Principal-Agent 007: Attacking and Defending in the
Name of Others
A Study on Delegated Investing and Risk-Preferences
Matko Porobija
Master thesis Psychology, Economic & Consumer Psychology Institute of Psychology
Faculty of Social and Behavioral Sciences – Leiden University Date: 13th of February, 2020
Student number: s1501488
First examiner of the university: Prof. dr. C.K.W. de Dreu Second examiner of the university: Dr. J.A.J. Gross
Contents
1. Introduction 3
1.0. Information Asymmetry 3
1.1. Risk-Preferences 4
1.2. Goal Conflicts 4
1.3. The Predator-Prey Contest Game 5
1.4. The PAP in the PPC 5
1.5. Influential Design Aspects 6
1.6. Literature on Delegated Investing and Risk 6
2. Methods 11 2.0. Sample 11 2.1. Materials 11 2.2. Procedure 12 3. Results 14 3.0. Descriptive Statistics 14 3.1. Investments, H1 14
3.2. Delegation, Roles and Risk-preference, H2 & H3 16
3.3. Exploratory Post-Hoc Speculation 17
4. Discussion 18
4.0. Investments, H1 18
4.1. Delegation, Roles and Risk-preference, H2 & H3 18
4.2. Exploratory Post-Hoc Speculation 22
4.3. Conclusion 22
4.4. Limitations & Future Research 23
Abstract
The interest of our study was to examine the relationship(s) between delegation and investing, risk-preferences, and attacker-defender role influences. We based our hypothetical grounds according to the assumptions provided by the theory of agency. We expected to observe a difference in principal’s and agent’s investment behavior, which would follow the pattern according to which risk-preferences are embodied within the PPC paradigm. Contrary to our assumptions, agents’ investments did not reflect what we expected according to agency theory. Namely, we found that agents displayed more risk-seeking behavior than would be expected. However, further analysis showed that this effect quite likely cannot be attributed to influences of risk-preference, or at least not in our experiment. We did not find any
meaningful correlational relationship between risk-preferences and delegatory investing. Therefore, we propose an alternative explanation for the effects of delegation on investing- one that operates through loss-aversion as opposed to risk-preference.
1. Introduction
Whether one wishes to invest in a hedge fund, a new home, or retirement plans, people often find themselves dependent on the knowledge and skills of other people. This type of dependence lays ground for what we know as the theory of agency. ''In its simplest form, agency theory assumes that social life is a series of contracts...'' Charles Perrow (1986, p. 224, as cited in Waterman & Meier, 1998), which can involve exchange of goods, knowledge, time and effort. People establish coalitions to achieve a certain goal. These coalitions
represent a Principal-Agent (P-A) relationship. This paper will refer to the classic definition of a P-A relationship posed by Jensen & Meckling (1976, p. 308), who define it as ‘’a
contract, under which one or more persons (the principal(s)) engage another person (the agent), to perform some service on their behalf which involves delegating some decision making to the agent”. It seems straightforward to conclude that the main reason for establishing P-A relationships pertains to outcomes, which cannot be achieved by the
principal. Consequently, the focus of a P-A dynamic lies in the process and result of delegated decision-making. That is, granting power of attorney to an agent who is believed to act in the principals' best interest. This belief, or violations thereof, form the basis of the
Principal-Agent Problem (PAP).
The PAP occurs when the underlying assumptions of coalition are violated, typically by the agent. It represents a conflict of interest between the agent and the principal, which may take form in a variety of contexts. For example, a mechanic (agent) over-pricing his services in order to maximize income at the expense of the car owner (principal). A politician giving false promises at the expense of the voter’s future well-being. Literature has identified three componential sources of the problem. Namely, information asymmetry, risk-preference differences, and goal conflicts (Eisenhardt, 1989; Waterman & Meier, 1998; Saam, 2007).
1.0. Information Asymmetry.
This refers to a discrepancy in information sharing between the agent and principal. The
asymmetry arises due to the principals' inability to know, or monitor, the agent's competences, intentions, knowledge, and actions (Saam, 2007). These are often referred to as ''hidden'' characteristics due to their implicit nature. Information sharing is essential to P-A
relationships, as much of the coalition depends on the principal's evaluation of agent effort, and ultimately, valuation of agent-generated outcomes. Information on effort is often
information flow acts in favor to the agent (Saam, 2007). This allows the agent to act out of self-interest by, for example, providing false information on effort or external costs.
1.1. Risk-preferences.
According to the standard theory of agency, principals are assumed to be risk-neutral, in contrast to agents who are assumed to be risk-averse (Eisenhardt, 1989). The reason for this is the principal’s ability to diversify (Saam, 2007). Conversely, the agent's ability to diversify is limited. In other words, the principal can always hire another agent, whereas the agent might find it harder to acquire a new customer. In addition, as the agent’s income is
dependent on generated outcomes and effort, any threat to the agents' pay-out is undesirable. Hence, the agent is assumed to be inherently risk-averse.
