^{tech}+U_{i,j,t}^{experience}$$

(4)

We use additive utility following standard discrete choice theory [46]. The four components contribute independently within a given agent type. However, heterogeneity across agent types is introduced through type-specific utility coefficients later in the paper: risk-averse agents have higher ${\beta }_{risk}$, while tech-savvy agents have higher ${\beta }_{tech}$ and faster learning. This means that although the utility function is additive, the effective weighting of components varies across the population—a form of observed heterogeneity in the mixed logit tradition [46].

• The cost component incorporates income-sensitive fee perception:

  $$U_{i,j,t}^{cost}=-f_j·{\left({\displaystyle \frac{Y_{ref}}{Y_i}}\right)}^{\gamma }$$

  (5)

  where $Y_{ref}$ is the reference income, $Y_i$ is agent i’s income, and $\gamma$ is the income elasticity of fee sensitivity [46]. Lower-income agents perceive the same fee as more costly, reflecting documented income effects in payment choice. $f_j$ is the fee for payment method j.
• The risk component for crypto is $U_{i,crypto,t}^{risk}=-{\beta }_{risk}·{\sigma }_t·(1-r_i)$. The penalty grows with volatility but shrinks for risk-tolerant agents. For dollars, $U_{i,dollar,t}^{risk}={\beta }_{stability}·(1-r_i)$ gives a stability bonus to risk-averse agents.
• The technology component for crypto is $U_{i,crypto,t}^{tech}={\beta }_{tech}·s_i$ (tech-savvy agents find it easier), and for dollars $U_{i,dollar,t}^{tech}={\beta }_{tech}·(1-s_i)$ (less tech-savvy agents prefer traditional payment).
• The experience component lets agents learn from their payment history:

  $$U_{i,j,t}^{experience}={\lambda }_i·{\displaystyle \frac{1}{m_i}}{\displaystyle \sum _{𝓁=1}^{m_i}}{\omega }_{𝓁}{U}_{i,j,t-𝓁}^{experience}$$

  (6)

  where ${\lambda }_i$ is the learning rate, $m_i$ is memory length, and ${\omega }_{𝓁}$ represents recency weights, satisfying ${\sum }_{𝓁=1}^{m_i}{\omega }_{𝓁}=1$ ($𝓁=1$ is most recent). The weights follow an exponential decay:

  $${\omega }_{𝓁}={\displaystyle \frac{{(1-\delta )}^{𝓁-1}}{Z}},Z={\displaystyle \sum _{k=1}^{m_i}}{(1-\delta )}^{k-1}={\displaystyle \frac{1-{(1-\delta )}^{m_i}}{\delta }}$$

  (7)

  where $\delta \in (0,1)$ is the recency decay parameter. This assigns normalized weight 1 to the most recent experience. Agents with longer memory smooth out noise; those with shorter memory react fast but are prone to recency bias.

The choice probability, $P{r}_{i,t}$ for crypto, follows a logistic function:

$$\underset{i,t}{\mathrm{Pr}}={\displaystyle \frac{1}{1+\exp \left(-\frac{U_{i,crypto,t}-U_{i,dollar,t}+I_{i,t}}{\tau }\right)}}$$

(8)

$\tau$ is logistic temperature; ${\mathrm{Pr}}_{i,t}$ is the choice probability (distinct from preference $p_{i,t}$); for temperature $\tau >0$, large $\tau$ makes choices near-random [26]; small $\tau$ makes them deterministic. $I_{i,t}$ is social influence on choosing crypto. It enters the choice probability as

$$I_{i,t}=w_i·\left({\overline{p}}_{{\mathcal{N}}_i,t}-p_{i,t}\right)·\left(\frac{1}{2}+\left|{\overline{p}}_{{\mathcal{N}}_i,t}-\frac{1}{2}\right|\right)$$

