Re-visting the Ultimatum Game: Understanding Responses to Robotic Opponents

Robots rarely (if ever) consider properties of fairness in their decision-making despite tangible research in adjacent fields. In psychology and human-computer interaction, the ultimatum game has been used to examine how people respond to perceptions of fairness and unfairness when making decisions by splitting a hypothetical pot of money. In the current study, it is used to examine how human decision-makers interact with intelligent agents, in an effort to see whether human opponents are treated the same or differently compared to artificial opponents. We conducted a mixed-design online study where participants played the Ultimatum game against three different opponents: humans, a random number generator, and one of two embodiments of an intelligent agent. The results of the N=108 participant study indicated that the embodiment of an intelligent agent has no effect on human responses to the Ultimatum game and suggests intelligent computer systems may be treated the same as humans.


INTRODUCTION
Resource allocation is a key part of any group of individuals, whether it be for determining the amount of attention to give a struggling student in a class or the order in which to deliver food to patrons at a restaurant.These are two real situations we see robots being researched and potentially placed in today [15,16].However, the optimal solutions to these resource allocation problems, such as solely aiding the struggling student while their peers are ahead or diverting attention only to current orders, may leave other students dissatisfed and restaurant-goers annoyed.This issue of perceived fairness also applies in human-robot teaming, where the strategic allocation of resources, however efcient, can lead people to have negative perceptions about the robot [3].Additionally, diferences in allocation do not only have consequences for agent perception; humans given less turns in a competitive tetris game, determined by a human or AI allocator, were found to have negative perceptions of their human opponents [5].In these collaborative scenarios, there exist expectations that autonomous systems must robustly team with human partners and work together with them, augmenting decision-making and performance in ways that are not always optimal.However, the question remains: how do humans perceive the fairness of such artifcial teammates when working together with them?For example, do human operators treat artifcial teammates the same way that they would treat other human teammates during resource allocation tasks?
One way to explore this question is to focus on decision-making task performance, and how humans react to input derived from either artifcial or human counterparts.The Ultimatum game is a decision-making task that has been used in the felds of economics and psychology to examine a subject's propensity for rational behavior in unfair circumstances [1].The Ultimatum game pits two opponents, a proposer and a responder, against one another in splitting an imaginary sum of money.The proposer chooses how the money is split; the responder can choose to either accept or reject the ofered split.If the responder rejects the split, neither player receives any of the money.In human-to-human trials of the Ultimatum game, it has been robustly demonstrated that the likelihood for rejection of ofers from human opponents increases with the perceived unfairness of said ofers [2,8,9,18].Essentially, people are less likely to take unfair ofers even when realistically they have nothing to lose.
While this game is a well-known demonstration of decisionmaking in psychology, little work [13,14,19] has been done to evaluate how responses in the Ultimatum game might change or be impacted in human-robot teams, especially when the opponents are described as intelligent agents.Our paper's main contribution involves expanding on [19] by providing a manipulation of apparent intelligence of artifcial opponents, while also manipulating the professed level of anthropomorphic embodiment of the opponent, to build a better understanding of social dynamics that infuence fairness perceptions in human-robot teaming.

RELATED WORK
Our interest in the Ultimatum game for robotics stemmed from parallel explorations of the Ultimatum game played against computers [10].Responses to computers were less afected by the current mood of participants, and computers were seen as more fair [10].Relatedly, computers have been perceived as more impartial than humans [4].But what happens when a computer has a robot embodiment?We wondered about robots that operate on similar perceived intelligence levels to modern computers as an interesting next case to study with the Ultimatum game.
A small amount of past work has already begun to explore the perception of robots in the context of the Ultimatum game.Torta et al. presented one of the earliest explorations of the Ultimatum game with robotic partners, focusing primarily on the efects of anthropomorphism on decision-making in an online study [19].The authors' study design modulated the relative fairness of the trade and the opponent type across computer, robot, and human.This team found higher rejection rates in the computer conditions (compared to against the robot or human opponents) in response to unfair ofers.They also observed that similar amounts of time were spent on making decisions for the human and robot conditions [19].The Ultimatum game has also been explored by Sandoval et al. in the context of robot strategy, where humans and robots alternated in being the proposer or responder.It was found that reciprocal behavior by the robot, where any ofer distribution by the person was accepted and matched by the robot, was the most likeable strategy [13].This same preferred behavior has been identifed with human opponents [14].Based on a robot strategy's, people perceived the robot's personality diferently as well [14].Our work serves to replicate past study fndings while directly comparing a greater number of relevant conditions in an improved study design.

