Temporal dynamics of cue integration for sense of agency in social comparative context

Yunyun Chen; Xintong Zou; Hong He; Xuemin Zhang

doi:10.1111/bjop.70039

. 2025 Oct 14;117(3):910–931. doi: 10.1111/bjop.70039

Temporal dynamics of cue integration for sense of agency in social comparative context

Yunyun Chen ¹, Xintong Zou ², Hong He ³, Xuemin Zhang ^2,^✉

PMCID: PMC13353239 PMID: 41084987

Abstract

Cue integration theory suggests that the sense of agency arises from the interaction of multiple cues, weighted by their reliability and availability. However, whether this integration is dynamic or static remains unclear. This study explored the potential dynamics of cue integration by examining the interplay between internal and external cues in social comparison contexts. Participants in the two experiments controlled a circle to a target location, with the circle's motion either fluent or disfluent. After completing the task, the participants received feedback on their performance relative to others, delivered in either a social (hand gestures in Experiment 1) or non‐social format (arrow symbols in Experiment 2), presented either before or after they provided agency ratings. Results revealed that both socially and non‐socially formatted feedback influenced agency ratings for future actions (forward modulation) as well as for past actions (backward modulation). Notably, a dynamic pattern of integration was evident only between socially formatted feedback and motion fluency: under disfluent motion, forward and backward effects of socially formatted feedback intensified over time. Conversely, with fluent motion, the impact of socially formatted feedback diminished over time. These findings underscore the complexity of cue integration, indicating a need to incorporate temporal dynamics into cue integration theory.

Keywords: cue integration theory, sense of agency, socially formatted feedback, temporal dynamics

BACKGROUND

Understanding the relationship between our actions and their outcomes, inducing changes in the external environment through coordinated bodily movements, leads individuals to generate a subjective experience of controlling their actions and consequently the external environment. This subjective experience of controlling one's actions and their outcomes is referred to as the sense of agency (SoA) (Christensen et al., 2016; Haggard, 2017; Haggard et al., 2002; Haggard & Chambon, 2012; Moore, 2016). For example, when we type on a keyboard, we are aware that it is our own action of typing, and we are the agents causing that action, while also understanding that the sound of the keyboard is triggered by our action. This conscious experience is considered closely linked to self‐awareness, supporting self‐awareness and other psychological processes related to the self (Georgieff & Jeannerod, 1998; Hon & Yeo, 2021; Wen & Imamizu, 2022).

A growing body of research has highlighted the role of multiple cues in shaping SoA, leading to the development of frameworks such as the Cue Integration Theory (Moore et al., 2009; Moore & Fletcher, 2012) and the Optimal Cue Integration Framework (Synofzik et al., 2008, 2009, 2013). A key aspect of cue integration is its recognition of diverse influences on SoA, encompassing sensorimotor, cognitive, and contextual cues (Gentsch et al., 2015). According to Moore and Fletcher's (2012) cue integration theory, the integration of these cues follows principles of Bayesian optimization, utilizing statistically optimal strategies to construct the SoA. Notably, not all cues contribute equally to the final perception of agency. For example, human perception tends to prioritize visual information due to its reliability (Helbig & Ernst, 2007), and in a similar vein, cue integration for agency also relies more heavily on cues that are more reliable or available, such as predictive sensorimotor signals. Building on this, the optimal cue integration framework (Synofzik et al., 2008, 2009, 2013) further elaborates the mechanisms behind this flexibility. It suggests that the relative weight of each agency‐related cue is adjusted based on its current reliability and availability, allowing individuals to flexibly switch between different cues in varying contexts.

Subsequent studies have provided substantial support for the cue integration theory. For example, Moore et al. (2009) showed that a prime stimulus before actions, congruent or incongruent with the action outcome, had no effect on SoA during intentional actions. However, in passive actions, congruent primes enhanced SoA. The results from Moore et al. (2009) align with the predictions of cue integration theory, suggesting that during intentional actions with reliable internal cues, the influence of external cues decreases, whereas in passive actions, where internal cues are less reliable, external cues play a greater role. Nonetheless, some research indicates that cues may also influence SoA in an additive or independent manner. For example, Barlas and Kopp (2018) found that action choice and outcome congruency independently contributed to SoA (but see Chen et al., 2023, for contrasting findings). Despite the complex nature of cue integration, much of the current research conceptualizes cue integration as a static process. This overlooks the possibility that the weighting of different cues may change over time. Moore et al. (2011) found that surprising stimuli influenced implicit SoA only in later trials, indicating that cue utilization evolves progressively as participants adapt to the associative learning context. This finding suggests that temporal factors should be taken into account when investigating cue integration for SoA, as certain effects might become more prominent after sustained exposure, meriting further exploration.