(9)

where ${\overline{p}}_{{\mathcal{N}}_i,t}={\displaystyle \frac{1}{|{\mathcal{N}}_i|}}{\sum }_{j\in {\mathcal{N}}_i}{p}_{j,t}$ is the mean neighbor preference, ${\mathcal{N}}_i$ is the set of i’s neighbors, $p_{j,t}$ is neighbor j’s crypto preference, and $w_i$ is i’s susceptibility to peer influence. Network parameters (N, K, $\varphi$) are set for realistic social circle sizes and small-world properties [47]; values appear in Section 3.1. The parenthetical term in Equation (9) is the gap between neighbors’ average crypto preference and the agent’s own. Positive gap pulls toward crypto; negative gap pulls toward dollars. Preferences update each step as

$$p_{i,t+1}=(1-\eta )p_{i,t}+\eta \underset{i,t}{\mathrm{Pr}}.$$

(10)

The preference $p_{i,t}$ drifts toward the computed choice probability $\eta$. ${\mathrm{Pr}}_{i,t}$ is the preference update rate. High $\eta$ makes preferences responsive and low $\eta$ represents higher inertia seen in real payment behavior [24]. The social factor, I, is a consensus amplification term ranging from $0.5$ (neighbors evenly split) to $1.5$ (full consensus). This captures the empirical finding that information cascades accelerate under agreement [32,33]: when most neighbors share a payment preference, the social signal is stronger than when they are divided. High-$w_i$ agents shift substantially when peers adopt crypto. Low-$w_i$ agents mostly ignore peers and rely on their own cost-risk calculation [34,36].

2.1.3. Transit Authority

The transit authority is a single institutional agent managing system-wide financial stability. It is characterized by the parameter vector

$$\mathbf{\Theta }=(C_{fixed},{\rho }_{conv},{\theta }_{buffer})$$

(11)

where $C_{fixed}$ represents fixed operational costs, ${\rho }_{conv}$ (Cryptocurrency Conversion Risk Factor) is exposed to conversion risk; ${\theta }_{buffer}$ (Liquidity Buffer Requirement) specifies how many days’ worth of average revenue the transit authority must keep on hand as immediately accessible funds. For instance, ${\theta }_{buffer}=1.5$ means the agency maintains reserves equal to 1.5 times its average daily revenue. This buffer ensures the authority can continue working even if cryptocurrency markets crash and conversion revenues temporarily dry up. The required reserve is simply $L_{required,t}={\theta }_{buffer}·{\overline{R}}_{daily}$—the buffer multiple times the running average of daily income. On the system side, the transit authority tracks financial health through a stability score, $S{c}_t\in [0,1]$, combining five risk dimensions:

$$S{c}_t=\max \left(0,1-15{\widehat{\sigma }}_{R,t}-2{\sigma }_t.A_t-{\rho }_{conv}.A_t-{\displaystyle \frac{|A_t-{\alpha }^{\ast }|}{\max ({\alpha }^{\ast },1-{\alpha }^{\ast })}}-2{\mathrm{CV}}_{30,t}\right)$$

(12)

Here ${\widehat{\sigma }}_{R,t}$ is the trailing 10-step standard deviation of revenue returns and ${\sigma }_t$ is the current market volatility. $A_t$ is the cryptocurrency adoption rate at time t, defined as the share of agents paying with crypto, $A_t={\displaystyle \frac{N_{crypto,t}}{N}}$. The adaptation rate results from individual decisions ${\rho }_{conv}$ is the conversion risk factor, ${\alpha }^{\ast }$ is the target crypto allocation, and ${\mathrm{CV}}_{30,t}={\widehat{\sigma }}_{R,30}/{\overline{R}}_{30}$ is the coefficient of variation of revenue over the trailing 30 steps. In this equation, the first term penalizes short-run revenue volatility. The second captures the interaction between market volatility and crypto exposure—high volatility combined with high adoption produces substantially lower stability. The third term captures liquidity exposure proportional to crypto volume. The fourth penalizes deviation from ${\alpha }^{\ast }$. The fifth penalizes sustained revenue dispersion over a longer window. Under severe stress, any single factor can drive the stability score to zero—reflecting that catastrophic risk in one dimension constitutes genuine financial instability regardless of other factors. In our simulation, we set ${\alpha }^{\ast }=0.20$ as a baseline—assuming the authority prefers mostly fiat revenue with modest crypto diversification. Since $S{c}_t$ does not enter the agent utility function (Equation (4)) it does not affect individual decisions and it is computed to compare policies where higher scores mean greater financial resilience.

