My Risk, Your Risk, and Our Risk: Costly Deviation in Delegated Risk-Taking Environments

Abstract

Risk choice delegation is pervasive in financial environments. While previous research has explored how agents balance self-interest with interests of passive investors little is known about how this balance is achieved when investors voluntarily decide the amount to invest or when risk is shared between agents and investors. Our findings show agents engage in costly deviation from their preferred risk level when choosing risk exposure levels, revealing a form of prosocial preferences. We further find that this deviation is sensitive to investment levels and institutional features like whether risk is shared and accountability opportunities by investors or a third party.

Keywords:

• Costly deviation
• Risk
• Experiment
• Decision-making for others

JEL CODES:

• C91
• D81
• L26

Acknowledgements

We are grateful for funding from the Baugh Center for Entrepreneurship & Free Enterprise and for helpful comments and suggestions provided by seminar participants at Baylor University, Sewanee: University of the South, the Southern Economic Association meeting, and the North America Economic Science Association Meeting and many others. The authors know of no other conflicts of interests related to this manuscript to disclose.

Notes

1 Note, due to space constraints, percentages in the task and in the instructions were rounded to the nearest percent, but exact dollar values corresponding with the gain or loss and expected values corresponding to the precise non-rounded percentages were always shown for each option in the experiment. We did this to ensure that participants always were aware of the exact manner in which decisions would affect payment.

1 These studies differ in terms of the game they use. For instance, Reynolds, Joseph, and Sherwood (2009) use binary prospects (a choice between a risky lottery and a guaranteed payment), while Eriksen and Kvalöy (2010) and Pollmann, Potters, and Trautmann (2014) use a game similar to that in Gneezy and Potters (1997). Chakravarty et al. (2011) and Andersson et al. (2016) use a multiple price list. Polman (2012) uses a coin toss game.

2 Charness and Jackson (2009) use a stag-hunt game. Sutter (2009) uses the Gneezy and Potters (1997) game. Finally, Pahlke, Strasser, and Vieider (2012) use a binary prospect where decision makers choose between a risky lottery and a guaranteed payment. Others use a multiple price list.

3 While previous studies also consider agents with their own stake (Füllbrunn and Luhan 2017 2020; Pahlke, Strasser, and Vieider 2012; Lefebvre and Vieider 2014; Andersson et al. 2016), the principals in these studies are considered passive players. Moreover, they do not vary the risk structure faced by the agents.

4 While there is active investment in trust game studies (e.g., Aimone and Houser 2011, 2013; Bohnet and Huck 2004; Bohnet and Zeckhauser 2004; Fehr and Rockenbach 2003), typically these studies do not include a risk component as part of the trustee’s decision. Either risk is completely absent on back-transfer from the trustee to the investor or the trustee’s decision is subject to risk from nature, and thus out of their control (Charness and Dufwenberg 2006). Thus, trust game studies do not directly apply to economic environments where divisions of gains and losses are preset and the pathway for determining the chances of gains and losses is decided by a delegate-agent.

5 Potential conflicting interests between investors and agents in our treatments (either in terms of risk preferences in Shared or risk exposure in Non-shared) are related to the literature that examines how agents make decisions when there are divided interests between the agents and principals (Andersson et al. 2020; Lefebvre and Vieider 2014). For example, Andersson et al. (2020) find that risk-delegates who face strong monetary incentives like bonuses and tournaments respond strongly to such incentives, leading to an increased risk exposure for the passive stakeholder. In the same vein, we explore the conditions when agents who are entrusted by active investors engage in costly deviation from their own preferred risk choices.

6 This paper reflects the same experiment as Aimone and Pan 2020) but each of the papers look at different sides of the experiment. Unlike this paper, Aimone and Pan 2020) explores data from the investors side and does not explore agents’ risk-decisions responding to the amount of delegation (level of investment), nor do they explore whether risk decisions respond to investor or third-party accountability decisions. See Appendix (reproduced with permission from that paper) for the experimental instructions.

7 The investor or the third party can either increase or decrease an agent’s earnings. We use “punishment” or “accountability” interchangeably, rather than using “punishment and reward,” for simplicity. Moreover, a lower reward than expected or hoped for can also be regarded as a type of punishment.

8 The experiment in Aimone and Pan 2020) is the same as the experiment here. That paper reports on the behavior of investors and third parties while this paper reports on different data, specifically the behavior of trustee agents.

