Crisis Response Modes in Collaborative Business Ecosystems: A Mathematical Framework from Plasticity to Antifragility

Collaborative business ecosystems (CBEs) are increasingly exposed to disruptive events (e.g., pandemics, supply chain breakdowns, cyberattacks) that challenge organizational adaptability and value creation. Traditional approaches to resilience and robustness often fail to capture the full range of systemic responses. This study introduces a unified mathematical framework to evaluate four crisis response modes—plasticity, resilience, transformative resilience, and antifragility—within complex adaptive networks. Grounded in complex systems and collaborative network theory, our model formalizes both internal organizational capabilities (e.g., adaptability, learning, innovation, structural flexibility) and strategic interventions (e.g., optionality, buffering, information sharing, fault-injection protocols), linking them to pre- and post-crisis performance via dynamic adjustment functions. A composite performance score is defined across four dimensions (Innovation, Contribution, Prestige, and Responsiveness to Business Opportunities), using capability–strategy interaction matrices, weighted performance change functions, and structural transformation modifiers. The sensitivity analysis and scenario simulations enable a comparative evaluation of organizational configurations, strategy impacts, and phase-transition thresholds under crisis. This indicator-based formulation provides a quantitative bridge between resilience theory and practice, facilitating evidence-based crisis management in networked business environments.