Comparing Static and Dynamic Decision Tasks Using Pupillometry: Expected Loss is More Important than Defined Reward

Abstract

We report on two experiments using pupillometry to explore decision-making. In Experiment 1, participants observed a static image of the game. In Experiment 2, participants interacted with a computer agent in a cooperative game. A Tobii Pro Fusion running at 120Hz tracked participants’ eyes. Ten participants completed nine trials in each experiment. Percentage change in pupil diameter from a baseline, in Experiment 1, is similar for both targets, suggesting that participants treat low and high rewards equally. In experiment 2, there is also little change in pupil diameter when participants select low-value targets. But when the participant chooses high-reward and the computer chooses a low reward, pupil diameter is affected. This suggests that when participants expect a high reward, but the computer does not cooperate, this is experienced as loss and pupil diameter increases. Loss is more important than reward (as Prospect Theory proposes) and relates to viewing opponent’s actions.

Introduction

Eye-tracking serves an important role in analyzing human activity. Variation in pupil size can indicate workload levels (Ma et al., 2024) which can support adaptative user interfaces (Kosch et al., 2018). We aim to discover whether pupillometry can detect decision strategy. Adaptive-gain theory (Aston-Jones & Cohen, 2005) postulates a relationship between pupil diameter and decision, and argues that pupil diameter increases with decision-space exploration (while pupil diameter reductions indicate decision-space exploitation). In this context, “exploring” is not just scanning for options, but implies an active search through which objects are interpreted in terms of reward or threat. As such, “explore” could relate to decision-making, acquiring relevant information, or reducing uncertainty.

Jepma and Nieuwenhuis (2011) had participants select cards from 4 decks to maximize payoff. Participants could select cards from one pack or could change to another pack if they expected higher-value cards. As predicted by adaptive-gain theory, when participants continued with the same deck, their pupil diameter either decreased or remained the same (i.e., the participant chose to exploit the current deck by continuing with it). When participants decided to switch to another deck, pupil diameter increased. Change in pupil size could also have occurred due to experience of loss when the current deck failed to provide sufficient reward. Indeed, Yechiam and Telpaz (2011) demonstrate “that losses led to significantly elevated pupil size and response time compared to equivalent gains during the decision task.” Kahneman and Tversky’s (1979) prospect theory could explain this finding, given that loss aversion has a greater influence on decisions than expected gains. Likewise, Peysakhovich et al. (2015) demonstrate that changes in pupil dilation could predict decisions in a maritime threat evaluation task, that is, threat could be a potential loss, or at least, a defined risk.

In summary, we hypothesize that pupil diameter changes according to both task demands and decision type. Of interest is whether changes due to decisions are consistent between static and dynamic versions of a task and whether the changes are more likely to result from expected gain or expected loss. Thus, we explore whether the dynamics of a two-player game affect experience of loss. That is, does a decision made in anticipation of the action of another player, differ from a decision made in response to the action of that player? More specifically, is “loss” more apparent when one can see the action of the other player? If this is the case, then one might expect differences in pupillometry between static and dynamic versions of the same game, and this might reflect differences in the interpretation of expected gains and losses in the game.

Approach

In this paper, we report two experiments that use changes in pupil size to explore decision-making. We used two versions of a two-player collaborative decision task. The task is a modification of a grid-world Stag-Hunt game (Baber et al., 2024). In Stag-Hunt, two players can either cooperate to capture a stag to gain higher reward for each or work alone to capture a hare for lower reward (Figure 1).

Figure 1.

Example of Grid-World Decision task. Participants assume the role of the Blue hunter and decide whether they will choose to hunt the Stag, in collaboration with the Red hunter, or opt to hunt hares alone. The Stag (if collected collaboratively) is worth five points. But if the participant opts to hunt stag and the red hunter chooses to hunt hare, then the reward is zero points for participant and one point for red hunter. When participants choose to hunt hare, they receive one point.

In Experiment 1, ten participants viewed a static image of a grid-world version of a collaborative game. This image includes two players (one in each of the upper corners of the grid), a stag, and two hares. Participants studied the image to decide between collaborating with the other player to catch the stag (and thus gain maximum points if both players collaborate) or working independently (and gain minimum points by catching a hare individually). While different configurations of objects changed on each trial, in all cases the stag and other player occupied adjacent squares (to suggest that the other player would most likely opt for stag). The participant’s biggest risk is that the other player might not collaborate and thus leave no reward.

