The opinion-dependent product spread over higher-order social networks

In the product spreading process, adoption decisions are typically modeled as being driven by pairwise influence, such as word-of-mouth communication, whereas higher-order social influence associated with community structures in social networks is often overlooked. In addition to social influence, self-evolving opinions toward products also play a crucial role in shaping adoption decisions. To jointly capture product-related opinions and higher-order social influence, we propose an opinion-dependent product spread framework over higher-order social networks by coupling product adoption with opinion formation on a two-layer directed hypergraph, while explicitly incorporating weak ties representing latent social relationships. In this framework, the adoption layer is modeled as a higher-order contagion process capturing group influence, whereas the opinion layer is modeled as a higher-order interaction process characterizing the effective cooperative behavior shaped by the collective actions of multiple agents. We establish convergence and stability conditions for all-adopted, non-adopted, and partially-adopted scenarios, and analyze the impact of higher-order interactions on the product spreading process. The framework is further extended to competitive markets to describe the dynamics of two competing products on higher-order social networks. Numerical simulations on synthetic and real-world hypergraphs indicate that higher-order interactions enhance adoption efficiency, increase steady-state adoption and opinion levels in partially-adopted scenarios, prolong product life cycles in non-adopted scenarios, and amplify winner-takes-all outcomes in competitive diffusion. These results highlight the decisive role of higher-order social influence in the product spreading process.