Robots deployed in public spaces must necessarily deal with situations that demand them to engage humans in a socially and culturally appropriate manner. However, social environments are often complex and ambiguous: many queries to the robot are collaborative (e.g. a family), and in case of conflicting queries, social robots need to participate in value decisions and negotiating multi-party interactions. Given the strong influence of the people's demographic information and social schema among people, such as relationships and hierarchies, the focus of this research is to examine whether and how people exhibit socio-psychological effects with a shared robot deployed at international events or spaces (e.g. airports). With the aim to investigate who robots should adapt to (children or adults) in multi-party situations within human-robot interactions in public spaces and whether this adaptation can be influenced by culture, this paper presents a cross-cultural study conducted online. The results include a number of interesting findings based on people's relationship with a child and their parental status. In addition, a number of cross-cultural differences were identified in respondents' attitude towards robot's multi-party adaptation in various public settings.