In Experiment 2, ten participants (who had not participated in Experiment 1) interacted with a computer agent. Participants moved one player, and the computer moved the other. Unknown to participants, the computer followed one of two policies: (1) collaborate on the majority (70%) of turns or (2) work independently 70% of the time. In this case, participants were playing with a computer that could either collaborate or not in the decision task.

Collection and Preparation of Data

A Tobii Pro Fusion running at 120 Hz tracked each participant’s pupil diameter. For each experiment, 10 participants completed 9 trials. Each trial involved a different configuration of the grid world. We used pupil diameter averaged across left and right eyes (which Tobii terms “pupil diameter filtered,” in millimetres) for analysis. Prior to analysis, we removed fixations of less than 100 ms (likely from blinking or saccades) and times of missing pupil diameter data (likely due to participants looking away from the screen). Rather than report mean pupil diameter, we calculated percentage change from baseline. This provided a cleaner means of normalising the data for comparison across conditions and participants, and allowed the analysis to accommodate environmental and physiological differences between individual trials. We defined each grid cell as an Area of Interest (AoI) and used this to determine the average pupil diameter for cells containing a specific object. In order to normalise data for comparison between participants and conditions, we analyse the data in terms of percentage change from baseline. Baseline pupil diameter was defined by two seconds of fixation prior to the decision task and on cells that did not contain specific objects. For the dynamic task, custom-built software recorded the grid cell for each object and then used the AoIs occupied by the object to calculate pupil diameter for each object.

Pupil diameter changes over the course of a single trial. Figure 2 illustrates correlated changes with the timing of specific events (e.g., pressing a key or fixating on a specific object). Fixation on objects also tends to increase pupil diameter.

Figure 2.

Defining events in eye-tracking data. This shows the elapsed time of the recording, using Figure 1, with the timing of specifc events (i.e., fixation on a specific object on the screen or pressing a key to move the blue player).

From this, one might expect the high-reward object (stag) to have a higher pupil diameter than low reward (hare). However, on average, the percentage change in pupil diameter in the static image experiment is similar for both targets (Figure 3). This suggests, perhaps, that participants treat low and high rewards equally.

Figure 3.

Comparison of % change in pupil diameter for first fixations on stag or hare. The pupil diameter for first fixation is subtracted from baseline diameter (when participants did not fixate on objects) and the percentage difference indicates change. In this analysis, the image is static and we compare change in pupil diameter when participants state that they intend to hunt stag. The results show no difference in change in pupil size.

In the dynamic task, however, there is a marked contrast between percent change in pupil diameter for the two computer policies (figure 4). When the computer agent predominantly chooses low rewards, little change in pupil diameter or difference in pupil diameter between rewards results (mean percentage change in pupil diameter of -1.2 for stag and −1.9 for hare). The pattern of results is comparable to those from the static image experiment. However, when the computer predominantly chooses high-reward targets, pupil diameter changes when the reward is not high (mean percentage change in pupil diameter of 1.6 for stag and 5.3 for hare, t(19 = −2.4, p < .05). This suggests that when the participant expects a high reward but it does not appear that the computer will cooperate, which is experienced as loss and thus pupil diameter increases.

Figure 4.

Comparison of percent change in pupil diameter for fixation on stag or hare in the dynamic version of task. In this case, the computer moves the red player in response to the participants’ movement of the blue player. When the computer has a high (70%) preference for collaboration in hunting stag, pupil diameter changes much more when participants fixate on the lower reward hare or when it appears the agent moves towards a hare rather than stag (and the participant expects to have no reward).

Conclusion

The paper makes three contributions to human factors and ergonomics theory and practice. For practice, the contribution is in the definition and analysis of pupillometry data, particularly in terms of defining when to sample pupil size and how to define baselines against which to compare these.

The first theoretical contribution regards whether loss is more important than reward for decision-making (as in Prospect Theory), which is more apparent in a dynamic version of the task. One suggestion is that “loss” becomes more concrete when the action of an opponent is visible. In the static condition, the participant can only assume the other player’s action, but in the dynamic version, it is observable. The second theoretical contribution is in terms of strategy, where we consider how to identify the likely decision that a person could be making. This could prove useful for decision support systems (DSSs). If we know that the person is likely to choose option A and the DSS also sees this as a viable option, then the DSS need not intervene in the decision. If, however, the DSS does not judge option A as viable, then the human decision-maker may benefit from the notification.