Downside exposure is measured by daily Value-at-Risk at 95% confidence:

$${\mathrm{VaR}}_{95,t}=R_{\mathrm{total},t}·A_t·{\sigma }_{\mathrm{daily}}·z_{0.95},$$

(13)

where $R_{\mathrm{total},t}$ is total daily revenue, ${\sigma }_{\mathrm{daily}}=\sigma /\sqrt{365}$ converts the annual volatility from the GBM diffusion process to its daily equivalent, and $z_{0.95}=1.645$. In plain terms, VaR₉₅ represents the worst single-day revenue loss from cryptocurrency price movements that the authority should expect 95% of the time.

2.1.4. Policy Framework Specification

In our setting, given the market environment, the transit authority must choose a fee and risk management strategy to protect their assets and stability. The model tests five policies (

Table 1. Overview of Transit Authority Policy Strategies.

Policy Type	Description
Baseline Policy	A reference fee structure with minimal cryptocurrency fees slightly above the USD fee level (3% vs. 2%), representing a near-neutral stance toward cryptocurrency adoption.
Conservative Policy	Cryptocurrency fees set significantly above the USD fee level (10%), actively discouraging crypto adoption to protect revenue stability.
Incentive Policy	Cryptocurrency fees set below the USD fee level (1%), actively encouraging crypto adoption to maximize payment diversity and network effects.
Dynamic Policy	Cryptocurrency fees that adjust automatically in response to real-time market volatility, starting from a 0.5% base fee.
Risk Management Policy	A comprehensive framework combining moderate cryptocurrency fees (5%) with enhanced hedging, automatic conversion protocols, and liquidity buffer requirements.

), spanning the spectrum from adoption-encouraging to risk-minimizing conservative policies.

The Dynamic Policy directly links fee levels to the volatility signal produced by the GBM diffusion process: $f_{crypto,t}=f_{base}+\alpha ·\max (0,{\sigma }_t-{\sigma }_{threshold})$. When the trailing volatility ${\sigma }_t$ exceeds the threshold, cryptocurrency fees rise proportionally, discouraging usage during periods of market stress. In calm markets, fees remain low, preserving adoption incentives. This creates an automatic stabilizer that responds to the same price dynamics driving agent risk perceptions.

The Risk Management Policy has three mechanisms. (1) Automatic conversion triggers when crypto revenue exceeds a threshold. (2) We employ an enhanced Hedging Strategy of $H_t={\rho }_{hedge}·R_{crypto,t}$, where ${\rho }_{hedge}$ indicates the percentage of cryptocurrency revenues immediately hedged through derivative instruments. (3) We define a liquidity buffer management value as $L_{required,t}={\theta }_{buffer}·{\overline{R}}_{daily}$.

3. Results and Analysis

3.1. Model Parameters and Assumptions

The simulation populates $N=1000$ heterogeneous agents drawn from six behavioral groups, each defined by ranges over risk tolerance $r_i$, age $a_i$, technological proficiency $s_i$, and additional behavioral parameters. Agent types are not mutually exclusive: an individual may simultaneously exhibit, for example, risk-seeking and tech-savvy characteristics, with parameters drawn from the intersection of applicable type ranges. To systematically explore the interaction between population composition, market environment, and policy design, we construct a four-dimensional scenario matrix (

Table 2. Scenario Matrix: Four Orthogonal Axes ($4\times 4\times 4\times 3=192$ Configurations).