Recent studies have increasingly turned their attention to how SoA is shaped by social effects (Vogel et al., 2021), such as social feedback—the evaluative information individuals receive from others about themselves or their behaviour (Xie et al., 2022; Zhang et al., 2022). Research suggests that social feedback can act as a delayed or retrospective cue, influencing SoA for previous actions. Specifically, negative social feedback (a cartoon sad face) enhances the magnitude of temporal binding (an implicit measure of SoA) between actions and their negative outcomes, compared with positive feedback (a cartoon smiling face) (Chen, He, et al., 2024). This finding highlights the feedback‐driven backward modulation effect on implicit SoA. Social feedback can also function as an online cue, shaping SoA for future actions. Chen, Zou, et al. (2024) found that individuals exhibited increased implicit SoA in trials following negative social feedback compared with those following positive feedback. The finding underscores the feedback‐driven forward modulation effect on implicit SoA. Given that participants in those studies could adjust their action to obtain better outcomes, the forward and backward modulations by social feedback may be driven by participants' proactive attempts to adjust their behaviour based on feedback (Chen, Zou, et al., 2024), reflecting a learning process from negative social feedback. In contrast, non‐social feedback (checkmarks and crosses) appears to exert only a backward modulation effect (Chen, Zou, et al., 2024). This dissociation highlights a potentially unique role of social cues in shaping SoA, warranting further investigation.

While previous studies have advanced our understanding of how social cues—particularly social feedback—influence SoA (Chen, He, et al., 2024; Chen, Zou, et al., 2024), they have largely overlooked another critical form of social effect: social comparative feedback. Social comparison, the process of evaluating oneself relative to others (e.g., Dijkstra et al., 2008; Wood, 1996), is pervasive in daily life, and comparisons with others provide individuals with valuable information about their abilities and social standing. As such, social comparison plays a key role in self‐assessment and the formation of self‐concept (Cheng & Lam, 2007), which are closely linked to the experience of agency (Hon & Yeo, 2021). However, to date, no study has specifically addressed how comparative feedback influences SoA, including whether such feedback exerts forward and backward effects. Individuals may receive comparison outcomes in various formats, such as socially enriched feedback (e.g., verbal comments ostensibly made by others) or socially neutral feedback (e.g., computer‐generated numeric scores) (e.g., Dijkstra et al., 2008). It remains unclear how different formats of social comparative feedback further modulate these effects. Therefore, the present study was designed to simulate a social comparison context, in which participants' performance on each trial was compared against the average performance of their peers. Experiment 1 primarily examined comparative feedback presented in a socially enriched format (socially formatted feedback), whereas Experiment 2 focused on comparative feedback presented in a socially neutral format (non‐socially formatted feedback). Drawing on previous research, we emphasized the social salience of comparative feedback in two ways: stimuli with strong social significance and explicit indications of human origin (Barker et al., 2018). Therefore, hand gesture images were used as feedback stimuli in Experiment 1, and participants were explicitly informed that the feedback was generated by the experimenter. In contrast, arrow symbols were used in Experiment 2, and participants were told that the feedback was computer‐generated. Beyond the manipulation of different formats, both experiments included a neutral condition alongside the standard positive and negative comparative feedback, aiming to more precisely determine whether modulation of SoA by feedback reflects enhancement due to positive comparative feedback (the positive‐enhancement effect), attenuation due to negative comparative feedback (the negative‐attenuation effect), or a combination of both. Because comparative feedback inherently involves evaluation relative to others, it is fundamentally social in nature. We hypothesized that comparative feedback would exert both forward and backward modulation effects, regardless of whether presented in socially or non‐socially formatted feedback (Hypothesis 1). However, which specific effect (positive‐enhancement or negative‐attenuation) is elicited by each feedback format, as well as whether the effects differ between the two, remains to be clarified.