METHODS
We conducted a mixed-design experiment to investigate the effects that the type of opponent (i.e., a random number generator (RNG), a human, and an artifcial intelligence in two embodiments) had on responses to the Ultimatum game.All study procedures were approved by our university's institutional review board under protocol #IRB-2019-0172.

Participants
The = 108 participants in our online study were undergraduates enrolled in an introductory-level psychology course.Participants were aged 18 to 42 years old ( = 20.7,= 4.65).79.6% of the participants were female, while 19.4% were male, and 0.9% reported other.Demographic breakdowns were as follows: 65% White, 19% Asian, 8% Hispanic, and 3% Black.

Central Manipulations
The mixed study design had participants play multiple rounds of the Ultimatum game, against diferent opponents.All participants played a round against (1) human opponents, (2) a random number generator (RNG), and (3) an artifcial intelligence (presented as IBM's Watson) within groups (see Fig. 1).However, the anthropomorphic characteristics of the AI opponent was varied between groups (based on randomized, balanced assignment); participants either played against an non-embodied computer or an embodied robot.The human opponents and random generator were presented in identical ways in all trials.
3.2.1 Opponents.The three types of opponents faced in the Ultimatum game trials are detailed below.
• Human: Participants were presented with a picture of a person with a designated name and told that this individual was making the presented ofer.• Random Number Generator: Participants were told that the presented ofer came from a random number generator.• Watson: Participants were informed that the Watson AI (as developed by IBM) was making the presented ofer.

Professed Watson
Embodiments.The Watson condition was presented as having one of two purported embodiments: as a computer or as a robot.Assignment of this embodiment was betweensubjects (i.e., each participant saw just one embodiment).
• Computer: The Watson prompt was accompanied by a picture of a computer facility.• Robot: The Watson prompt was accompanied by a picture of a NAO robot.

Procedure
Participants played three rounds of the Ultimatum game in a Qualtrics Survey, and they were instructed to try to maximize the amount of money they would receive within each round.The rounds were linked to each opponent type mentioned above (i.e., human, random number generator, and Watson [with the assigned embodiment for that participant]).Before the start of the Watson round, participants were given a brief description of the WATSON AI and its purpose as described by IBM.Each round consisted of 10 trials.The study fow is shown in Fig 1.
In each trial, the opponent would ofer a split of a $10 pot, and participants had the option to either reject or accept the proposal.Standard rules of the Ultimatum game applied, such that if the participant accepts the ofer, the pot is split as described; however, if the participant declines said ofer, neither player receives any portion.Three of the 10 trials for each round were designed to be neutral, where the opponent ofered an even $5 split, while the remaining seven of the trials proposed either $1, $2, $3, or $4 to the participant, which are unfair in the sense that the opponent receives a larger portion of the money to be split.
After the study, participants completed a demographics questionnaire, questions about their attitudes towards robots, and a manipulation check.

Measures
The number of accepted and rejected ofers were tracked for each opponent.Demographic questions recorded participants' age, gender, race, and major at the end of the study.Next, we collected information on participants' existing views of robots (using the standard Negative Attitudes About Robots Scale (NARS) [17]) and their experience with robots and AI.A fnal manipulation check question probed the participant's ability to recall the defnition of the Watson AI as described at the start of the Watson trials.

Analysis
The analyses in this short paper focus on the accepted unfair ofers during the Ultimatum game, the accepted neutral ofers during the Ultimatum game, and the collected NARS data.The ofer acceptance data was evaluated using a two-way mixed model analysis of variance (ANOVA) test with an = 0.05 signifcance level.Greenhouse-Geiser corrections were applied to account for any spherecity violations.In the case of signifcant main efects, we used a Bonferroni test to identify signifcant pairwise diferences.With the use of the mixed-model ANOVA, the efect size was reported in the form of generalized eta-squared ( 2 ) to improve crossstudy comparability [11].Efect sizes were interpreted relative to Funder and Ozer's updated guidelines [7] after Cohen's original work [6].We used t-tests with an = 0.05 signifcance level to compare NARS ratings between the participant groups assigned to each Watson embodiment.Bonferroni tests were again used to identify signifcance.All statistical analyses were conducted using R [12].