1.2. Goal Conflicts.
Both parties enter a contractual agreement under the assumption of utility
maximization (Eisenhardt, 1989; Waterman & Meier, 1998; Saam, 2007). The principal expects to maximize returns, in addition, the agent expects to maximize income. However, the conflict arises due to the agent’s pay-out function, which is confounded by his/her invested effort. Namely, the more effort the agent invests, the greater the agent's disutility (Saam, 2007). In effect, the agent wants to maximize income by minimizing effort. On the other hand, the principal wants to maximize profit by urging maximum agent effort. In view of the standard agency theory, this creates a conundrum. Both parties' utility gains rely on agent effort, yet in contradicting ways. It is important to note that different P-A models treat agent effort differently. In part because it is difficult to observe these efforts, and partially because effort may not be essential to the agent's compensation. Rather, according to the positivist view of agency (Eisenhardt, 1989), principals may only consider outcome-based contracts and reward the agent independently of effort. For the purpose of this paper, however, we will not dwell into different contractual models.
Thus far, we have discussed the components that comprise the PAP. Now, we will consider the paradigm in which we intend to study the problem, and the extent to which the problem is applicable to our design.
1.3. The Predator-Prey Contest Game.
The game was designed by De Dreu, Giacomantonio, Giffin, & Vecchiato (2018) in effort to operationalize conflict in a game-theoretical model from a bimodal point of view. It represents a conflict with differential incentive and outcome structures, defining those who attack (‘Predator’) and those who defend (‘Prey’). The incentives of the two sides are clearly distinguishable if we consider attacking as means to improve one's current state of affairs through, for instance, monetary gain. In contrast, the incentive of the defender lies in retaining the current state of affairs by, for example, deterring attacks (De Dreu & Gross, 2018). Hence, the game relies on mixed-strategies Nash equilibria, illustrating what the authors best describe as a Match strategy for defense, and a Mismatch strategy for attack. It is in favor of the
attacker to mismatch the defensive force, while the defense tries to match the fore of the attacker. Respectively, the game’s pay-out system is structured according to the side’s incentive. The attacker and defender invest a certain amount, (x),(y), out of endowment e (=10 €, De Dreu et al., 2018). The investments are lost, but the remains are not. More specifically, if the attacker invests more than the defender, the attacker has won the round. Consequently, the attacker keeps his endowment remains and collects everything the defender had left, leaving the defender at nothing. If the defender invests more or equal to the attacker, the defender has won the round. In this case, both the attacker and the defender get to keep their own endowment remains. Be that as it may, the defending side cannot gain (-more than it was endowed with), while the attacking side cannot lose (-more than it was endowed with). The defender’s best effort in maximizing utility would be to precisely match the investment force exerted by the attacker, denoted by investing x=y. In contrast, the attacker’s best effort in maximizing utility would be to mismatch the defending investment force by the minimum of 1e unit (out of e =10), as denoted by investing y=x+1.
1.4. The PAP in the PPC.
In crude terms, the objective of the participant in the PPC is to out-invest his opponent with the lowest possible investment. The investment and outcome structure can be
manipulated in a way to simulate P-A decision-making. That is, by manipulating whether the decision, and outcome, solely affect the decision-maker himself (principal), or whether these affect another person paired to the decision-maker (principal-agent). we create the possibility of delegatory investment decision-making. Thus, given the centrality of delegation in P-A relationships, we believe the PPC neatly allows for the study of the PAP. This research will
focus on the risk-preference aspect of the problem, as we aim to challenge agency theory’s assumptions on this matter.
1.5. Influential Design Aspects.
In order to investigate the effect of risk-preferences, it is important to consider the other two determinants of the PAP, namely, information asymmetries and goal conflicts. Granted that most, if not all, participants will never have participated in a similar study, we are safe in assuming that all subjects will share a similar level of understanding of the PPC. None of the participants will be likely to have more experience in this kind of investing than others. This implies that a degree of knowledge variation between the principal and the agent will be eliminated, thus suppressing initial information discrepancies. Moreover, our design corrects for effort obscurities by implementing an informational feedback system. The system will inform the principal about the efforts and outcomes made by the agent after each
investment round. This feedback approach relates to the monitoring systems proposed to mitigate hidden agent actions (Eisenhardt, 1989; Saam, 2007). In relation to goal conflicts, we incorporate a sanctioning system that allows the principal to reward or punish the agent based on his performance and generated outcome. This sanctioning approach relates to reward systems, and partly to vertical integration (Eisenhardt, 1989; Saam, 2007), which are proposed to mitigate hidden information, actions and intentions. Taken together, the
possibility of sanctioning should co-align the incentives of the agent and the principal through rewards. In addition, it should encourage the agent to abide to the principal’s goals through the possibility of punishment, according to fear incentivization.
1.6. Literature on Delegated Investing and Risk.
Chakravarty, Harrison, Haruvy & Rutström (2011) studied P-A risk-preferences using Holt & Laury’s (2002) Multiple Price List (MPL) format, and a variant of the First-Price Sealed-Bid Auction. In the MPL task, participants are asked to make ten choices in two different sets of lotteries with varying probabilities and different expected values. Roles were manipulated by assigning two different outcome mechanisms. Namely, outcomes that only affects the decision maker (principal) and outcomes that solely affect the subject paired to the decision maker (agent).