On the other hand, previous studies have not examined how feedback cues—serving as either online (forward modulation) or delayed (i.e., backward modulation) information—interact with sensorimotor cues such as motion fluency. As a result, the characteristics of cue integration remain poorly understood. Lafleur et al. (2020) examined the influence of sensorimotor cues (consistency between actions and outcomes) and social contextual cues (single‐agent versus dual‐agent scenarios) on SoA. Participants freely applied varying levels of force to produce corresponding changes on a screen and were asked to report their SoA over the outcomes. The study found that SoA was more strongly reduced by sensorimotor inconsistency in the dual‐agent condition than in the single‐agent condition, indicating an interaction whereby unreliable social cues increased reliance on sensorimotor consistency. This finding indicates that cue integration in social contexts also follows an interaction‐based mechanism, and the influence of social cues on SoA may change depending on the reliability of the sensorimotor cue. However, as discussed earlier (Moore et al., 2011), cue integration may not be static but dynamically adjusted over time. Building on this, we hypothesize that comparative feedback will interact with sensorimotor cues, and that this interaction will exhibit temporal dynamics: the effect of comparative feedback may weaken over time under reliable sensorimotor cues, whereas under unreliable sensorimotor cues, the effect of feedback may gradually increase. Importantly, we expect this dynamic interaction to be more pronounced when feedback is presented in a socially enriched format, as comparative feedback with a higher degree of social salience may trigger stronger self‐evaluation (Hypothesis 2).

To address these questions, the present study employed a continuous movement paradigm (Le Bars et al., 2020, 2022) where participants continuously pressed keys to move a target to a specified location. Consistent with Le Bars et al. (2020, 2022), the smoothness of the target's movement was manipulated to indicate reliable and unreliable sensorimotor cues. The comparative feedback regarding the participants' performance relative to the average of others—either presented in a social (Experiment 1) or non‐social format (Experiment 2), was provided upon successful task completion. The comparative feedback varied in valence (positive, neutral, or negative). In previous studies, feedback was typically presented after action completion, followed by a measurement of SoA—an arrangement that primarily captures backward modulation, where forward effects had to be inferred indirectly by artificially categorizing the feedback in the previous trial. To more cleanly examine forward modulation, we implemented a separate forward block in which feedback was delivered after the judgement of agency, allowing it to serve as an online cue concurrent with the action in the following trial. This design enabled us to directly test whether and how feedback, together with sensorimotor cues, shapes the upcoming SoA independent of retrospective influences (the feedback‐driven forward modulation effect). A backward block was also implemented where feedback was presented after the action but before the judgement of agency, potentially affecting SoA for the current trial (the feedback‐backward modulation effect). Additionally, using a linear mixed model analysis, we examined whether and how the integration between sensorimotor cues and feedback changed on a trial‐by‐trial basis.

EXPERIMENT 1: EFFECTS OF SOCIALLY FORMATTED COMPARATIVE FEEDBACK ON SoA

Method

Participants

Linear mixed models (LMM) were employed to analyse the data. Given the absence of existing data directly applicable to both our research objectives and the statistical methods employed, the sample size was determined through simulation‐based power analyses using the mixedpower package in R (Kumle et al., 2018, 2021). The fixed effect coefficients (e.g., β = −.20 for the three‐way interaction) were derived from preliminary pilot data based on 10 participants. The simulations indicated that a minimum sample size of 20 participants was necessary to achieve over 80% statistical power for detecting the three‐way interaction of interest (see Data Analysis section). To be more conservative, 26 volunteers with normal or corrected‐to‐normal vision aged 18–30 (M = 22.19, SD = 2.70) were recruited. All participants provided written informed consent.

Apparatus

Experiment 1 is an online experiment programmed using CSS, JavaScript, and JS. The experimental programme was sent to the participant's computer, and participants were instructed via video connection to adjust their screen resolution to 1366 × 768 pixels and open the experiment programme in full‐screen mode using the Google Chrome browser. Furthermore, the participants were positioned 60 cm away from the computer screen, following instructions given by the experimenter. A live video link was maintained throughout the session to ensure that the participant's environment remained quiet during the experiment.

Procedure

The experiment consists of a practice session and a formal experiment.