Axis	Scenario	Param. 1	Param. 2	Param. 3
Risk Attitude	Equal	33% moderate	33% averse	33% seeking
	Conservative	25% moderate	50% averse	25% seeking
	Moderate-Heavy	50% moderate	25% averse	25% seeking
	Risk-Seeking-Heavy	25% moderate	25% averse	50% seeking
Tech Adoption	Tech-05	5% savvy	95% low-tech
	Tech-20	20% savvy	80% low-tech
	Tech-50	50% savvy	50% low-tech
	Tech-80	80% savvy	20% low-tech
Social Influence	Social-10	10% followers
	Social-30	30% followers
	Social-50	50% followers
	Social-70	70% followers
Market Condition	Bullish	$\mu =+0.40$	$\sigma =0.35$
	Neutral	$\mu =+0.05$	$\sigma =0.50$
	Bearish	$\mu =-0.30$	$\sigma =0.80$

) comprising four risk-attitude compositions, four technology-adoption levels, four social-influence intensities, and three market conditions, yielding $4\times 4\times 4\times 3=192$ distinct configurations.

Table 3. Complete Model Parameter Specification.

Parameter	Value/Range
Market Environment
Initial price $P_0$	$50,000
Drift/volatility ($\mu$, $\sigma$)	$+0.05$/$0.50$
Time step $\Delta t$	$1/365$ (daily)
Price floor	$100
Social Network (Watts–Strogatz)
Agents N/neighbors K/rewiring $\varphi$	1000/10/0.30
Clustering C/path length L	≈0.6/≈3.5
Policy Regimes ($f_{USD}=2\%$ for all)
Baseline/Conservative/Incentive $f_{crypto}$	3%/10%/1%
Dynamic $f_{crypto,t}$	$0.005+0.2\max (0,{\sigma }_t-0.6)$
Risk Mgmt $f_{crypto}$ (${\rho }_{hedge}$, ${\theta }_{conv}$, ${\tau }_{buffer}$)	5% (0.8, 0.3, 1.5)
Transit Authority
Conversion risk factor ${\rho }_{conv}$	0.30
Concentration target ${\alpha }^{\ast }$	0.20
Income ref. $Y_{ref}$/elasticity $\gamma$	$70,000/0.40
Market Condition Scenarios
Bullish: drift $\mu$/volatility $\sigma$	$+0.40$/$0.35$
Neutral: drift $\mu$/volatility $\sigma$	$+0.05$/$0.50$
Bearish: drift $\mu$/volatility $\sigma$	$-0.30$/$0.80$
Vol. multipliers	1.0, 1.4, 0.7, 1.2
Drift shifts	0.0, −0.10, +0.08, −0.05
Agent Types (parameter ranges)
Moderate Risk: $r_i$, age, $s_i$	$[0.3,0.7]$, 25–65, $[0.4,0.7]$
Risk-Averse: $r_i$, age, $s_i$	$[0.05,0.30]$, 45–100, $[0.05,0.4]$
Risk-Seeking: $r_i$, age, $s_i$	$[0.70,0.98]$, 18–45, $[0.6,0.95]$
Tech-Savvy: $r_i$, age, $s_i$	$[0.30,0.85]$, 18–40, $[0.8,0.98]$
Low-Tech: $r_i$, age, $s_i$	$[0.05,0.35]$, 50–100, $[0.02,0.3]$
Social Follower: $r_i$, age, $w_i$	$[0.25,0.65]$, 20–60, $[0.55,0.95]$

and

Table 4. Behavioral Parameter Specification with Sensitivity Ranges and Type-Specific Coefficients literature justification: ${\beta }_{risk}$—loss-aversion ratios [22]; ${\beta }_{stability}$—status quo bias in payment choice [25]; ${\beta }_{tech}$—TAM perceived ease-of-use [45]; $\tau$—bounded rationality in discrete choice [46]; $\eta$—habit persistence in payment behavior [24]; $\delta$—exponential recency weighting [48]; ${\alpha }^{\ast }$—conservative fiat-majority position for transit revenue.