Their results suggested that participants were significantly less risk-averse when deciding for other people. The authors then computed probabilistic estimates of change in risk-aversion scores, corresponding to participants’ shift from the ‘self’ to the ‘agent’
condition. The probability that a subject would make less risk-averse choices when deciding for others was 0.57. In contrast, the probability that a subject would make more risk-averse choices was only 0.05. They continued by computing the constant relative risk aversion (CRRA) coefficients using maximum likelihood estimates. The analysis revealed that participants’ CRRA coefficient was significantly lower when deciding for other people’s money (by 0.44). In addition, deciding for others was associated with a larger Fechner error, showing that participants experienced more distorted utility estimates. More specifically, implying that participants experienced ‘’…less sensitivity to differences in expected utility when acting for others than when acting for self’’ (Chakravarty et al., 2011, p. 907). To generalize their findings, the authors used the same analytical model to describe the results from their auction bid task. Those results confirmed that relative risk aversion was
significantly lower in agents who bid on behalf of others, while some agents even displayed prominent risk-seeking behavior.
A significant limitation of this study pertains to the use of hypothetical consequences.
Harrison (2006) showed that there is a clear link between lower levels of risk-aversion when dealing with hypothetical outcomes as opposed to real ones. The problem here was an absence of monetary consequences to the agents, thus creating a ‘hypothetical loss’ situation which only affected the principal. A solution to this could be to, for instance, implement a
transaction deposit where a percentage of the agents assets face liquidation in the case of a botched investment. A system similar to what is commonly found on leverage trading platforms. Another possibility is a sanctioning system through which principals could reward/punish agents according to their effort or generated outcome. To further explore the extent to which monetary consequences make a difference in P-A investment behaviour, we consider the study mentioned below.
Andersson, Holm, Tyran & Wengström (2014) studied risk-taking on behalf of others with the possibility of incurred loss. Their design included four separate MPL tasks, each representing a different treatment condition. Two treatments were framed for principal decision-making, one with real payments and one with hypothetical payments (no payment). The other two treatments pertained to agent decision-making, one with payments only to principal, and one with payments that affect both the principal and the agent. Each participant was placed in one of the treatment conditions, which were further divided into two sets. Namely, a set of treatments that included the possibility of incurred loss, and a set without the
possibility of loss. Thus, in one of the sets’ conditions, agents could suffer direct monetary consequence. Their initial results suggested that treatment condition had no effect on risk-taking when losses were not included. Irrespectively of whether participants decided for themselves or others, with consequence only to self or shared with others, risk-taking was the same across all conditions. However, when losses were a possibility, they observed significant differences between the principal (with real payment) condition and all the other treatment conditions. Their results show that having the possibility of incurred loss increased risk-taking in agents, but not in principals. Furthermore, it showed that agents engaged in risk-taking independently of whether their actions affected only the principals’ monetary outcome or both of their outcomes. The authors concluded that participants took more risk with other people’s money due to a ‘’hypothetical bias’’ dissociation. They then conducted a CRRA structural analysis to conclude that this shift in risk-taking was mainly driven by a reduction in loss-aversion.
The results of these studies seem to clash with the assumptions of the standard theory of agency. Namely, agents who are assumed to be risk-averse displayed more risk-seeking behavior than would accordingly be presumed. In order to question these findings, and to test the assumptions of agency theory, this research will investigate whether investments are influenced by mere enactment of delegation within the PPC, as well as the extent to which this is driven by risk-preferences. We hypothesize that H1:agents over-invest relative to the
principals, irrespectively of role. We could argue that, in general, by investing more, the
subject increases his chances of winning at the expense of capital, and thereby minimizes the risk of losing (for now, if we do not consider role-contingent pay-out rules). We account that our subjects might not completely discern the difference between winning and profiting within the PPC game. Especially if half of the time the consequence is not theirs to bare. Our primary hypothesis is based on Agency’s assumption that agents will by default act more risk-aversively. We believe this may happen irrespectively of the role-contingent pay-out rules, given a degree of novelty our subjects will feel facing the PPC game. So, in a primitive way, we expect agents to invest more out of their endowment compared to principals, irrespectively of their role. Essentially, this hypothesis serves as a baseline check. We intend to frame the interpretation of this result in terms of an overarching trend, which we will use to compare with the interpretations of subsequent results further down the line. This will allow us to infer a fault line between the global effect of delegation and the role-specific effect of delegation within the PPC.
