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Modeling Trust and Liquidity Under Payment System Stress: A Multi-Agent Approach

Masoud Amouzgar

TL;DR

It is proved that, under mild conditions on memory persistence and threshold gating, aggregate withdrawal pressure can peak strictly after the outage nadir, including during the recovery phase, and payment substitution via instant transfer consistently reduces peak avoidance, yet its effect on cumulative outflows is non-monotonic under realistic merchant broadcast persistence.

Abstract

Operational disruptions in retail payments can induce behavioral responses that outlast technical recovery and may amplify liquidity stress. We propose a multi-agent model linking card payment outages to trust dynamics, channel avoidance, and threshold-gated withdrawals. Customers and merchants interact through repeated payment attempts, while customers additionally influence one another on a Watts-Strogatz small-world network. Customers update bounded memory variables capturing accumulated negative experience (scar) and perceived systemic risk (rumor), with merchants contributing persistent broadcast signals that may lag operational recovery. We prove that, under mild conditions on memory persistence and threshold gating, aggregate withdrawal pressure can peak strictly after the outage nadir, including during the recovery phase. Simulations reproduce behavioral hysteresis and confirm delayed peaks of outflows. We further study payment substitution via instant transfer: substitution consistently reduces peak avoidance, yet its effect on cumulative outflows is non-monotonic under realistic merchant broadcast persistence. Robustness experiments across random seeds show stable qualitative behavior. The model highlights why "status green" is not equivalent to risk resolution and motivates incident response strategies that address perception, merchant messaging, and post-recovery communication in addition to technical remediation.

Modeling Trust and Liquidity Under Payment System Stress: A Multi-Agent Approach

TL;DR

It is proved that, under mild conditions on memory persistence and threshold gating, aggregate withdrawal pressure can peak strictly after the outage nadir, including during the recovery phase, and payment substitution via instant transfer consistently reduces peak avoidance, yet its effect on cumulative outflows is non-monotonic under realistic merchant broadcast persistence.

Abstract

Operational disruptions in retail payments can induce behavioral responses that outlast technical recovery and may amplify liquidity stress. We propose a multi-agent model linking card payment outages to trust dynamics, channel avoidance, and threshold-gated withdrawals. Customers and merchants interact through repeated payment attempts, while customers additionally influence one another on a Watts-Strogatz small-world network. Customers update bounded memory variables capturing accumulated negative experience (scar) and perceived systemic risk (rumor), with merchants contributing persistent broadcast signals that may lag operational recovery. We prove that, under mild conditions on memory persistence and threshold gating, aggregate withdrawal pressure can peak strictly after the outage nadir, including during the recovery phase. Simulations reproduce behavioral hysteresis and confirm delayed peaks of outflows. We further study payment substitution via instant transfer: substitution consistently reduces peak avoidance, yet its effect on cumulative outflows is non-monotonic under realistic merchant broadcast persistence. Robustness experiments across random seeds show stable qualitative behavior. The model highlights why "status green" is not equivalent to risk resolution and motivates incident response strategies that address perception, merchant messaging, and post-recovery communication in addition to technical remediation.
Paper Structure (80 sections, 1 theorem, 19 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 80 sections, 1 theorem, 19 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Bank Runs and Liquidity Stress
  4. Threshold Models and Social Contagion
  5. Agent-Based Models of Financial Contagion
  6. Operational Risk and Payment System Resilience
  7. Positioning of This Work
  8. Model Overview
  9. Agent Definitions and State Variables
  10. Customer Agents
  11. Merchant Agents
  12. Payment Infrastructure
  13. Social Network Structure
  14. Merchant Exposure Patterns
  15. Dynamics and Update Rules
  16. ...and 65 more sections

Key Result

Theorem 1

Let $W(t)$ denote aggregate withdrawal outflow at time $t$, and let denote the time of minimum payment success probability (the outage nadir). Under Assumptions A1--A4, there exist outage and recovery trajectories such that That is, the peak of aggregate withdrawal pressure occurs strictly after the worst technical payment performance.

Figures (7)

  • Figure 1: Payment outage and behavioral response. The payment success probability (left axis) reaches its minimum during the outage, while customer avoidance and merchant broadcast severity (right axis) peak later and decay slowly during recovery.
  • Figure 2: Delayed emergence of withdrawal pressure. Aggregate withdrawal outflow peaks after the outage nadir, often during the recovery phase, confirming Theorem \ref{['thm:delayed_peak']}.
  • Figure 3: Effect of merchant broadcast persistence. Sticky degraded broadcasts sustain elevated avoidance even after operational recovery, whereas immediate broadcast clearing leads to faster behavioral normalization.
  • Figure 4: Peak avoidance with and without payment substitution. Instant transfer availability consistently reduces peak avoidance across random seeds.
  • Figure 5: Liquidity impact of payment substitution. While substitution reduces peak panic, its effect on cumulative withdrawals is non-monotonic under realistic merchant broadcast persistence.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Theorem 1: Delayed Peak of Run Pressure