*2.1. Perceived Risk of COVID-19 and Customer–Robot Engagement*

Perceived risk is a variable connected to the probability and magnitude of the occurrence of the damage [29], which has been widely used to explain consumer behavior [8,30]. Consumer behavior researchers define perceived risk in terms of uncertainty and consequences. Perceived risk increases with higher levels of uncertainty and/or the chance of greater associated negative consequences [31,32]. For example, if a consumer is considering choosing an unfamiliar restaurant for a dinner party, the perceived risk associated with this choice could arise because he or she does not know how the dishes of the restaurant will taste (uncertainty) and is worried that guests will think poorly of him or her if it is

not a good restaurant (negative consequences). In this study, we defined the perceived risk of COVID-19 as the possibility and the consequences as COVID-19 causing illness or death [32–34].

Following protection motivation theory [26,27], we propose that perceived risk triggered by COVID-19 will improve customer–robot engagement. When customers perceive the COVID-19 pandemic is riskier, they will perceive higher levels of uncertainty and infection [34,35]. Human beings are often regarded as the natural carriers of COVID-19 transmission. To reduce the risk of COVID-19, customers tend to be more avoidant of social contact with human staff than in normal times and attempt to social distance in restaurants and hotels. Indeed, choosing to engage with a service robot means a kind of avoidance to human frontline staff, which is viewed as a protection from being infected with COVID-19 [8,27,28].

Service robots can function as programmable tools which can sense, think, and act to engage in social interactions [14,15,36,37]. Prior research mostly focused on the context of general service, and this research documented reactance against service robots and autonomous technologies [19–23]. However, little focus has been on situations where customers would possibly prefer service robots and would choose to engage with a service robot [24,25]. It is necessary to explore the antecedents for consumers to engage with service robots and the underlying psychological mechanisms.

As a way to build and strengthen customer relationships, customer engagement can help companies establish a competitive advantage and achieve success [38]. In addition, it can improve customer satisfaction, customer loyalty, and company performance [38–40]. Customer engagement is a multi-dimensional concept, including cognitive, emotional, and behavioral aspects [39,41–43]. Previous research has focused on customer engagement with brand [38,40], community [41], organization [44], and other traditional objectives in marketing practice.

In the COVID-19 pandemic, there are more service robots employed in hotels and restaurants [8,15], and customers have begun to engage with these robots. Thus, we introduce the concept of customer engagement in the context of service robots. We define customer engagement with service robots (hereafter, customer–robot engagement) as the customer's personal connection to service robots that goes beyond transactions, including the reaction in cognition, emotion, and behavior [45]. Customer–robot engagement in the context of hospitality consists of attention, enthusiasm, and interaction. Attention describes the extent of customer paying attention to the service robot [46,47]; enthusiasm means how much customers are interested in and excited to be serviced by the robot [44,48]; interaction points out that customers share service robots with others or participate in online and offline activities related to a service robot [44,48,49].

In line with protection motivation theory [26,27,50], we explore the effect of the perceived risk of COVID-19 on customer–robot engagement in the hotel and restaurant industries. Protection motivation theory is a social cognitive theory that was developed to explain the influences of health threats on health attitudes and behaviors [26–28,50]. According to protection motivation theory, threat appraisal and coping appraisal are the two primary drivers of health behavior [26,27]. Threat appraisal refers to the beliefs about the severity and susceptibility of the health threat to the given person, which concerns the health threat's nature, its seriousness, and the propensity of it eventuating to affect the individual [26,34]. Coping appraisal refers to the evaluation of health-protective behavioral alternatives and responses to avoid the health threat and the negative consequences, which focuses on the effectiveness of the coping response to impede the threat [26,27,51].

When risk is salient, customers will show preference to a hotel with a service robot staff than a hotel with human staff [52]. Thus, when perceived risk is higher, the motivation is stronger to cope with uncertainty and the subsequent consequences [26,27,50]. Further, customers will be more likely to engage with the service robots. Specifically, customers will pay more attention to the service robots, will show more enthusiasm to the service robots, and will have more interactions with the service robots.

In sum, it is expected that customers who perceive a high level of risk for COVID-19 are more likely to engage with service robots in restaurant and hospitality services. Therefore, we propose the following hypotheses:

**Hypothesis 1a (H1a).** *Perceived risk of COVID-19 has a positive influence on customer–robot engagement, i.e., customers' attention to service robots*.

**Hypothesis 1b (H1b).** *Perceived risk of COVID-19 has a positive influence on customer–robot engagement, i.e., customers' enthusiasm in service robots*.

**Hypothesis 1c (H1c).** *Perceived risk of COVID-19 has a positive influence on customer–robot engagement, i.e., customers' interaction with service robots*.

#### *2.2. The Mediating Role of Social Distancing*

According to protection motivation theory, a higher perceived health risk will lead customers to take measures to avoid risks and protect themselves [28,51]. For example, consumers will reduce some purchase behaviors, which may bring negative consequences [53]. They will become more conservative, keeping their distance from new or risky products and services [30]. In addition, they will avoid negative consequences and take measures to protect themselves. In the COVID-19 pandemic, social distancing is a crucial measure to protect consumers when they perceive the risk of transmission of COVID-19.

Many governments promoted the prevention policies of quarantining or social distancing (i.e., maintaining a physical distance of at least 2 m (6 feet)) [54]. It is hard to keep this precise distance for most customers. A number of customers choose to reduce social contacts in order to maintain social distance and to comply with the government's prevention policy. Furthermore, many consumers have reduced their international travel and have cut down on other journeys to areas with large COVID outbreaks. In the COVID-19 pandemic, social distancing is considered an effective coping response to impede the COVID-19 threat [8,10,54]. For this reason, customers will be more willing to socially distance as a kind of protective or coping method in service places when they perceive a higher risk of COVID-19. Once they perceive higher health risks, they will be active in protective behaviors [26,51], including social distancing. Even after quarantine, many customers continued to engage in avoidance and protective behaviors in service places [55]. Therefore, we infer that the perceived risk of COVID-19 will influence customer social distancing.

If customers want to keep social distancing, they will likely embrace some options that would reduce social contact [52]. Once the intention of keeping social distancing was increased, people would decrease direct contact with humans [12], and they will be more likely to engage with services provided by robots. Even service robots can convey social meaning to customers; they are mostly functional service robots, which perform labor such as ordering or delivery in hotels and restaurants. Engagement with service robots can replace some social activities and reduce risk from social contact. Engagement with a service robot can be viewed as a protective method, which can reduce the chances of being infected with COVID-19. In addition, service robots can interact with humans, replacing some social activities [23]. Based on these functions of service robots, service robots can be an attractive consumer choice to protect themselves in the context of a public health emergency. Specifically, customers will pay more attention to service robots, show more enthusiasm to service robots, and seek out more interactions with service robots. As a result, we propose the following hypotheses:

**Hypothesis 2a (H2a).** *The influence of perceived risk of COVID-19 on customer–robot engagement, i.e., customers' attention to service robots*.

**Hypothesis 2b (H2b).** *The influence of perceived risk of COVID-19 on customer–robot engagement, i.e., customers' enthusiasm in service robots*.

**Hypothesis 2c (H2c).** *The influence of perceived risk of COVID-19 on customer–robot engagement, i.e., customers' interaction with service robots, is mediated by the social distancing*.