We further want to know whether risk-preference effects are congruent with the game’s role-objectives. Thus, we hypothesize H2: agents to over-invest in attack more than principals. Due to the game’s pay-out structure, we expect to observe over-investments only
in attack, because different rules apply for defense. Even though profit maximization works equally for both roles - winning the round with the smallest possible investment, the
difference in pay-out between attackers and defenders creates a difference in the way risk is embodied between the two roles. In that sense, we can translate magnitude of investment into a language of risk-preference. In attack, the higher the investment, the less it can be
considered a risk-seeking decision. That is because attackers cannot lose per se; their
investments are lost, but their remaining endowment is not. As a result, it is more affordable and less risky for the attackers to invest high. Whereas, in defense, the higher the investment, the more it can be considered a risk-seeking decision. Unlike attackers, defenders do not profit from winning directly, rather their profits reflect only what was left from their initial endowment. As a result, investing high is less affordable and more risky for the defenders. In that sense, we could say that low-investing attackers like to gamble because low investments bare most risk of losing, yet create most potential profit. Likewise, high-investing defenders like to gamble because high investments bare least risk of losing, yet offer least possible profit. For that reason, and since agents are thought to be risk-averse by default, we expect the agents to over-invest in attack relative to the principals.
As a last point of interest in this study we wanted to know the extent to which role-influences in the PPC determine investment behavior from the side of the agents. Based on previous findings from De Dreu et al. (2018), we hypothesize H3: agents to over-invest in
attack, but not in defense. Contrary to the assumptions of rational utility maximization, through a series of experiments, the authors have shown that both attackers and defenders consistently deviated from their respective Nash equilibria. One of the conclusions was that people invest less effort in attack than in defense, due to prosocial preferences- exemplified by other-concern and empathy. Our research aims to build-up on their findings by comparing investments from an agency point of view. We expect agents not to abide to the findings given by De Dreu et al. (2018), in so much as we believe it is likely the agents won’t be restrained by prosociality towards the opponent. Rather, the prosocial nature of the P-A contract is likely to shift this prosocial motive towards the agent’s principal. Due to this, and in consideration with the risk-averse nature of agent, we expect the agents to over-investment in attack, but not in defense.
2. Methods and Materials
2.0. Sample.
Subjects were recruited from the city of Leiden, the Netherlands. The inclusion criteria
were a sufficient knowledge of the English language and being older than 16 years of age. Subjects were predominantly students of psychology recruited from faculty grounds. Data was not collected anonymously but was saved and coded to ensure a relevant degree of anonymity. This research did not include any sort of deception nor unobtrusive methods. Participants were given an informed consent form prior to participation and were provided with all necessary information regarding the experiment. At the end of the study, participants received a short debrief, were payed, and kindly asked to leave.
2.1. Materials.
Participants took part in the Predator-Prey Contest game by De Dreu et al. (2018) that was described in the introduction section. In addition to data collected from the game,
participants filled out a questionnaire assessing their social preferences using the Slider Measure of Social Value Orientation. This measure contains 15 item choices which ask the participant to allocate a resource over a defined continuum of joint pay-offs, which affect another person (Murphy, Ackermann, & Handgraaf, 2011). Furthermore, participants' risk preferences were assessed using the gamble task from Gross, Faber, & De Dreu (?), which resembles the Multiple Price List format measure. The measure mirrors the Multiple Price List format (MPL), which asks subjects to choose between two lottery choices A and B in a set of 10 scenarios. Initially, the expected values of the two lottery choices differ by large. For example, in the first scenario choice A offers a 10% chance of receiving 2$ and a 90% chance of receiving 1.60$, equaling to 1.64$ in expected value (Andersen, Harrison, Lau, &
Rutström, 2006). Whereas, the expected value offered by choice B’s chances equals to 0.45$.
Further down the line, the two choice’s expected values increase, and at half-way point choice B’s value starts surpassing the value of choice A. Thus, in consideration with the flow and arrangement of discrepancies in chances and values, we expect risk-seekers to choose option B early on- deciding for B in spite of the seemingly irrational trade value; and risk-averse subjects to choose option A near the end of the scenario list. Furthermore, we expect risk-neutral subjects to switch from picking choice A onto choice B on the half-way mark, since the expected values do not differ at that point.
The MPL measure allows us to calculate a subject’s range of relative risk-aversion (CRRA), given the subjects preferential position at which the subject decided to switch from choosing choice A to choosing choice B. The CRRA statistic tries to embody one’s risk-preference onto a relative continuum, however, the range of this continuum depends on the design/version of the MPL format. Nonetheless, the interpretation of the statistic remains the same, as we account for the relative numerical proportions of subjects scores the continuum.
2.2. Procedure.
Subjects were invited to the lab in groups of 6 – 24 participants at a time. Once the subjects arrived, prior to the beginning of the experiment, we held an introductory briefing explaining the set-up, procedure and steps required to be taken by the participants. The
session started once the subjects were escorted into the room and seated. Each participant was seated in their own isolating cubicle, equipped with a computer, keyboard and mouse. On screen, subjects received detailed instructions for the Predator-Prey Contest Game (PPC) and were assigned the role of attacker or defender (unknown to them). We paired each subject to another subject in the room, forming a dyadic principal-agent relationship. The subjects remained paired throughout the whole session. It is important to note, however, formed dyads were anonymous to each other both on-screen and in flesh. This might undermine real-world
Following a short comprehension check, participants were asked to make 60 investment decisions across 2 blocks of 30 trials. The subject was asked to make his
investment by typing in a number from 1 to 10. After investing, each subject had to wait for their counterpart to invest. Only when both parties made an investment did the trial continue. This holds for each block of testing. After each trial, the screen would display feedback on their investment, other’s investment, and the contest’s outcome.
