## 2 The Relevance of the Sense of Agency in Virtual Reality
### Sense of Agency: Theoretical Models  
Researching mechanisms to improve the sense of agency when interacting in an IVE imply knowing the psychological mechanisms that influence that perception. There are two main models to describe the neurocognitive models underlying the SoA [13], the Comparator Model and The Theory of Apparent Mental Causation. The first one suggests that the SoA primarily comes from underlying processes of motor control and it is inferred retrospectively, after the action is performed, based on its external consequences. This suggests that the SoA comes from the comparison between sensory predictions and real sensory feedback. The second one focuses on situational signals and suggests that the SoA is linked to the correspondence between the external events and our intentions.  
During the last decades, the perspective that has dominated research about the sense of agency is the one based on the Comparator Model. However, according to [14], the complete system of the SoA may be more complex and imply multiple processes on different cognitive levels. In addition to the comparative mechanism, many other factors contribute to a large degree to the SoA. These factors are, for instance, the selection of actions, the intention, the effort, the emotion, the retrospective inference, the achieved objectives and the social interaction. There are also other studies that suggest factors that do not influence the sense of agency. For example, the results in [15] show that presence and agency are not influenced by the appearance or the type of visualisation of the avatar.  
Research conducted in [14] shows a definition of SoA in terms of two layers: the sense of agency of one's own actions (body agency) and the sense of agency about the external events (external agency) (see Figure 2).  
The first layer implies self-consciousness: when one feels that their consciousness controls their body. The second layer is relevant for the interaction with the environment: when one feels in control of external events and that the environment is reacting coherently to their actions. This two-layer definition seems interesting for its application on IVEs, because it relates to the SoA. In fact, it relates not only to the avatar's behaviour, but also to the reactions from the environment. Thus, it involves multiple senses, such as sight, hearing and touch. This is relevant because research shows that the human sense of agency becomes stronger or weaker depending on the senses involved in the action. In the context of IVEs, the senses of sight and hearing have been extensively implemented. However, the sense of touch can greatly enhance the realism and immersion of the experience, but few environments have been developed taking into account haptic feedback. Haptic feedback can simulate physical interactions within the virtual world, making virtual experiences more tangible and believable ([16; 17]). Haptic influence in user experience was also studied in [18], where the authors suggested that haptic feedback on its own generates at least a better sense of presence than visual feedback. Stimulating the sense of touch by interacting with other agents and with virtual content can profoundly impact the user's psychological and emotional state.