As shown in Figure 1, the participants' task was to move a black ball from a starting point to an end‐point using the four directional keys on the keyboard. The screen background was white (RGB = 255, 255, 255), with the starting point represented by a grey square (RGB = 170, 170, 170), which remained at the center of the screen throughout the task. The end‐point was represented by a blue square (RGB = 0, 0, 255), which randomly appeared in one of the four squares located at the edges of the screen. The square formed by the centres of the four squares had a side length of 712 pixels.

Trial structure of Experiment 1. (a) In the backward block, the feedback is provided after the circle motion is completed but before the subjective SoA rating. Individuals' rating of the current trial's SoA could be influenced by the feedback provided. (b) In the forward block, the feedback is presented after individuals provided their ratings of SoA. Therefore, ratings of the current trial's SoA could be influenced only by feedback on previous trials. This study focused solely on the preceding trial.

The experiment began by presenting a fixation point ‘+’ (500 ms). Subsequently, the five squares were displayed on the screen for 2000 ms (with the end‐point marked in blue) to allow participants to prepare in advance. After 2000 ms, a black ball appeared in the centre of the grey square, and the participants were required to quickly move the ball from the starting point to the end‐point within 15 s. It is important to note that each key press can only prompt the ball to respond once. If the ball failed to reach the end‐point within the specified time, the trial ended and a failure message would be presented to the participant. In the high fluency condition, each key press caused the ball to advance by 6 pixels, whereas in the low fluency condition, the distance the ball travelled in response to each key press was randomly selected from one of four values: 1, 2, 10, or 11 pixels (i.e., 6 pixels ±4 or 5). This design, adapted from Le Bars et al. (2020), was intended to create a less fluent experience while maintaining an average movement speed comparable to that in the high fluency condition. Throughout the experiment, the participants were instructed to move the ball along the diagonal direction as much as possible, and they generally followed our instruction and attempted to move diagonally (See Appendix S1 for more details). Once the ball entered the blue square completely, key presses became ineffective, and the ball stopped responding to individual key presses. After 1000 ms, all stimuli disappeared.

In the backward block (Figure 1a), the participants received the picture of the hand gesture (200 × 300 pixels) regarding their control over the ball's movement process (2000 ms). They were informed that the feedback was based on their task completion time and reflected their level of control over the ball's movement – that is, their ability to quickly and accurately stop the ball at the target. The feedback compared their completion time on each trial to the average time of all previous participants. An upward thumb gesture image signified that the participant's control over the ball's movement in this trial was equal to or better than the average control (positive feedback), a downward thumb gesture image indicated that the participant's control over the ball's movement was worse than the average control (negative feedback), and a flat fist gesture image indicated the neutral feedback, meaning that the experimenter did not provide the outcome of the performance comparison on that trial. This set‐up aimed to simulate a social evaluation context in which feedback is sometimes withheld, thereby allowing us to examine the effect of receiving versus not receiving social comparison. In fact, the feedback was randomly provided, with each type of feedback occurring one‐third of the time. After the feedback presentation, the participants were asked to rate the extent to which they felt they controlled the ball's movement using a scale of 1–9 (no time limit). The question was: ‘During the movement of the ball, how much did you feel the movement of the ball was controlled by your key presses?’ A higher score indicated that the participants felt they had greater control over the movement of the ball. The method involved directly clicking on the empty circle in front of the corresponding number with the mouse. When the cursor was over it, it changed to a light grey solid circle. Clicking represented the participant's choice, and then the next trial began.

In the forward block (Figure 1b), the participants were initially asked to provide their judgement of agency. Following this, the feedback was displayed for 2000 ms, after which the next trial commenced.

At the end of the experiment, the participants were asked an open‐ended question: ‘Did you notice anything unusual during the experiment?’ This allowed them to report any irregularities or suspicions they experienced during the task.

Design

Each participant received 120 trials, consisting of 2 (fluency: high, low) × 3 (feedback: positive, neutral, negative) × 2 (block: retrospective, prospective) × 10 replications after a six‐trial practice session, where only neutral feedback was presented.

When investigating forward modulation by socially formatted feedback on SoA, trials were categorized based on fluency in the current trial and feedback from the previous trial. When exploring backward modulation by social feedback on SoA, feedback from the previous trial was also taken into account, in addition to fluency and feedback from the current trial.