Block 1: Principals. Subjects invested with their own money on their own behalf. In other words, subjects’ investments came out of their own endowment, and the outcomes of these investments only affected the subjects themselves. The subject bares all responsibility for his investments.
Block 2: Agents. Participants invested with the endowment of the subject they were paired with. In this case, the subject whose endowment was delegated bares the consequence of their partner’s decision. In other words, subjects invested with the money delegated to them by their partner, and the outcomes of these investments only affected the partner who had
delegated the money. The investing subjects bare no consequence for their investment decisions made on behalf their partner. However, since our sanctioning system allows the principal to punish the agent, incurred loss is a possibility and some consequence does apply. Block 3: Reward & punishment. Following the second investment block, subjects were asked to assign punishments, or rewards, to agents for their efforts. More specifically, subjects were presented with 10 investment decisions from the previous block, and were asked to indicate how much of their own endowment (max. e = 3) they were willing to award, or, how much of their agents’ endowment they were willing to take as punishment (max. e = -3). These decisions affected the principal-subject’s final pay-out, as the reward money was taken out of ones’ own endowment, and punishment money was added to it.
Once the experimental blocks finished, subjects answered a short questionnaire assessing their social preferences with the Slider Measure of Social Value Orientation, and their risk preferences with the gamble tasks from Gross, Faber & De Dreu. All subjects except those who were late, absent, or excused, received their payment (show-up fee + earnings from the experiment). Experimental earnings were calculated outcome averages of 12 trials, where 2 trials were randomly selected from each of the two investment blocks. The total duration of an experimental session was approximately 1 hour.
3. Results 3.0. Descriptive Statistics.
Participants were mostly students recruited from the University of Leiden. The vast majority of participants studied psychology (77.1%) and most were from the Netherlands (35.9%) and Germany (18%). 28% of participants said they already had experience with a similar type of experiment. Almost all subjects were in their early 20s.
3.1. Investments.
To test our hypothesis that agents over-invest relative to the principals, irrespectively of role, we conducted a 2 (Delegation) X 2 (Role) X 30 (Time) within-dyad repeated
measures ANOVA. Despite our statistically sufficient sample size (N ≥ 25), investment data spread across the two testing blocks were checked for normality using the Kolmogorov-Smirnov test for attackers and defenders respectively. The test showed all but one dataset- principals in attack, to be normally distributed, D(57)=.079, p=.200. None of the observations had a standardized residual value larger than 3, and the largest Cook’s distance did not exceed 1. We note that Mauchly’s test showed a violation of sphericity (X2(434)= 958.79, p<.001). Thus, we used the Greenhouse-Geisser estimates to correct the degrees of freedom for our analyses (ε=.361).
The test of within-subjects effects showed a significant effect of Delegation, F(1,56)=6.602, p=.013, ηp2=.105. Principals in both roles on average invested more (M=4.811, SE=.290) out of their resource pool (e=10 €) compared to agents (M=4.499, SE=.298), see Figure 1a. The small difference between the two investments means (MP – MA = |.312|) was enough to reach significance due to its large effects size. The main effect of Role was found to be highly significant, F(1,56)=45.697, p<.001, ηp2=.449, where defenders on average invested more (M=4.985, SE=.281) than attackers (M=4.325, SE=.302), see Figure
Figure 1a. Boxplots showing mean investments (out of endowment e =10€) of principals and agents across 30
rounds of the PPC game. Principals on average invested more (M=4.811, SE=.290)than agents (M=4.499, SE=.298).
Figure 1b. Boxplots showing mean investments (out of endowment e =10€) of attackers and defenders across 30
rounds of the PPC game. Defenders on average invested more (M=4.985, SE=.281) than attackers (M=4.325, SE=.302).
The interaction of Time*Delegation was found to be non-significant, F(11.228, 628.795)=1.121, p=.341, ηp2=.02. Moreover, all subsequent interaction effects were found to be non-significant, a summary can be seen in Table 1 below.
Note. Table 1 shows the SPSS output result summary of our 2 (Delegation) X 2 (Role) X 30 (Time) Repeated
Measures ANOVA analysis, showing the F-value, p-value and effect size value for each effect.
3.2. Delegation, Roles and Risk-preferences.
To test our hypotheses that H2: agents over-invest in attack more than principals, we referred to our previous analysis, which yielded a non-significant Delegation*Role interaction effect, F(1.900, 502.567)=.212, p=.647, ηp2=.004, and thus found no significant differences between attacking principals and attacking agents. A summary of their respective means can be seen in Table 2. We referred to the same analysis for hypothesis H3: agents over-invest in
attack, but not in defense. We found no significant difference between agent’s investments in
attack and defense. To confirm the trend of our findings, we correlated investments from principals and agents in both attack and defense with their respective risk-preference (R-P) scores. We found (highly)non-significant correlations between all pairs of variables in question. See Table 3.
