With the rising complexity of contemporary smart city development and deteriorating environmental and economic sustainability, the triple bottom line (TBL), i.e., social, environmental, and economic sustainability, calls for the engagement of open innovation-style technologies [1]. Open source is an open innovation model in the digital era [2]. Open-source diffusion constitutes an information propagation paradigm, anchored on the tenets of unrestricted access, collective sharing, and amendment of source codes, knowledge, and information resources. Initially rooted in the field of computer software development, it encompasses not only the application of open-source software and open-source hardware, but also the sharing and utilization of open-source resources such as open-source data; it embodies a community-powered innovation model. The characteristics of open-source diffusion, such as openness, sharing, transparency, and customisability [3], fit with the idea of green AI aiming at efficient, sustainable and equitable development of smart cities and future technologies ^[4][5][4,5], and it can provide a supportive and facilitating mechanism for autonomous systems and smart digital sustainable implementations [6].

The development of open-source operating systems, as a crucial vehicle for open-source diffusion, contributes to the diversification of intelligent technologies and enables market freedom of choice ^{[7][8][9][10]}[7,8,9,10]. In competition among open-source operating systems (Table 1), kernel update and optimization of an operating system is a core task of the open-source platform ^[11][12][11,12]. Kernel is the core of an open-source operating system, which controls the operation of computer hardware and provides services for applications. Open-source software includes the kernel of the open-source operating system, as well as other application programs, tools, and libraries, which constitute an open-source software ecosystem [13]. The source code of the operating system kernel is open for sharing [14], and people can use, modify, and disseminate it freely. Open-source operating systems have diverse brands and business models [15], and the license adopted also affects its development, distribution, and use [16].

Currently, the Android–iOS–Windows triple oligarchy of operating systems needs to be broken ^[17][18][17,18], which not only reduces user dependency risks and introduces more competitors, igniting greater innovation vitality, but also holds significant importance in mitigating the risk of supply chain disruptions. In parallel, the lack of resources, developers or maintainers in the open source community, or unhealthy software industry structures and trade conflicts can lead to supply chain disruption risks for open-source operating system software. Therefore, intelligent device manufacturers have started actively developing their own open-source operating systems to counter the threat of proprietary software monopolies and technology disruptions, also adopting incentive mechanisms such as software policies [19], open data [20], infrastructure ^[21][22][21,22], talent cultivation [23], and global collaboration ^[21][22][21,22] to further promote open-source diffusion [24].

To mitigate the risks associated with the supply chain of the Android–iOS–Windows triple oligarchy, open-source platforms can endeavour to expand their user communities and attract more developers to participate. Additionally, governments can enhance regulations, incentivize maintenance efforts, and allocate public resources and funding to foster the diffusion of open-source technologies and contribute to the sustainability, fairness, and efficiency of smart digital technologies. Therefore, this research is grounded in the theory of open-source diffusion and utilizes an evolutionary game approach to investigate the evolving dynamics among three key stakeholders: open-source platforms, users, and governments, within the realm of open-source diffusion.

2. Open Source in Smart Digital Technologies

Smart digital technologies become common solutions to urban crises associated with the climate, epidemics, natural disasters, and socio-economic factors ^[25][26][25,26] concerning the triple bottom line (TBL), i.e., social, environmental, and economic sustainability [1]. Artificial intelligence is rapidly becoming a key element of smart cities ^[27][28][27,28], helping to improve efficiency and automation [29]. Such technology poses significant risks of privacy violations and disruption through opaque decision-making processes [30]. Emerging challenges, including massive data, heterogeneities, complex dependencies, distributed storage and computing, and data [31], are open issues that need to be confronted by smart digital technologies. The triopoly shaped by Android–iOS–Windows has brought about a technological ecological monopoly, limiting competition and innovation [17], thus leading to a lack of diversity and flexibility in the development of smart digital technologies and smart cities [18] as well as restricting consumer choice and innovation [32]. Open-source operating systems, such as Debian 12 [33], Ubuntu 23 [34], and HarmonyOS 4 [34], and open-source software, such as PyTorch 2 [35] and SciPy 1 [36], promote technology sharing and cooperation, break monopolies, establish open technology platforms [37], build collaborative ecosystems, and cultivate an open innovation culture [38]. Thus, smart digital technologies and the sustainable development of smart cities complement open source and open innovation [39], and together they promote the sustainable development of society [40]. Open innovation and open source are intricately connected. As outlined by Chesbrough ^[41][42][41,42], at the heart of open innovation lies the pursuit of external innovation resources from both within and outside the organization in order to generate value [43], enhance the efficiency and quality of innovation [44], spur technological transformation [45], and drive business model innovation [46]. Additionally, it promotes international collaboration and knowledge sharing ^[47][48][47,48], facilitates the reconfiguration and optimization of intellectual property and industrial chains [49], and fosters the overall development of industries and economies ^[50][51][50,51]. By adopting the paradigm of open innovation, open source is an internet-based collaborative model that pools efforts of crowd intelligence through the open sharing of knowledge and technical resources [52] to improve efficiency and quality of innovation [53]; this advocates free, shared, and co-creation [3], and it effectively addresses technological inequities and privacy violations [54]. Open-source operating systems promote technological security [55], technological pluralism [56] and smart digital infrastructure [57]. Open source as public goods expanding business models, based on its tacit knowledge [58], can be the activation engine for innovative regional development ^[59][60][59,60] and smart technologies ^{[4][40][61][62]}[4,40,61,62]. During the evolution of open source [63], attention concerning the ecosystem radiates from hardware and software to their developers, users, communities, platforms and other relevant organizations and government departments [64], achieving fast, flexible, and secure application development through collaborations [65].