Data analysis

Considering the random effects and the unbalanced experimental design in the forward block, the data were analysed using LMM via lme4 (Bates et al., 2015) and lmerTest (Kuznetsova et al., 2017) packages for R (R Core Team, 2016). More importantly, traditional data analysis methods average data across trials, overlooking phenomena that can only be revealed at the trial level. LMMs allow for examining how the interactions between predictors change across trials, thereby uncovering the temporal dynamic characteristics of cue integration. Starting with the full model, we included random intercepts for participants and used principal component analysis (PCA) (Barr et al., 2013) to progressively eliminate redundant variables with minimal contribution in the random slopes part until the model converged. The parameter (b) for each variable and its associated t‐tests (t, p) were calculated using the Satterthwaite approximation for degrees of freedom (Kuznetsova et al., 2017).

Data cleaning

Participants were excluded if they explicitly reported that the feedback stimuli were randomly presented or not reflective of their actual performance. No participant reported such suspicions; therefore, no one was excluded based on this criterion.

In the backward block, the first trial for each participant and the trials that followed a failing trial were excluded from further analysis (3.27%). Similarly, in the forward block, the first trial from each participant and the trials that followed a failing trial were excluded (3.29%).

Results

Forward modulation of SoA by socially formatted feedback¹

The means of the ratings in different conditions are shown in Figure 2a. Considering that individuals have not yet received feedback when judging their agency, the influence of feedback in the current trial on ratings was not taken into account. However, previous feedback may affect ratings on current trials. Therefore, fluency, previous feedback, trial number, and their interactions were included in the model. Additionally, since individuals may adjust their judgement of agency based on task performance, task completion time (standardized) was included as a fixed covariate in the model.

(a) Ratings as a function of fluency and socially formatted feedback on previous trials (forward block). (b) Ratings as a function of fluency and socially formatted feedback on current trials (backward block). Error bars represent 95% CI. The black dot represents the group mean and each grey dot represents a participant's ranting score.

Each of the three feedback conditions was coded using two dummy variables: positive (0.67, −0.33), neutral (−0.33, −0.33), and negative (−0.33, 0.67). This resulted in two contrast‐coded predictors: PrePosiFeed (positive = 0.67, neutral = −0.33, negative = −0.33) and PreNegaFeed (positive = −0.33, neutral = −0.33, negative = 0.67). Both contrast‐coded predictors were entered simultaneously into the model. Consequently, the parameter estimate for the PreNegaFeed represents the difference between the mean of the dependent variable in the negative feedback condition and that in the neutral feedback condition. Similarly, the parameter estimate for the PrePosiFeed represents the difference between the mean of the dependent variable in the positive feedback condition and that in the neutral feedback condition. Fluency (simple coding: fluency = 0.5, disfluency = −0.5) represents the fluency condition. For more model information, please see the Appendix S1.

The model revealed that the high fluency condition resulted in a significantly higher SoA rating compared with the low fluency condition, b = 0.66, SE = 0.16, t ₍₂₅₎ = 4.29, p < .001, 95% CI = [0.35, 0.97]. The participants gave significantly higher SoA ratings when they received positive feedback in the previous trial compared with when they received neutral feedback, b = 0.19, SE = 0.08, t ₍₃₉₎ = 2.30, p = .027, 95% CI = [0.03, 0.35]. Task performance had a significantly negative impact on SoA ratings (b = −0.52, SE = 0.04, t ₍₂₆₎ = −12.46, p < .001, 95% CI = [−0.61, −0.44]): the longer the task completion time, the lower the SoA rating.

