Behavioral-economic Games with Commercially Available Robots

Behavioral-economic games such as the dictator game have been a popular method for studying human-human interactions which can also be used to study human--robot interaction. Using commercially available robots, we showed participants photographs of 18 robots, and had them play a dictator game against these robots after answering a set of 12 questions regarding each robot's characteristics. Using principal component analysis and linear mixed effects modeling, we found that we could reduce our original 12 robot characteristics to three components---likability for the robot, anthropomorphism, and utility---which individually predicted dictator game offers. The findings are potentially of interest to robot designers and social scientists.


INTRODUCTION
Paradigms from the feld of social psychology and behavioral economics can be valuable tools for investigating human-robot interaction.One example is economic games, in which participants share or divide amounts of money or tokens.In one particular economic game, the dictator game, participants are ofered an amount of money that the participant can share with another participant.Based on the assumptions of rational self-interest, one would expect a player to keep the entire stake for themselves, giving nothing to the other player.However, this is not what we see in experimental settings using a "standard" dictator game, where only 40% of participants keep the entire stake for themselves [6].Interpretations of the amount of money ofered in the dictator game range from altruism to strategic behavior conforming to social norms [4,5].
Dictator games in human-robot interaction are scarce but are vital to understanding the public psychology of robots as a window to social interaction.This in turn can reveal the changing fabric of human-robot relationships.
The growing interest among social scientists, designers and engineers to study human behavior towards robots is leading to a greater understanding of how we think, feel, and behave towards robots; rooted in tendencies for mindless social behavior, anthropomorphism, uncanny feelings, and formation of emotional attachments [1].This study is among the frst to test behavioral economic interactions with commercially available robots using the dictator game along with measuring tendencies towards these robots to fnd which could be underlying psychological mechanisms that guide behavioral-economic decision making.If we mindlessly apply social rules to robots-judging technology as if they are human (media equation; [9]), then one should observe similar behavior in dictator games with robots as those with humans.

CURRENT STUDY
Earlier work on anthropomorphism has investigated human-robot interaction in the context of the economic games (e.g.[2,8]).Several fndings suggest that participants cooperate with or give away money to a robot and are guided by how anthropomorphic the robot appears to be.In the current study, we aimed to expand on several earlier fndings (e.g.[2,7,10]).First, we selected 18 commercially available robots listed on the IEEE website, maximizing heterogeneity.Second, we used multiple measures of judgment toward robots aimed at understanding why people give money to robots.Specifcally, we investigated the relationship between anthropomorphic qualities, likeability, and utility of robots with dictator game ofers.As far as we are aware, this is one of the frst studies to have examined behavioral economic game behavior for a wide variety of commercial robots in India, an emerging market in the global south-and hardly represented in the human-robot interaction space.

METHOD 3.1 Participants
We recruited 361 undergraduate engineering students from a university in India.All participated for course credit and did not receive any monetary award.

Procedure
Participants were instructed to open a web survey.On each page, they were shown a photograph of one of 18 robots in random order (see Appendix A), and 12 questions asking about that robot's characteristics, followed by a question about how much they are willing to give to the robot-as the dictator game question (see Appendix A), before continuing to the next robot.The 12 questions about robot characteristics were answered using a continuous slider, with labels from "not at all" to "very much".The dictator game was not played for actual money but was phrased as a hypothetical ("If you were given |250, how much would you give this robot?Please enter a value between 0 and 250.").

Stimuli
We used photographs of 18 diferent commercially available robots from the IEEE Spectrum robots website [11], ranging from industrial to humanoid robots.Robot names were not shown to participants.
Appendix A lists all robots used, as well as all questions asked.We refrained from using established scales such as ROSAS in favor of using a short but heterogeneous set of questions.

Principal components analysis
We performed a principal components analysis (PCA) on the 12 questions about robot characteristics with oblique rotation (promax).The scree plot, together with an assessment of interpretability, showed an infexion justifying retaining three components.Table 1 shows the component loadings after rotation.The items on the three components suggest that component 1 represents a measure of anthropomorphism, including physical and cognitive similarity to humans.Component 2 represents general likability, and component 3 seems to represent a measure of utility.We will refer to these components as the Anthropomorphism index (AI), Likeability index (LI), and Utility index (UI), respectively.