3. Infrastructure Risk Mitigation

With the advancement of information technology and digital transformation, an increasing number of enterprises now rely on software operating systems, and the risk of software supply chain disruption has gradually received more attention [66]. The risk of software supply chain disruption typically includes software vulnerabilities and malicious code, supplier bankruptcy, cyberattacks, and global crises, resulting in major impacts on a company’s business operations and data security [67]. Enterprises need to take effective measures to manage the risks in software supply chain disruption [68], establish socio-technical frameworks [69], and reduce the impact of disruptions. Open source helps enterprises mitigate the risks of software supply chain disruption ^[70][71][70,71]. For instance, enterprises can use open-source software vulnerability scanners to scan for vulnerabilities in software systems and detect and repair potential issues in a timely manner [72]. Furthermore, enterprises can use open-source software supply chain security auditing tools to check source codes and assess whether security practices and processes of the suppliers comply with standards [73]. Long-term cooperation with software suppliers can also reduce the occurrence and impact of software supply chain disruption [74]. When seeking software suppliers, enterprises should focus on their reliability, technical capabilities, and security measures, establishing long-term cooperative relationships. Moreover, enterprises should work with software suppliers to explore novel security solutions, establish mutually trusted cooperative relationships, and jointly address the risk of software supply chain disruption [75]. Open source has the advantage of coping with the risk of software supply disruptions. However, open source does not reach a wide enough audience, and its low market share is major disadvantages ^[76][77][76,77]. Thus, the mechanism of open-source diffusion has become an urgent issue needing to be addressed.

4. Open-Source Diffusion

Joseph Schumpeter was the first scholar to discuss the issues of technological diffusion and product diffusion [78]. He believed technological diffusion was the process through which new technologies gradually spread from research centres to peripheral areas. In this process, the flow of technology from innovators to imitators was viewed as a kind of knowledge “penetration”, which promoted productivity growth. Rapid diffusion of technology could greatly accelerate economic growth. Product diffusion was a special form of technological diffusion, referring to the process of expanding products produced originally in one country or region to other countries and regions through exportation, franchising, and other means. Product diffusion could bring wider markets and higher profits, further promoting economic growth. The scope of technology diffusion mainly includes the domestic and global markets, intra- and inter-enterprise markets, and government markets [79]. The models for calculating technology diffusion include the innovation diffusion model, incentive model, and contagion model [80]. In practice, technology diffusion connects product diffusion. Product diffusion refers to the process of introducing and promoting new products in the market, including market demand, market segmentation, and promotion strategies [81]. Open-source software is diffused at the level of artificial artifacts ^[82][83][82,83]. The essence of open-source diffusion is the shared spreading of source code and technical documentation as well as asynchronous participatory innovative iterations [84]. Community-driven operation facilitates rapid software diffusion [85], and open-source software developers interact with users on community platforms to acquire user needs and proactively address relevant user issues, thus providing technical support and upgrade services to increase user retention and loyalty. Industry applications promote open-source diffusion [86] by integrating open-source software into vertical application systems; it enables vertical industries and application areas, increases software market value and demand, and achieves rapid diffusion and profit. In social network operation [87], open source software can use social media and other network platforms for community and brand promotion, actively expand user networks and increase software awareness. In summary, open source has characteristics of openness and sharing, and is a paradigm of open innovation. Its diffusion model has unique methods. Open-source diffusion is expected to further promote smart digital infrastructure and sustainability as well as mitigate software supply chain risks.