Parameter	Symbol	Baseline	Range
Risk penalty	${\beta }_{risk}$	1.2	[0.5, 2.5]
Stability bonus	${\beta }_{stability}$	0.2	[0.05, 0.5]
Tech convenience	${\beta }_{tech}$	0.5	[0.2, 1.0]
Temperature	$\tau$	0.5	[0.1, 2.0]
Update rate	$\eta$	0.05	[0.01, 0.15]
Recency decay	$\delta$	0.3	[0.1, 0.6]
Concentration target	${\alpha }^{\ast }$	0.20	[0.10, 0.40]
Type-Specific Utility Coefficients
Agent Type	${\beta }_{risk}$/${\beta }_{tech}$/${\beta }_{stability}$	$\tau$	$\eta$
Risk-Averse	2.0/0.3/0.4	0.3	0.02
Moderate Risk	1.2/0.5/0.2	0.5	0.05
Risk-Seeking	0.6/0.7/0.1	0.8	0.10
Tech-Savvy	0.9/1.0/0.2	0.6	0.08
Low-Tech	1.8/0.2/0.3	0.3	0.02
High-Income	0.8/0.6/0.2	0.7	0.08
Social Follower	1.2/0.5/0.2	0.5	0.07

present all behavioral parameters with their baseline values, sensitivity ranges, and type-specific calibrations. The baseline values correspond to the moderate risk agent type. In the simulation, each agent type receives calibrated coefficient values reflecting its behavioral profile. When an agent belongs to multiple types (Section 2.1), its coefficients are the arithmetic mean of the applicable type rows.

Agent income follows a log-normal distribution $Y_i\sim \mathrm{LogNormal}({\mu }_Y,{\sigma }_Y)$ with ${\sigma }_Y=0.55$, producing a mean income of approximately $82,000, a standard deviation of $49,000, and a range of $25,000–$200,000. The location parameter ${\mu }_Y$ is conditioned on the active scenario axes, shifting the median from the baseline value of $70,000 in accordance with empirically documented income–behavior correlations, assuming wealthier populations have greater risk tolerance [22], higher digital literacy, and greater financial independence from peer influence. The cryptocurrency adoption rate $A_t$ for 1000 individuals follows the logistic choice decisions (Equation (8)). Each individual decides based on cost, risk, technological convenience, experience, and social influence.

Before presenting results, we acknowledge several simplifying assumptions. The GBM diffusion does not capture stochastic volatility or long-memory effects; the flash crash stress test (Section 3) partially addresses tail risk but does not model volatility clustering. The utility function omits psychological factors such as status effects and deeper habit formation. Static demographics preclude population turnover, the Watts–Strogatz network abstracts from homophily, and perfect liquidity assumptions may not hold during severe stress. These limitations are discussed further in Section 4.

Because agent-based simulations are stochastic—each run samples different random draws from the GBM diffusion process and from agent initialization—we employ a multi-seed replication strategy to ensure statistical robustness. Each of the 960 scenario configurations (5 policies × 192 population–market combinations) is run with 15 independent random seeds, yielding 14,400 total simulation runs.

3.2. Cross-Analysis Results

We begin by evaluating how adoption and stability vary across the four scenario axes under the Baseline Policy. Each of the 192 configurations is run 15 times with independent seeds, and we report means with 95% confidence intervals. As mentioned previously, these results are illustrative rather than predictive. They demonstrate the framework’s capacity for structured scenario analysis when calibrated with real-world data.

Table 5. Marginal effects of each scenario axis on adoption and stability, averaged over all levels of the remaining axes. Baseline Policy, $N=1000$ agents, 365 steps, 15 replications.

Scenario Level	Avg Adoption (%)	Avg Stability
Market Condition
Bullish ($\mu$ = +0.40, $\sigma$ = 0.35)	20.1	0.607
Neutral ($\mu$ = +0.05, $\sigma$ = 0.50)	17.6	0.598
Bearish ($\mu$ = −0.30, $\sigma$ = 0.80)	14.1	0.579
Risk Attitude Composition
Risk-Seeking-Heavy (50% seeking)	20.6	0.532
Equal (33/33/33)	17.2	0.597
Moderate-Heavy (50% moderate)	17.3	0.594
Conservative (50% averse)	14.0	0.655
Technology Adoption Level
Tech-80 (80% tech-savvy)	36.9	0.283
Tech-50 (50% tech-savvy)	23.6	0.605
Tech-20 (20% tech-savvy)	7.3	0.742
Tech-05 (5% tech-savvy)	1.3	0.748
Social Influence Intensity
Social-10 (10% followers)	18.1	0.576
Social-30 (30% followers)	17.6	0.588
Social-50 (50% followers)	17.0	0.600
Social-70 (70% followers)	16.5	0.613

presents the marginal effect of each axis, averaged over all levels of the other axes.