9 We follow the norm in the literature on trust game experiments by using investments in the $0 to $10 range. This is of course low in comparison to what would be the levels of investments present in naturally occurring environments. Our goal is not to make point predictions about what behavior by agents will be, instead we are seeking to identify patterns of behaviors. An increase in stake size may have an impact on decisions, yet based on the literature on trust game, the qualitative result that trustees still send back is expected to remain (Johansson-Stenman, Mahmud, and Martinsson 2005). Meanwhile, we would expect that agents would be more risk averse in general with higher stakes in the Solo game (as in Holt and Laury 2002), however it is unclear though whether this increased risk aversion in the Solo environment would lead to systematically different costly deviation decisions in non-Solo environments. We encourage future researchers to consider exploring how the behaviors we identify in this study vary with stake sizes.

10 See the appendix for details of the strategy method procedure, reproduced with permission from Aimone and Pan 2020).

11 The Shared treatment entails no inequality between investor and agent either before or after the outcome is realized while the Non-Shared treatment entails only a realization inequality (except in the case of Project 1). In our experiment, agents make their risk choices before the outcome is realized and thus there is no expected inequality during the decision-making process.

12 Such relationships even exist between doctors and patients. Patients (the investor stakeholder) and doctors (the delegated agent) agree upon a specific type of surgery to undertake for a medical problem, but the decisions made in the operating room under unforeseen circumstances are left to the discretion of the doctor. In this case, fear of punishment may lead a doctor to choose a more risk-averse option even if the doctor and patient might both individually prefer a less risk-averse approach.

13 We are cautious to interpret deviations as a lower bound of prosocial behavior as agents may believe that investors share their risk preferences and thus believe that they are making a prosocial decision.

14 A Nash equilibrium does not necessarily predict any deviation, especially in the Shared treatment where agent and investor interests are perfectly aligned. Even in the Non-shared treatment, an agent may expect no punishment if a decision is made in a careful non-shirking manner (Gurdal et al. 2013), particularly when the agent’s decision is judged on the choice (Ex-ante) rather than the outcome (Ex-post).

15 For our purposes, outcome bias indicates that a subject’s evaluation of a decision is influenced by the realized outcome of uncertainty even if such outcome is out of the control of their decision maker. In our environment, it implies that given the same risky project choice by an agent, others perceive the decision more favorably after a high outcome than after a low outcome of the risky project. Baron and Hershey (1988) showed that subjects rated thinking as better when the outcome of the option not chosen turned out poorly than when it turned out well.

16 This study’s protocol (IRB14-0688) was reviewed and approved by Harvard’s Harvard University-Area Committee on the Use of Human Subjects and participants received a consent form. The project was also approved by Baylor University’s Institutional Review Board (#586440-1).

17 The following tests are two-sided Wilcoxon signed-rank test unless otherwise noted.

18 The following tests are two-sided Wilcoxon signed-rank tests unless otherwise noted. P-values are Bonferroni-corrected for two multiple comparisons for Shared and Non-shared and p-values are Bonferroni-corrected for three multiple comparisons at three investment levels. The p-values would remain significant at the 0.05 level even if we corrected for all twelve multiple comparisons.

19 See supplemental Table 1 for a version of Table 4 with p-values updated to reflect 10000 simulations of random behavior. See the Supplemental Text Tables S2-S4 for alternative models other than a Tobit to account for the censored nature of the Costly Deviation Index. Table S2 uses a standard OLS modeling technique, Table S3 uses a Poisson model, and Table S4 converts the Costly Deviation Index into a binary variable to explore whether a participant deviates positively or not. Each of these models generally finds similar significant increased deviations under Ex-post punishment. Only the binary version of deviation shows a marginal or significant influence of Ex-ante punishment in some circumstances. These alternative models also vary model 1, allowing for an exploration of punishment as a pooled dummy variable.

20 Croson and Konow (2009) use a variant of the dictator game without uncertainty that tests for distributive and reciprocal preference. Pollmann, Potters, and Truatmann (2014) find that accountability increases risk averse choices when an agent works purely as a delegate. Pahlke, Strasser, and Vieider (2015) find that justification significantly reduces loss-averse choices among agents who work as delegates. The latter two papers focus on only stakeholder enforcement.

21 The Madoff and Theranos scandals are focal examples of clearly illegal decision-making where third-party (government) litigation occurred.