Dictator game behavior
Between robots, the average proportion of the dictator game stake ofered to each robot ranged from 0.31 (Cubelets) to 0.74 (Sophia).Across robots, the average proportion of the dictator game stake ofered was 0.50.Across participants, the average proportion of the dictator game stake ofered-averaged over all robots-ranged from 0.00 (never giving anything to a robots) to 1.00 (always giving the entire stake to each robot).The distribution of the proportion of the dictator game stake ofered per participant is shown in Figure 1.

Efects of robot type
There was a main efect of robot type on the proportion of the dictator game stake given away, F(17, 6120) = 137.5,p < .001, 2 = 0.13.The distribution of dictator game stake ofered by robot type is shown in Figure 2. As is visible in Figure 2, more humanoid robots (Sophia, NAO, Asimo, Pepper) tend to receive a larger proportion of the dictator game stake, with Sophia being the top recipient.There was also a main efect of robot type on all three PCA components, Fs(17, 6120) > 176.4,ps < .001, 2 s > 0.23.

Predictors of dictator game behavior
We performed a linear mixed efects analysis of the relationship between several perceived robot characteristics and dictator game behavior.As fxed efects, we entered each robot characteristic (i.e. each question asked, excluding all other robot characteristics) into the model.As random efects, we had intercepts for subjects and robots, as well as by-subject and by-robot random slopes for the efect of the fxed factor.Visual inspection of residual plots did not reveal any obvious deviations from homoscedasticity or normality.P-values were obtained by likelihood ratio tests of the full model with the efect in question against the model without the efect in question.All variables were scaled to the [0, 1] interval.
All tested fxed efects afected dictator game behavior ( 2 (1)s > 39.54, ps < 0.001).Estimates of the coefcients are displayed in Table 3 (Appendix B), and indicate the diference in the proportion ofered in the dictator game between participants rating the characteristic as 0 (minimum) versus 1 (maximum), i.e. every 0.1 increase in the response to "How much do you like this robot?"leads to a 0.037 increase in dictator game proportion ofered.
Next, we performed a linear mixed efects analysis of the relationship between the component loadings returned from our PCA and dictator game behavior.As fxed efects, we entered all three component loadings into the model.As random efects, we had intercepts for subjects and robots.This resulted in a signifcant model ( 2(3) = 2485.5,p < 0.001) with all three predictors p < 0.001 showing that all three components contribute to dictator game behavior.

DISCUSSION
Based on several papers highlighting the importance of anthropomorphization on prosocial behavior toward robots [2,7,10], we investigated the determinants of dictator game behavior against diferent types of robots.Dictator game behavior difered strongly between diferent robots, and on average people were willing to give away half of the stake.Although hypothetical dictator games result in larger stakes given away than real ones, overall patterns seem to remain consistent in our earlier-not yet published-work comparing hypothetical vs. real money stakes.This is somewhat similar to dictator game studies with human opponents such as [3], where a large proportion of people give away money in hypothetical dictator games.This underscores the possibility of the media equation: integrating robots-even commercial ones-as social actors, with humanoid robots being given the maximum share.
Additionally, we studied the determinants of dictator game behavior and their structure.Hence, we predicted dictator game behavior from three PCA components: Anthropomorphism index (AI), Likeability index (LI), and Utility index (UI).Comparing the estimated coefcients, likeability of a robot was the most important determinant of dictator game behavior, followed by utility and anthropomorphism.This shows that although anthropomorphism does have an efect on dictator game behavior, other factors seem to be more important.Humanoid robots received most money in our hypothetical dictator game, but we conclude that social interactions and decisions can be driven by both likeness towards a robot and anthropomorphism, with a potential social component of the Utility index, as the questions mainly pertain to social situations.These fndings are potentially of interest to robot designers.This is among the few studies from a non-Western emerging market where many robot companies are planning to expand in the near future.As we move towards international sales of these robots, cross-cultural studies could shed more light on the universality of these components as a determinant of dictator game behavior.Such studies can provide an interesting view of robots that can impact various other felds.

Figure 1 :
Figure 1: Histogram of the average proportion of the dictator game stake ofered for each participant.

Figure 2 :
Figure 2: Smoothed density estimates of mean proportion of dictator game stake ofered to each robot.Black vertical lines indicate the median value.

Table 1 :
Component loadings for all items.