Technology adoption produces the largest swing ($\Delta =35.6$ pp between Tech-05 and Tech-80), followed by risk attitude ($\Delta =6.6$ pp) and market condition ($\Delta =6.0$ pp). Stability scores show meaningful differentiation. For example, high-tech scenarios (0.283) face substantially greater financial risk than low-tech scenarios (0.748), because the market-volatility×crypto-exposure interaction amplifies risk as adoption grows.

Figure 2 presents the full Risk × Tech interaction as a color-coded heatmap—one panel per market condition—with marginal effects ($\Delta$) annotated on the right and bottom of each panel.

As we notice, the technology effect is more significant. Moving from Tech-20 to Tech-80 increases adoption by ∼28–34% within each panel, while risk attitude adds ∼3–6% and market condition ∼5% across panels. The maximum in this subset (Baseline Policy, Social-50) is 45.5% (Bullish + Risk-Seeking + Tech-80). Across the full 960-configuration matrix, adoption ranges from 0.7% to 49.4%, demonstrating why multi-dimensional scenario planning is essential.

3.3. Policy Impact Analysis Across Different Market Conditions

We now evaluate how all five policies perform under each market regime. The three market scenarios produce qualitatively different price dynamics. Bullish markets feature steady appreciation with low volatility, while bearish conditions combine declining prices with high volatility that directly amplifies agents’ risk penalties. Figure 3 reports the 15 policy–market combinations, each averaged over all population configurations and 15 replications.

The Incentive and Dynamic policies achieve the highest adoption across all market conditions, outperforming the Conservative Policy. Stability scores are inversely related to adoption: the Conservative Policy achieves the highest stability (0.622 in bullish) by limiting crypto exposure, while the Dynamic Policy yields the lowest (0.571 in bearish).

3.4. Concentration Penalty Sensitivity Analysis

To address concerns regarding the influence of the stability score specification on reported results, we compare our default penalty (${\alpha }^{\ast }=0.20$) against the case where the concentration penalty is removed entirely. Because $S{c}_t$ is a post hoc evaluation metric that does not feed back into agent decisions, adoption rates are identical across both specifications—only the reported stability scores change.

Table 6. Stability Score Sensitivity to Concentration Penalty Specification. All runs use GBM diffusion; $S{c}_t$ is evaluated post hoc from the same price paths and adoption trajectories.

Scenario	Adoption (%)	$\mathit{Sc}$ (${\mathit{\alpha }}^{\mathbf{*}}\mathbf{=}\mathbf{0.20}$)	$\mathit{Sc}$ (No Penalty)
Bullish + Tech-80 + Risk-Seeking	45.5%	0.204	0.536
Neutral + Tech-50 + Equal	23.6%	0.633	0.679
Bearish + Tech-20 + Conservative	4.1%	0.718	0.901

reports results for representative scenarios.

Removing the penalty yields higher absolute scores (0.536–0.901 vs. 0.204–0.718) but preserves the relative ranking across scenarios, confirming that conclusions are robust to the penalty specification.

3.5. System Resilience Under Market Crash

The preceding results demonstrate how the GBM diffusion process interacts with agent heterogeneity under normal and scenario-varied conditions. To assess how the system responds to extreme market events—beyond what the continuous diffusion typically generates—we inject a flash crash: a 50% single-day price decline on day 60 (after the system has reached behavioral equilibrium). This extreme event approximates the kind of tail shock that the jump-diffusion specification (Equation (3)) is designed to capture stochastically; here we impose it deterministically for controlled analysis. We compare the Baseline Policy (no hedging) against the Risk Management Policy (80% hedging, 150% liquidity buffer).

