MSC Thesis
Groupthink in a principal-agent setting
Mark van Oldeniel
Supervisor: Dr. P. HeijnenJanuary 11, 2019
Abstract
1
Introduction
A common desire for consensus can develop in groups of people working together. This consensus attitude may come at the expense of critical reasoning, critical reflection, and critical evaluation of the consequences of certain decisions. This phenomenon is called groupthink, a term first introduced by Janis (1971). Groupthink might result in a col-lective form of willfull blindness. Warning signals are neglected or denied as they might harm the consensus in the group, or might cause the individual bringing up the signals to be met with dissent.
The consequences of groupthink can be disastrous as bad decisions might be made as a result of a lack of critical reflection. Janis (1971) studied policy decisions and identified that groupthink played a role in the Bay of Pigs invasion and escalation of the Vietnam war. More recently, groupthink seems to have played a role in the Volkswagen emissions scandal (Heath, 2015), and may have caused the IMF to miss the risks that lead to the 2008 global financial crisis (Beattie, 2011). Warning signals were neglected or selectively interpreted.
B´enabou (2012) provides a theoretical model of collective denial and willfull blindness within a firm. Agents work on a joint project and their payoff depends on the actions of themselves and their colleagues. Agents derive anticipatory utility from their future prospects. This creates an incentive to deny negative signals, as denying those signals might allow the agent to have the anticipatory pleasure of a good future.
(2011) argues that the aggressive targets set within Volkswagen, may have resulted in a corporate culture that did not accept defeat. Given the potential disastrous effects of groupthink, firms should be interested in finding ways to limit groupthink if it has the potential to harm the firm. In my model, firms will get the possibility to set the contracts of agents, and hence to influence the incentives faced by agents. I will show that by adjusting certain parts of the contract, the firm might make groupthink more or less likely. More specifically, I will show that by making salaries less dependent on the outcome of the project, groupthink is less likely. In addition, I will show that a firm always has an incentive to limit groupthink.
The remainder of this thesis is as follows: In section 2, I will discuss relevant literature, in section 3, my model will be introduced. Next, I will solve my model via backward induction, discussing several cases, in section 4, before moving to the contracting phase in section 5. Section 6 concludes my thesis.
2
Literature
My model aims to contribute to the theoretical literature on groupthink, and in a broader sense the literature surrounding attitudes towards information and self-deception. In addi-tion, I will incorporate a principal-agent structure, relating my model to the (behavioural) contract theory literature.
an individual. 1
However, there are many situations in which individuals actively avoid information. Golman et al. (2017) provides an overview of theoretical and empirical research on infor-mation avoidance. They identify two broad categories of reasons for inforinfor-mation avoid-ance. Firstly, individuals engage in information avoidance for hedonic reasons. Certain types of information, such as hearing that you have a disease, change your beliefs about the future. The anticipation of the future may directly impact how you feel and have direct utility-consequences. This direct impact of information on utility can create an incentive to avoid information. Secondly, individuals engage in information avoidance for strategic reasons. Individuals may for example avoid information that could demotivate them, or avoid information if they fear that knowing the information might morally or ethically compel them to act on it.
In addition to theoretical models, there is a wide range of empirical evidence that shows that individuals avoid information. Eil and Rao (2011), for example, show that subjects who receive bad news do not update their beliefs in a Bayesian way. Subjects underrespond to bad news, while being closer to proper updating when receiving good news. In their experiment, individuals were ranked on their attractiveness and on their IQ and received information about their ranking compared to other participants. The good news-bad news effect shows that people may be reluctant to adjust their beliefs downward, as beliefs may have direct utility consequences. An empirical example in line with selective forgetting is provided by Shu and Gino (2012). In their experiment, participants who cheated recalled less items from a moral code, even if they were payed to accurately remember these items.
Groupthink can be seen as a form of information avoidance for hedonic reasons. By
1An exception to this is that in certain interpersonal interactions, being ignorant can be a strategic
biasedly interpreting information and by neglecting warning signs, individuals may enjoy the belief in a ’good’ future.
In my model, as in B´enabou (2012), individuals engage in information avoidance by strategically interpreting pieces of information. Bad signals may be neglected or forgotten. This theoretical mechanism has featured in a stream of papers by Bnabou and Tirole, which have used this mechanism in models dealing with self-confidence, identity, and belief management (B´enabou and Tirole, 2002,2011,2016). To uphold self-confidence, pleasant beliefs, or to protect one’s identity, individuals may benefit from selectively avoiding unfavourable information.