2 x 2 x 30 RM-ANOVA Result Summary
Effect F Sig. (p) ηp2 Time 3.859 <.001 .064 Delegation 6.602 .013 .105 Role 45.697 <.001 .449 Time*Delegation 1.121 .341 .020 Time*Role 1.143 .309 .020 Delegation*Role .212 .647 .004 Time*Delegation*Role .548 .896 .010
Note. Table 2 shows the estimated marginal means summary, showing the means (and standard errors) for each
group per condition.
Note. Table 3 shows Pearson correlations, and their respective (p-values), between principals and agents and
their risk-preference scores for both attackers and defenders.
3.3. Exploratory Post-Hoc Speculation.
For purposes outside of the initial scope of our hypotheses (discussed later), we conducted another within-dyad 2 x 2 x 30 repeated measures ANOVA on reaction time scores. We used a logarithmic transformation to normalize the reaction time data. We checked for outliers and removed 11 extreme cases – those exceeding the 1.5 Inter-Quartile Range mark. We note that Mauchly’s test again showed a violation of sphericity (X2(434)= 635.123, p<.001). Thus, we used the Greenhouse-Geisser estimates to correct the degrees of freedom for our analyses (ε=.412). We found a significant main effect of Time,
F(11.939,549.180)=65.887, p<.001, ηp2=.589, as well as Delegation, F(1, 46)=127.164, p<.001, ηp2=.734. Principals on average had longer reaction times (M=.712, SE=.014) compared to agents (M=.589, SE=.016), see Figure 2a. The main effect of Role was found to
Table 2
Est. Marginal Means Summary
Delegation Role Attack Defense Principal 4.498 (.316) 5.125 (.275) Agent 4.152 (.308) 4.846 (.301) Table 3
Correlation Matrix Summary
Principals-Attack Principals-Defense Agents-Attack Agents-Defense
Risk-Pref. Attack .04 (.745) .07 (.581) .03 (.807) .003 (.985)
be highly non-significant, F(1, 56)=.010, p=.920. The interaction effect of Time*Delegation was found to be highly significant, F(15.246, 701.319)=9.462, p<.001, ηp2=.171. The reaction times of principals in the first round was significantly longer (M=1.177, SE=.022) than that of agents (M=.938, SE=.023). However, we see this difference narrowing down by round 15, where the difference between the two means stabilizes and continues to narrow; M=.563, SE=.023 for agents, and M=.662, SE=.022 for principals. This trend is present for both attackers and defenders, see Figure 2a.
The interaction effect of Time*Role was found to be highly non-significant, F(13.593, 625.285)=.837, p=.626. The interaction effect of Delegation*Role was found to be non-significant, F(1, 46)=1.623, p=.209. Interestingly, however, the three-way interaction of Time*Delegation*Role has shown to be highly suggestive, leaning towards significance at a higher (p=.10) Alpha level, F(14.857, 683.422)=1.523, p=.092, ηp2=.032.
Figure 2a. Mean reaction times of principals and agents as attackers (left) and defenders (right) across 30 rounds
4. Discussion
4.0. Investments, H1.
Our primary hypothesis stated that agents over-invest relative to the principals, irrespectively of role. Interestingly, our analysis showed that, in fact, subjects invested
relatively more out of the endowment as principals than as agents. For that reason we reject our hypothesis H1. Our results contradict our initial expectation, however, they do
complement the findings by Chakravarty et al. (2011) and Andersson et al. (2014). In their studies, like ours, agents have displayed more risk-seeking behavior than would be presumed. To take these results at face value, it would imply that delegation had the opposite effect of what was expected according to agency theory. Subject’s investments on average lowered in magnitude due to delegation. This could imply that, in the global sense of investing,
delegation increased risk-seeking in agents. However, we cannot hold such claims, as we did not yet account for the role-contingent rules which define the PPC as a match/miss-match investment game. Notwithstanding, our initial results come as a surprise. We will discuss these further in more detail whilst considering our next hypotheses in order to put these findings into a more adequate context of the PPC game.
4.1. Delegation, Roles and Risk-preference, H2 & H3.
Our secondary hypothesis stated that H2: agents over-invest in attack more than
principals, and our third hypothesis stated that H3: agents over-invest in attack, but not in
defense. We based our expectations on the assumption that agents over-invest due to an
increased sense of risk-aversion imposed by delegation. Over-investment is an indicator of risk-seeking specifically for attack, and not defense. Hence, we expected agents to over-invest in attack relatively more compared to their own investments in defense, as well as relatively more compared to the principals in overall. However, we did not find any difference between principal’s and agent’s over-investments in attack. Therefore, we reject our hypothesis H2. Furthermore, we did not see a difference between agent’s own investments in attack and defense. We replicated De Dreu et al.’s (2018) results in that attackers do invest less in
comparison to the defenders. Yet, this effect of roles seems not to have translated into a contributing factor when it comes to the effect of delegation on investing. Effectively, we conclude that it does not matter to the agent whether the mission is to attack or defend for his client in the PPC. We reject our hypothesis H3.