Table 7. Flash Crash Stress Test: 50% Price Decline on Day 60. Price process: GBM diffusion with a deterministic $-50\%$ multiplicative shock on day 60 (analogous to a large jump in the jump-diffusion specification). Values are means across 15 replications. “pp” = percentage points (absolute change in adoption rate).

Metric	Baseline Policy	Risk Mgmt Policy
Pre-crash adoption (days 53–59)	18.4%	17.9%
Post-crash adoption (days 60–67)	5.0%	4.8%
Adoption drop (7 days post-crash)	−13.4 pp	−13.1 pp
VaR95 (day of crash)	$42.1	$16.8 (after hedging)
Recovery time to pre-crash adoption	∼19 days	∼19 days

reports the results.

A 50% crash causes adoption to fall from ∼18% to ∼5% within one week, as the volatility spike makes the risk penalty dominate agent utility. Recovery takes ∼19 days (the trailing volatility window length). Both policies produce nearly identical adoption drops because the Risk Management Policy hedges financial exposure without altering agent utility. However, the financial impact differs substantially: the Baseline Policy’s VaR₉₅ spikes to $42.1 on crash day, while the Risk Management Policy’s 80% hedging reduces this to $16.8—a 60% reduction in downside exposure despite identical behavioral responses.

Notably, within each market condition separately, population effects (technology + risk attitude) exceed policy effects by 18–26×: the full policy spectrum (1% to 10% fee) shifts adoption by only 1.5–2.7%, while technology literacy alone accounts for a 38–47% range. This suggests that, under these assumptions, digital literacy investments may be far more influential than fee optimization.

4. Discussion

The primary contribution of this work is the analytical framework itself—the specific numerical outcomes are contingent on synthetic calibrations, but the structured reasoning of the framework can be transferred to real-world planning and calibrated with empirical data. The multi-dimensional configuration matrix reveals that technology adoption dominates all other scenario axes, suggesting that digital literacy investments may be far more impactful than fee optimization. Market regime exerts a larger effect on outcomes than any policy lever, implying that transit authorities should prioritize adaptive mechanisms that perform robustly across conditions rather than optimizing for a single expected scenario. The model also captures temporal dynamics—regime-driven adoption shifts within days, asymmetric loss-aversion responses, and shorter recovery timelines after crashes—that static analyses cannot represent.

These findings align with and extend several threads in the existing literature. The dominance of technology literacy as a driver of adoption is consistent with the Technology Acceptance Model [45], which identifies perceived ease-of-use as a primary determinant of technology adoption—our results quantify this effect in the specific context of transit payment systems. The observation that social influence has a relatively modest effect under most configurations contrasts with theoretical predictions of strong cascading behavior [32,33], suggesting that in routine payment decisions, individual cost-risk calculations may dominate peer effects. The adoption–stability trade-off we identify parallels findings from the two-sided market literature [39], where platform operators must balance user acquisition against financial sustainability. From a smart city planning perspective, these results suggest that cryptocurrency integration should be evaluated as part of broader digital infrastructure investments rather than in isolation. Cities pursuing smart mobility strategies [44] may find that investments in digital literacy and payment infrastructure yield co-benefits across multiple services beyond transit, including parking, bike-sharing, and congestion pricing systems. For digital payment ecosystems, the framework highlights that the viability of any new payment instrument depends critically on the existing technological readiness of the user population—a finding with direct implications for phased deployment strategies where authorities first build digital competency before introducing volatile payment options.

A practical concern that our model does not address is network congestion: blockchain confirmation times are variable, and during periods of high transaction volume (e.g., Bitcoin backlogs exceeding 50 MB) passengers could face delays at fare gates. Transit authorities would need adaptive operating guidelines to handle these episodes without creating bottlenecks. First, a pre-funded wallet model—where riders load transit balances during off-peak network times and trips deduct locally—eliminates real-time blockchain dependency entirely; our model’s assumption of instantaneous payment processing is most realistic under this architecture. Second, automatic fallback protocols could monitor network congestion metrics and temporarily revert to fiat-only acceptance when confirmation times exceed a threshold (e.g., 15 min), ensuring uninterrupted fare collection. Third, authorities could select alternative assets with faster confirmation times during periods of congestion. The flash crash results (Table 7) further suggest that authorities should maintain fiat reserves sufficient to cover approximately three weeks of reduced crypto revenue following any major disruption, whether from price crashes or network outages.