B´enabou (2012) provides a theoretical model of groupthink. Agents working on a joint project have anticipatory preferences. These preferences can create an incentive to selectively interpret signals about the prospect of the project. More specifically, agents may have an incentive to disregard bad news. A key feature in this model is that the denial of bad news is contagious if it is harmful to others, and self-limiting when it is beneficial. The main intuition behind this Mutually Assured Delusion (MAD) is that the anticipatory benefit of disregarding bad news is larger if an agent is hurt by other agents engaging in denial. If an agent benefits from other agents disregarding bad news, accepting bad news may not hurt as much.
In B´enabou (2012), agents choose whether or not to correctly interpret a signal about the prospect of a joint project. This decision depends on exogenous factors and firms are not able to affect whether groupthink will occur. My model will add a contracting stage to this model, which will give the firm the ability to influence the contract that agents sign. Via this contract the firm can influence the incentives agents face and may make groupthink more or less likely.
Traditional contract theory, as discussed in Bolton and Dewatripont (2005), typically assumes agents to rationally choose the option that maximizes their (expected) utility. The main problem in contract setting is usually information asymmetry and the problems resulting from it. For example, firms may not be able to perfectly observe the ability of the workers it hirers, which may lead to adverse selection and screening problems. Another problem is that firms may not always be able to observe how hard each worker works. This may lead to moral hazard problems, as agents may not put in effort. To overcome this moral hazard problem, firms may try to set a contract that would allow agents to earn a higher wage if firm profits are high, which would result in an incentive to work hard.
In these models, agents tend to have preferences in line with classical economic mod-els. However, over the past decades, behavioural economic research, based on research in psychology, has found many situations in which individuals do not behave in line with these classical models. This behavioural economic research has also proposed alterna-tive models of individual behaviour. Two examples of these insights are loss-aversion and present-bias. Loss aversion is based on prospect theory (Kahneman and Tversky, 1979,Tversky and Kahneman, 1992), and refers to the finding that individuals tend to dislike losses, compared to some reference point, more than that they like gains. An example of present bias is if individuals prefer to receive 100 euro today over 101 euro to-morrow, but, at the same time, prefer to receive 101 euro 31 days from now over receiving 100 euro 30 days from now.
model will have a similar distinction between a fully rational principal (the firm), and agents that behave according to a model that takes into account the psychological finding that people can engage in wishfull thinking.2
3
The Model
The model in this thesis will build heavily upon the model in B´enabou (2012). Compared to that model a contracting stage, where the firm sets a contract and agents may accept it, will be added. Despite its similarities with the paper by Benabou, I will write down all the steps involved in explaining and solving the models to ensure that this thesis can be read on a stand-alone base.
3.1
The setting
A firm (the principal) has a project with an uncertain productivity and needs a group of N identical workers (agents) to complete the project. The model has 4 periods.
At t = 0, the firm will offer an identical contract to all agents, which agents can accept or decline. The salary of an agent will consist of a fixed part, denoted with F , and a variable part that depends on the outcome of the project. The salary will be paid at t = 3. The extent to which the salary depends on the outcome of the project is denoted by φ. For the agents to accept the contract, their expected utility of doing so should be higher than the expected utility they could get from working somewhere else (their outside option, O). This results in an individual rationality constraint for the agent, given by (1).
2Agents within my model are also rational, in the sense that given their preferences and the constraints
IRagent: U0i ≥ O (1)
This IR-constraint states that agent i will only accept the contract if the (expected) utility of accepting the contract at t = 0 exceeds their outside option (O). For simplicity, I will assume that the firm has all the bargaining power and hence that it can set the contract such that the expected utility of the agent is exactly equal to his outside option. At t = 1 agents get a common signal about the productivity of the project. This signal might be either high or low, σ = {H, L}. A low signal means bad news about the prospect of the project. In case of a high signal the expected productivity is θ = θH, and
θ = θLin case of a low signal. ∆θ ≡ θH− θL > 0, θH > 0, and θLcan be either positive or
negative. The a priori probability to receive a high signal is q, the probability to receive a low signal is 1 − q.