Furthermore, a significant interaction between Fluency and PreNegaFeed was observed (b = −0.42, SE = 0.15, t ₍₃₄₎ = 2.71, p = .010, 95% CI = [−0.69, −0.12]), qualified by a significant three‐way interaction among Fluency, PreNegaFeed, and TrialNum (b = 0.36, SE = 0.16, t ₍₃₈₎ = 2.26, p = .030, 95% CI = [0.04, 0.68]). Simple slope analysis revealed that when the ball moved fluently, the weakening effect of previous negative feedback (as compared with previous neutral social feedback) was significant in the mid‐experiment (at the mean trial) with b = −0.27, SE = 0.11, t = −2.59, p = .01. It was marginally significant in the early experiment (−1 SD trial) (b = −0.27, SE = 0.15, t = −1.84, p = .07) and late experiment (+1 SD trial) (b = −0.28, SE = 0.14, t = −1.93, p > .05). When the ball moved disfluently, previous negative feedback increased SoA rating compared with previous neutral feedback in the early experiment, with b = 0.52, SE = 0.15, t = 3.56, p < .01. As the experiment progressed, this effect weakened and reversed (mid‐experiment: b = 0.15, SE = 0.10, t = 1.45, p = .15; late experiment: b = −0.22, SE = 0.14, t = −1.55, p = .12).

Further analysis

To further clarify the valence‐specific temporal effects observed earlier, we conducted an additional analysis aimed at directly testing whether the difference between positive and negative feedback varied across time, beyond comparisons to the neutral baseline. To this end, each of the three feedback conditions was coded using two dummy variables: positive (0.67, −0.33), neutral (0.67, −0.33), and negative (−0.33, −0.33). This resulted in two contrast‐coded predictors: PreNeuFeed (coded as neutral = 0.67, positive = −0.33, negative = −0.33) and PrePosiFeed (coded as positive = 0.67, neutral = −0.33, negative = −0.33). The parameter estimate for PreNeuFeed represented the difference between previous neutral and previous negative feedback, while the parameter estimate for PrePosiFeed represented the difference between previous positive and previous negative feedback.

The results indicated that the interaction between Fluency, PrePosiFeed, and TrialNum was significant, with b = −0.42, SE = 0.15, Z = −2.80, p = .004, 95% CI = [−0.71, −0.13]. Simple slope analysis (Figure 3) revealed that when the ball movement was not fluent, the difference between previous positive and negative feedback increased over the course of the experiment (early experiment: b = −0.22, SE = 0.15, t = −1.44, p = .15; mid‐experiment: b = 0.17, SE = 0.11, t = 1.51, p = .17; late experiment: b = 0.55, SE = 0.15, t = 3.62, p < .01). Conversely, when the ball movement was fluent, the difference between previous positive and negative feedback decreased over the course of the experiment (early experiment: b = 0.36, SE = 0.15, t = 2.41, p = .02; mid‐experiment: b = 0.32, SE = 0.11, t = 2.96, p < .01; late experiment: b = 0.28, SE = 0.15, t = 1.87, p = .06). These findings suggested that the forward modulation effect of socially formatted feedback weakened over time when the ball movement was fluent, while it strengthened over time when the ball movement was not fluent.

Interaction between fluency and previous socially formatted feedback over time. The light coral area represents the difference between previous positive and negative feedback, and the dotted line shows the fitted line for this difference. An asterisk (*) indicates that the difference changes over time significantly.

Backward modulation of SoA by socially formatted feedback

The means of the rating in different conditions are shown in Figure 2b. In this analysis of backward modulation, we aimed to examine how feedback and fluency in the current trial interact to influence the ratings. However, because participants' ratings may also be influenced by feedback from the previous trial, we included previous feedback as a covariate in the model to control for potential carryover effects. This approach allowed us to isolate the effect of current feedback without confounding influences from forward modulation (see Appendix S1 for detailed model specifications). For clarity, two contrast‐coded predictors were entered simultaneously in the model: PosiFeed (positive = 0.67, neutral = −0.33, negative = −0.33) and NegaFeed (positive = −0.33, neutral = −0.33, negative = 0.67).

The model revealed that fluency significantly influenced the judgement of agency (b = 0.67, SE = 0.16, t ₍₂₅₎ = 4.19, p < .001, 95% CI = [0.35, 1.00]), with high fluency significantly enhancing the judgement of agency compared with low fluency. Additionally, compared with the neutral condition with no explicit feedback, positive feedback significantly enhanced the judgement of agency (b = 0.70, SE = 0.13, t ₍₂₅₎ = 5.63, p < .001, 95% CI = [0.45, 0.95]), while negative feedback significantly decreased it (b = −0.73, SE = 0.11, t ₍₂₆₎ = −6.83, p < .001, 95% CI = [−0.95, 0.52]), indicating a significant feedback‐driven backward modulation effect on SoA. Additionally, it was observed that when the preceding trial involved negative feedback compared with neutral feedback, there was a significant decrease in the agency ratings (b = −0.18, SE = 0.06, Z = −3.00, p = .007, 95% CI = [−0.30, −0.05]), indicating the potential presence of forward modulation of feedback in the backward block. Task completion time significantly negatively impacted the agency rating (b = −0.31, SE = 0.05, t ₍₂₅₎ = −6.88, p < .001, 95% CI = [−0.40, −0.22]), with longer task completion times associated with lower SoA ratings.

