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With the evolution of the turbulent environment constantly triggering the emergence of a trust crisis between organizations, how can university–industry (U–I) alliances respond to the trust crisis when conducting green technology innovation (GTI) activities? This paper aims to address this issue.

The authors examined the process of trust crisis damage, including trust first suffering instantaneous impair as well as subsequently indirectly affecting GTI level, and ultimately hurting the profitability of green innovations. In this paper, a piecewise deterministic dynamic model is deployed to portray the trust and the GTI levels in GTI activities of U–I alliances.

The authors analyze the equilibrium results under decentralized and centralized decision-making modes to obtain the following conclusions: Trust levels are affected by a combination of hazard and damage (short and long term) rates, shifting from steady growth to decline in the presence of low hazard and damage rates. However, the GTI level has been growing steadily. It is essential to consider factors such as the hazard rate, the damage rate in the short and long terms, and the change in marginal profit in determining whether to pursue an efficiency- or recovery-friendly strategy in the face of a trust crisis. The authors found that two approaches can mitigate trust crisis losses: implementing a centralized decision-making mode (i.e. shared governance) and reducing pre-crisis trust-building investments. This study offers several insights for businesses and academics to respond to a trust crisis.

The present research can be extended in several directions. Instead of distinguishing attribution of trust crisis, the authors use hazard rate, short- and long-term damage rates and change in marginal profitability to distinguish the scale of trust crises. Future scholars can further add an attribution approach to enrich the classification of trust crises. Moreover, the authors only consider trust crises because of unexpected events in a turbulent environment; in fact, a trust crisis may also be a plateauing process, yet the authors do not study this situation.

First, the authors explore what factors affect the level of trust and the level of GTI when a trust crisis occurs. Second, the authors provide guidelines on how businesses and academics can coordinate their trust-building and GTI efforts when faced with a trust crisis in a turbulent environment.

First, the interaction between psychology and innovation management is explored in this paper. Although empirical studies have shown that trust in U–I alliances is related to innovation performance, and scholars have developed differential game models to portray the GTI process, building a differential game model to explore such an interaction is still scarce. Second, the authors incorporate inter-organizational trust level into the GTI level in university–industry collaboration, applying differential equations to portray the trust building and GTI processes, respectively, to reveal the importance of trust in CTI activities. Third, the authors establish a piecewise deterministic dynamic game model wherein the impact of crisis shocks is not equal to zero, which is inconsistent with most previous studies of Brownian motion.

This research delves into the realm of Business Model Innovation (BMI), integrating it with the human-centric, sustainable, and resilient principles of Industry 5.0, proposing a new theoretical framework.

An abductive approach has been chosen to expand existing knowledge developing new ideas based on emerging phenomena. Data were gathered via semi-structured interviews with directors, managers and curators of public institutions in Italy, Switzerland, Germany and Spain encompassing Galleries, Libraries, Archives, and Museums (GLAM). These data were subsequently subjected to thematic analysis.

The findings indicate that the main enablers for Business Model Innovation (BMI) in combination with Industry 5.0 encompassed stakeholder, customer and organizational engagement, collaborative environment, knowledge and innovation management, and sustainability. These drivers were effectively leveraged through three pivotal facilitators-inhibitors: technology, resources, and leadership.

The principal constraints are rooted in the narrow contextual focus and the limited participants number. However, upcoming research efforts may broaden the horizons of this multifaceted and extensive investigation.

This study is groundbreaking as it fills a significant gap in the existing literature by integrating Business Model Innovation (BMI) with the Industry 5.0 paradigm, a novel approach that has not been explored previously. Additionally, the inclusion of GLAM institutions in this research adds a unique dimension, as they have been largely overlooked in both research domains.