Despite the fact that agents actually under-invested relative to the principals, we know that this trend did not persist when it comes to the specifics of the game’s role-contingent rules. In terms of risk and how it is embodied within the two roles, agent’s behavior did not follow the pattern of investments that we would have expected according to agency’s assumption of risk-aversion. Firstly, under-investments in attack imply risk-seeking in the PPC. Our agents did display more risk-seeking relative to the principals. However, this was not true for defense, as principals had higher investments than agents. This means that
defending agents displayed less risk-seeking and more risk-aversion relative to the principals, as well as relative to themselves in attack. Since this pattern of investment is not congruent with the expected pattern according to which risk-preferences manifest themselves in the PPC, it leaves us thinking that the effect of delegation was not driven by risk-preferences per se. We shall now consider literature that may be offering an alternative explanation.
Chakravarty et al. (2011) argued that agents experience a distortion in the way they process utility-based estimations as they shift from the ‘self’ to the ‘agent’ condition. More specifically, they experience a down-shift in their sensitivity to derived utility. In order to try and ameliorate that, we imposed a sanctioning and feedback system – suggested to co-align the goals and incentives of the principal and the agent (Eisenhardt, 1989; Waterman & Meier, 1998; Saam, 2007). However, despite our efforts, it is likely that agents could not be
incentivized enough to reach a level of ‘decision-embodiment’ as they would when investing for themselves. This idea of embodiment complements Andersson et al.’s (2014) argument that delegation causes a dissociation from loss-aversion as a cognitive bias. The logic
presumes that the less the agent ‘embodies’ the investment decision as his own, the easier it is to dissociate from any loss-aversion related to the transaction.
To account for the alternative that our subject’s change in investment behavior was driven by loss-aversion and not aversion, we correlated mean investments with risk-preference scores for each group per condition. We expected to observe significantly positive correlations between R-P scores and investments for all groups. This would have given us an idea about how strongly risk-preferences affect investments within the PPC game. The higher one would have scored on their risk-preference measure (more risk-aversion), the higher one’s investments on average would have been in defense and lower in attack. Whereas, had one scored low on the risk-preference measure, one’s investments would have been respectively lower in defense and higher in attack. This type of pattern would have been proof of a relationship between risk-preference and delegated investing specifically within the PPC
game. However, our data did not provide us with such evidence, nor did we observe any correlation between risk-preferences and investments for that matter.
The absence of meaningful correlational evidence is suggestive of several things. Firstly, the effect of delegation that we had observed very likely isn’t attributable to
influences of risk-preference, at least not in our agents. To make matters worse, however, we are left to think that risk-preferences likely play no role at all when it comes to investing, at least not in our study. With respect to our within-dyad design, each subject was a principal and an agent; thus, even if risk-preferential influences emerged only after delegation, we would have noticed a pattern of difference in correlational magnitude between the groups of principals and agents. As a result, we believe we can frame an alternative explanation in terms of loss- as opposed to risk-aversion. Research has shown that people prefer minimizing losses compared to maximizing gains. Or, in other words, people are on average more loss-averse than they are risk-averse (Tversky & Kahneman, 1979; Kahneman & Tversky, 2013). Even so, the alternative explanation faces its own difficulties too. The studies of Chakravarty et al. (2011) and Andersson et al. (2014) have shown that i) risk-preferences do have an effect on choice gambles, ii) delegation does have an effect on risk-preferences, iii) delegation does have an effect on choice gambles, and iv) these effects were likely driven by loss-aversion. Essentially, the unspoken consensus among these two studies is that risk-preferences mediate the effect of delegation on loss-aversion, resulting in less risk-aversive gamble behavior.
Perhaps it would be interesting to explore whether dissociation from loss-aversion necessarily equates to a change in risk-preference. We argue for the possibility that our agents experienced a dissociation from loss-aversion, but that this did not necessarily result in a an apparent change in their risk-preference, as claimed by Andersson et al. (2014). We found some neuro-anatomical evidence to supports this. According to De Martino, Camerer, & Adolphs (2010), patients with amygdala lesions seem more risk-seeking in gambles compared to controls. Apparently not due to an increased drive for risk-seeking. Rather, the authors argue it is because of their readiness to accept mixed gain-loss gambles due to a reduction in loss-aversion. Despite their increased readiness to accept gambles, their patients exhibited substantial dislike towards increasing outcome variance. In other words, they displayed an equally preferential dislike for risk choices as did the control subjects. The authors suggest risk-aversion and loss-aversion might be governed by different neural networks.
