## 2 Related Works
### Joint Attention in HRI
The participants interacted with two virtual robots--one that aligned its gaze with user-selected objects (JA condition) and one with an inconsistent gaze (non-JA). Trust was assessed post-interaction and one week later using a 14-item trust scale and net promoter score. The results showed no significant JA effect on trust, but initial trust was a strong predictor of long-term perception. The study highlighted the nuanced context-dependent role of JA in shaping interpersonal trust over time. In recent studies, [PERSON] [37] examined JA in HRI using a gaze-leading task, testing how robot gaze behavior (following vs. not following) and perceived disposition (joint vs. disjoint) influenced return-to-face saccades and user impressions. The participants selected on-screen objects while the robot faces responded with gaze shifts. The results showed faster return saccades when the joint robots behaved unexpectedly, suggesting increased sensitivity to gaze incongruence in these cases. In the same line, [PERSON] et al. [38] explored how the presence of a child-like robot showing gaze-based JA influenced users' drawing behavior. In a two-site experiment, the participants completed a drawing task first alone and then in front of a humanoid robot (iCub or Nico) with RJA capabilities. The results showed that the users tended to draw larger and faster in the presence of the robot, especially those who reported feeling closer to it, according to the IOS scale. These changes suggest that even minimal JA cues can subtly shape user behavior. The previous studies illustrate a range of approaches and evaluation methods used to examine the role of JA in HRI. Early work such as that of [PERSON] and [PERSON] [31] explored gesture-based and gaze-following mechanisms for establishing JA, contributing foundational insights into the technical feasibility of such interactions. More recent efforts examined JA in child-robot interaction contexts, as seen in [PERSON] et al. [32], where attentional cues were used to support word learning, or in the long-term in-home study by [PERSON] et al. [33], which demonstrated generalizable social skill improvements in children with Autism Spectrum Disorder (ASD). [PERSON] et al. [35] further compared responses to JA cues in children with and without autism, highlighting the robot's ability to evoke JA behaviors across diverse user groups. In parallel, studies such as [PERSON] et al. [19] have stressed the role of turn-taking for natural coordination, while [PERSON] et al. [34] and [PERSON] and [PERSON] [36] emphasized user-centered outcomes related to social presence and humanness. More recently, [PERSON] [16] introduced trust as a critical dimension influenced by JA behaviors. For instance, [PERSON] [37] investigated users' saccadic behavior in response to robot gaze congruence, while [PERSON] et al. [38] analyzed how the presence of a JA-capable robot influenced users' drawing patterns. These studies highlight how minimal gaze-based cues can subtly modulate user behavior, even in non-goal-directed contexts. Taken together, the studies discussed above demonstrate that implementing JA mechanisms in robots can enhance various aspects of HRI, such as attention alignment, social presence, trust, and task performance. These effects have typically been assessed using behavioral observations or subjective ratings, providing valuable insights into how users perceive and respond to attentional cues. However, while these dimensions have been well established, less attention has been paid to how JA mechanisms influence users' on-going engagement, particularly when comparing autonomous robots equipped with JA capabilities to those without. Understanding the impact of this metric could be useful for designing robots that not only initiate socially meaningful behaviors but also sustain user involvement throughout the interaction.