All findings are conditional on the assumed calibration and cannot be used for recommendations. The specific adoption rates (0.7–49.4%) and stability scores are outcomes of the parameter specification; different rider demographics or different policies would produce quantitatively different outcomes while preserving the framework’s qualitative capabilities. The stability score’s configurable concentration target (${\alpha }^{\ast }$) affects score magnitudes but not the ranking of policies or scenarios (Table 6).

We acknowledge several limitations in our analysis. The baseline GBM diffusion underestimates tail risk (partially addressed by the flash crash stress test); a full stochastic volatility model would be a valuable addition to this study but remains a future extension. The utility function does not account for security anxiety, status effects, and deeper habit formation of individuals over time. Static demographics preclude population turnover, the Watts–Strogatz network abstracts from homophily, and regulatory dynamics are excluded. The most important next step is empirical calibration through real transaction data from pilot programs—survey-based estimation of agent distributions and risk attitudes for specific rider populations would transform the framework into a quantitatively grounded planning tool.

5. Conclusions

This paper presents an agent-based framework for evaluating cryptocurrency integration in transit payment systems. The model couples a GBM price diffusion process with heterogeneous agents who make payment decisions based on cost, risk tolerance, technological comfort, experience, and peer influence. We tested five policy regimes across a comprehensive scenario matrix spanning diverse population compositions and market conditions (bullish, bearish or neutral).

Three conceptual findings emerge from the analysis, though we note that these are conditional on the assumed parameter settings and synthetic calibrations rather than empirically validated relationships. First, under the assumed conditions, technology literacy dominates all other factors in determining adoption outcomes—by a wide margin over risk attitudes, market conditions, and fee policy combined. This suggests that transit authorities considering cryptocurrency payment may benefit from investing in rider-facing digital literacy and onboarding infrastructure rather than focusing narrowly on fee optimization, if they are willing to motivate use of alternative payment methods. Second, the simulations indicate a fundamental trade-off between adoption and financial stability: policies that encourage cryptocurrency usage tend to expose the authority to greater revenue volatility, but use of smart institutional hedging mechanisms can substantially reduce downside risk without suppressing rider behavior. Third, extreme market events cause rapid behavioral shifts that no fee policy can prevent; our stress tests suggest that maintaining adequate liquidity reserves and fallback protocols may be essential to ensure operational continuity during recovery periods.

The framework’s value lies not in the specific quantitative outputs—those outcomes are contingent on assumed parameters—but in the structured reasoning it enables. Transit authorities can use it to identify which planning variables appear to matter most for their context, stress-test policies under adverse conditions, and compare strategies across demographic scenarios before committing to real-world deployment. The multi-dimensional design reveals interaction effects that single-factor analyses would miss entirely, such as the amplification of risk-attitude differences in high-technology populations. However, we emphasize that empirical validation with real-world transaction data is necessary before these simulation-derived insights can inform actual policy decisions.

Several directions would extend this work. The most immediate priority is empirical calibration: survey-based estimation of agent type distributions, risk attitudes, and technology comfort levels for specific transit rider populations would enhance the contribution of the work. On the modeling side, incorporating stochastic volatility dynamics would better capture the volatility clustering observed in real cryptocurrency markets. Extending the agent specification to include dynamic demographics (cohort turnover, evolving digital literacy over time) and richer social network structures (homophily, community detection) would improve realism for longer planning horizons. Finally, expanding the policy space to include multi-asset strategies—where authorities accept stablecoins and CBDCs alongside volatile cryptocurrencies—would reflect the increasingly diverse digital payment landscape that transit systems will face in coming years.