Importantly, there was a significant interaction among Fluency, NegaFeed, and TrialNum, b = 0.31, SE = 0.14, Z = 2.21, p = .022, 95% CI = [0.05, 0.58]. As shown in Figure 4, simple slope analysis revealed that when the ball moved disfluently, the weakening effect of negative feedback gradually intensified as the experiment progressed (early phase: b = −0.47, SE = 0.16, t = −2.92, p < .01; mid‐phase: b = −0.63, SE = 0.13, t = −4.92, p < .01; late phase: b = −0.79, SE = 0.16, t = −5.06, p < .01). Conversely, when the ball moved fluently, the weakening effect of negative feedback gradually diminished as the experiment progressed (early phase: b = −0.97, SE = 0.16, t = −6.16, p < .01; mid‐phase: b = −0.83, SE = 0.13, t = −6.51, p < .01; late phase: b = −0.69, SE = 0.16, t = −4.35, p < .01). These results indicate that the enhancing effect of positive feedback remained stable throughout the experiment, while the weakening effect of negative feedback intensified as the experiment progressed during periods of non‐fluent ball movement, suggesting that the backward modulation effect of socially formatted feedback strengthens over time during non‐fluent movement. Conversely, the weakening effect of negative feedback diminished as the experiment progressed during periods of fluent ball movement, indicating that the backward modulation effect of socially formatted feedback weakens over time during fluent movement.

Interaction between fluency and socially formatted feedback over time. The light blue area represents the difference between neutral and negative feedback, and the dotted line shows the fitted line for this difference. An asterisk (*) indicates that the difference changes over time significantly.

Discussion

Experiment 1 investigated the pattern of the integration between sensorimotor cues and socially formatted feedback during the generation of SoA when the feedback acted as a delayed and an online cue, respectively. The results indicate that sensorimotor cues are powerful cues affecting SoA, with smoother movements leading to a stronger SoA. Although we did not make an a priori prediction regarding this effect, it is consistent with previous findings and therefore can be considered reliable (Le Bars et al., 2020, 2022; Metcalfe et al., 2013). On the other hand, as hypothesized a priori, the socially formatted feedback can influence the evaluation of SoA for actions that have already occurred (the backward modulation) as well as for actions that are about to be performed (the forward modulation).

Importantly, consistent with our predictions, the interaction between the motion fluency and the feedback varied over the course of the experiment. When the motion was fluent, indicating reliable sensorimotor cues, the forward and backward modulation effects of the feedback diminished over time; however, when the motion was disfluent, suggesting unreliable sensorimotor cues, both modulation effects of the feedback strengthened as the experiment progressed. These findings bolster the cue integration theory while also adding depth to it. In situations where sensorimotor cues are unreliable, the impact of external cues on SoA intensifies (Wen et al., 2017), whereas in cases of reliable sensorimotor cues, the influence of external cues on SoA diminishes. Furthermore, this study illustrates the dynamic nature of integrating internal and external cues in a social comparative context, thereby advancing the cue integration theory.

Previous study has shown that social and non‐social feedback modulate implicit SoA in distinct ways (Chen, Zou, et al., 2024). However, it remains unclear whether comparative feedback conveying socially relevant information—but presented in a non‐social format—can elicit forward modulation in addition to the backward modulation typically observed. Moreover, it warrants further investigation whether the dynamic properties of cue integration are generalizable or specifically tied to socially enriched feedback. Addressing these questions will help clarify whether it is the social content or the presentation format that primarily drives the effects observed in Experiment 1. Accordingly, Experiment 2 focused on feedback conveying social comparison outcomes in a non‐social format, that is, arrow stimuli.