We do not claim our agents had lesioned amygdalae, however, it is possible that delegation affected their fear-related mechanisms and thus caused a change in their sense of loss-aversion. A similar conclusion has been drawn in the research by Tremblay, Cocker, Hosking, Zeeb, Rogers, & Winstanley (2014), who studied dissociable effects of amygdala-lesioned rats in uncertain gain-loss gambling tasks. They show that amygdala lesions dampen decision-making biases related to (dis-)preference for losses, and not gains. The rats, as well, displayed an increased readiness to endure loss, as opposed to an increased readiness to take a gamble. In contrast, studies such as that of Tom, Fox, Trepel, & Poldrack (2007), argue that it is unlikely that risk- and loss- aversion operate through separate systems. Through a series of neuro-imaging studies, the authors have shown that both loss and gain related processes are coded by the same neural networks. The conclusion was that, rather it being due to an
increased activity in processing of negative emotions, loss-aversion was predominantly driven by an activity decrease in regions responsible for coding subjective value.
In consideration with the abovementioned literature, it remains unclear whether these constructs can operate independently of each other. Nonetheless, this type of explanation fits best with our data for two reasons. Firstly, the investment pattern that we had observed did not follow the expected pattern according to which risk-preferences are assumed. Moreover, we found no correlational evidence to even support a risk-based explanation. Secondly, however, we think the investment pattern did follow a pattern according to which loss-aversion would be assumed in the PPC. We will now break this down into an explanation appropriate for the context of the PPC.
Unlike risk-preferences, loss-aversion does not account for prospective gains. Rather, the probabilistic estimates of (dis)utility change in loss-aversion are believed to be driven purely by potential loss (Tremblay et al., 2014). Hence, given that our agents under-invested irrespectively of their role, it goes to show that they didn’t account for the role-contingent profit rules which dictate the array of prospective gains. Evidently, we could say that our agents didn’t invest with a focus on gains. Thus, in relation to the expected value
maximization principle, we believe our agents invested according to what held the largest expected value for them – not losing a guaranteed resource, as opposed to potentially maximizing the principal’s profit, through uncertain gambles. Despite the fact that the endowment technically wasn’t the agent’s, it seems reasonable – under the assumption of loss-aversion, that agents still preferred retaining a secured resource than gambling for prospective resources. This is somewhat evident from the fact that our agents on average
never invested more than half of their endowment, unlike principals. Moreover, since endowments and its rules are equal across all of the conditions, investments guided by loss-aversion should also not differ per condition. This, indeed, was the case in our study. In contrast, if investments were guided by risk-aversion, the pattern of investments should then differ for attack and defense respectively. This was not the case in our study. As a result, we believe our agent’s investment behavior was driven by loss-aversion, and not their risk-preferences.
4.2. Exploratory Post-Hoc Speculation.
We wanted to explore whether reaction times could be considered as means of risk-management. We speculated that longer reaction times could reflect on investments as a cognitive byproduct of risk-aversion. However, we would like to note that in consideration with our experimental design, perhaps it would be better to call it decision time instead of reaction time. Logically, we though -the more time one takes to consider the best investment choice, the less risk one imposes onto himself. Similarly, we could assume that shorter decision times represent the hastiness of a more risk-seeking decision process. We did observe an effect of delegation on decision time, where agents on average deliberated significantly shorter than principals. As a result, we build up on our previous argument and suggest that dissociation from loss-aversion may be apparent through shorter decision times. According to Mason, Capitanio, Machado, Mendoza, & Amaral (2006), this might be the case. Their research on amygdala-lesioned primates suggests there is a relationship between amygdala dysfunction and approach times to potentially threatening stimuli. Again, whether a change in decision time reflects on a change in risk-preference or merely a loss-aversion process is another question for future research.
4.3. Conclusion.
To sum up, our data determined that delegation does have an effect on investing in the predator-prey contest game. Within the PPC, agent’s investments decrease in magnitude, irrespectively of their role. In terms of risk, this would imply that agency caused our subjects to invest in a more risk-seeking manner on average. However, since this pattern did not follow the expected investment pattern under which risk is embodied by the two roles, (low
investments in attack or high investments in defense) we cannot say that the effect of delegation that we had observed was due to a change in risk-preference. According to our results, risk-preferences most likely don’t influence investing behavior within the PPC.
Therefore, we have to refute agency’s assumption on agent risk-aversion. We believe a possible explanation for our results might be an effect which operated through loss-aversion as opposed to risk-preferences. We think that delegation causes a change in the agents’ degree to which they associate or disassociate with loss-aversion related to the transaction, which may or may not affect subsequently underlying constructs. In that regard, neuro-anatomical evidence provides us with ambiguous information on this possibility.
4.4. Limitations & Future Research.
Firstly, a significant limitation of our study was the limited array of diversity in our sample. The vast majority of our participants were Caucasians from the Netherlands, of whom almost all studied psychology. Had we dealt with a more diverse sample of subjects, our results could be more generalizable in terms of the average person. Secondly, it seemed that a significant portion of subjects had difficulties truly understanding the game’s rules and its set-up. The short lab time that we spent with our participants limited us in our capacity to explain the game as thoroughly as they might need. In that sense, making the game’s instructions even clearer and structured might have helped. Thirdly, our study did not employ pre- and post-test measurements to observe a direct change in risk-preference. In order to gain a more detailed understanding, and to draw more causal conclusions, we suggest the use of pre- and post-testing for future research.
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