RESULTS AND DISCUSSION
All 108 participants completed the full study.The following subsections illustrate the results of the analyses (Sections 4.1-4.2) and provide discussion on the implications of our fndings (Section 4.3).

Ofer Acceptance Results
The mixed-model ANOVA test showed signifcant efects in participant acceptance of unfair ofers: Opponent: ( (1.71, 181.03) = 8.414, < 0.001, 2 = 0.021) From the results of the two-way mixed model ANOVA we found that there were signifcant diferences across opponents.There were no signifcant efects found between the presented embodiments or for the interaction between embodiments and opponents ( > 0.7 for both).Results of the unfair trials can be seen in Fig 2.
A pair of subsequent ANOVAs, one for each embodiment group, was performed to identify in what cases the opponent diference was signifcant.Signifcance was found in the ANOVA for one of the embodiments in the acceptance of unfair ofers: Opponent, within Robot Group: ( (1.55, 80.7) = 7.38, = 0.006, 2 = 0.028) A pairwise analysis comparing the opponents within the robot embodiment found that more unfair trials were accepted if the opponent was a random number generator versus when the opponent was a human.Similarly, participants were found to accept more unfair trials if the opponent was a random number generator versus Watson.Diferences in the acceptance of the neutral ofers were not found to be signifcant across any of the manipulations or manipulation pairings (all > 0.240).The results were in line with expectations from past research with humans that found a majority of neutral ofers to be accepted.Boxplot results for the neutral trials can be seen in Fig 3.

Negative Attitudes about Robots
The t-tests revealed no signifcant diferences in reported attitudes toward robots between the two embodiment groups ( > 0.600 for all tests).Results for each of the standard NARS scales appear in Fig. 4.

Discussion
Overall, the ANOVAs revealed important information regarding how users perceived the emobodiments of Watson.Embodiment did not have a signifcant efect on ofer acceptance, and AI opponents did not elicit signifcantly diferent game behaviors compared to human opponents.At the same time, human and AI opponents  were treated diferently than the studied 'unintelligent' computing system (i.e., the random number generator).This result is in contrast with [19], which found a diference in how participants responded to a more human-like robot condition vs. a non-anthropomorphic computer condition.This divergence in results could be in part due to the diferences between the conducted studies; for example, we used a diferent range of human appearances for our human opponent, and the past related study used a wider range of computer and robot images.The reference work was also conducted 10 years ago, a span of time over which expectations of robots and computers could have very well changed.Future work could explore the ability of our work to replicate in modern times, as well as with similar and diferent stimulus design approaches.
The main fndings of 1) AI embodiment having no signifcant efect on game behavior and 2) AI opponents being treated identically to humans have ramifcations for tasks like human-robot teaming.Existing paradigms for fairness in psychology could act as a basis for building understanding for future fairness algorithms, depending on how far the overlap stretches.As highlighted earlier in the paper, fairness is a necessary property for enabling robots to be capable of resource allocation with positive social outcomes for themselves and interlocutors.Possible next steps based on our work include investigating how basic physical characteristics of robots interact with or are moderating perceptions of cognitive agency in the Ultimatum game.

CONCLUSION
In this work, we performed an online study to investigate how a robot opponent is treated in the Ultimatum game, and varied the degree of professed intelligence and embodiment of this opponent.Our fndings matched those of some previous work, but diferently showed that the embodiment of an artifcial agent had no efect on the responses to the Ultimatum game.Additionally, we found that people treat intelligent computer systems the same as humans.This work can help researchers and practitioners better design interactions with robots in teaming situations.

Figure 1 :
Figure 1: Sequence of the study design.Participants start by playing against the random number generator, then human opponents, then one of the intelligent agents, respectively.

Figure 2 :
Figure 2: Boxplot of the percent of unfair trials accepted, where "+" represents the mean location, the bolded line represents the median, and dots represent outliers.

Figure 3 :
Figure 3: Number of neutral trials accepted.Bars represent the mean and brackets represent standard error.

Figure 4 :
Figure 4: NARS results, categorized by the three standard scales of negative attitudes about interactions with robots, the social infuence of robots, and possible emotional responses of robots.