Agents may have an incentive to misinterpret a low signal. Upon observing a low signal, agents choose how to interpret the signal. Agents may choose to accept the facts realistically, which will cause the signal to be encoded in the memory truthfully. Agents can also choose to engage in denial, which entails wrongly encoding a low signal as an high signal in the memory. There are cognitive costs associated with denial (m ≥ 0).3
At t = 2, agents have to make an effort choice ei ∈ {0, 1}, with costs of effort cei. The
effort choice is simple, agents either put in effort (ei = 1) or are inactive (ei = 0). Agents
will only put in effort if it increases their expected utility compared to inaction.
In addition, agents get anticipatory feelings resulting from thinking about their future salary, sEi
2[U3i], where s ≥ 0 stands for savouring or susceptibility, which represent the
3This choice about the interpretation of a signal might happen consciously or unconsciously. In
psychological effects of hopefulness, dread, and similar emotions. These anticipatory feelings will depend on the agent’s expectations about the future. Anticipatory feeling result in agents preferring to have hopeful beliefs about the future, which may create an incentive to misinterpret a low signal at t = 1.
While agents may engage in self-deception and misinterpret a low signal, this is not unconstrained. At t = 2, an agent might not remember the actual signal they received, but they will be aware of their tendency to misinterpret a low signal. So if an agent remembers a high signal, they will be aware that this might be the result of their misinterpretation of a low signal. The agent’s rate of realism (λ) is given by (2).
λi ≡ P r[ˆσi = L|σ = L] (2)
The agent’s rate of realism is defined as the probability that they remember the signal to be low (ˆσi = L), given that the true signal was low (σ = L). If λ = 1 an agent always
realistically encodes a low signal as a low signal, while if λ = 0 an agent is always in denial and encodes a low signal as a high signal. If 0 ≤ λ ≤ 1, an agent mixes between engaging in denial and realism.
When an agent remembers a high signal at t = 2, their posterior belief about the true signal being high is represented in (3).
P r[σ = H|ˆσi = H, λi] = q
q + (1 − q)(1 − λi) ≡ r(λ
i) (3)
indeed was high). However, if an agent engages in pure denial (λi = 0), their posterior is only q and an agent at t = 2 will thus act on their prior, since remembering a high signal is not informative about the true signal that was received.
At t = 3, final payoffs realize. The expected salary of an agent is represented in (4).
U3i ≡ φθ[αei+ (1 − α)e−i] + F (4)
The salary consists of a fixed payment (F ) and depends on the outcome of the project. The extent to which final salary depends on the outcome of the project is determined by φ. Both φ and F are specified in the contract at t = 0. The returns to the project depends on the productivity of the project (θ). Returns to the project also depend on the effort of the agent itself (ei) and on the average effort put in by other agents (e−i ≡ 1
n−1
P
j6=ie j).
The degree of interdependence is given by 1 − α ∈ [0, 1 − 1/n], which reflects the degree to which the project is a joint effort.
The profits of a firm are represented in (5).
Π3 ≡ θV N X i ei− N X i U3i (5)
Profits depend on the realized productivity (θ) and the effort chosen by all workers. The costs of the firm consists of paying salaries, which are given by (4). Productivity is scaled up by V > 1 to ensure that for φ = 1 and F = 0 (as in the model by B´enabou (2012)) profits are positive if θ > 0.
Period 0 Period 1 Period 2 Period 3
• Contracting stage; Firm chooses fixed fee (F ) and degree to which salary depends on outcome (φ) Agents will accept contract as long as; IR-agent: U0i≥ O • Signal about project value θ • Recall (attention, awareness): • H → H % L → L Action choice ei= {0, 1} Cost cei Anticipatory feelings: hope, dread, anxiety; sEi 2[U3i] Final payoffs Ui
3≡ φθ[αei+ (1 − α)e−i] + F
e−i=n−11 P j6=iej Π3= θVPNi e i−PN i U i 3 Figure 1. Timeline
4
Solving the model
I will solve the model via backward induction, which is similar to the approach in B´enabou (2012). Since I included a fixed payment (F ) and a possibility to scale up or down the variable payment (φ), specific results will differ. The tradeoffs faced by the agents in my model collapse to the tradeoffs they face in B´enabou (2012) for φ = 1 and F = 0. The key implication of my model is that, by strategically setting the fixed payment and the scale of the variable payment, a firm might make groupthink or denial equilibria more or less likely. When expected productivity is negative in case of a low signal (θL< 0), a firm
should prefer agents to be realistic, while if productivity is positive in case of a low signal (θL > 0), denial might not be as bad.
Since no decisions have to be taken at t = 3, the backward induction will start at t = 2.
4.1
Period 2
U2i = −cei+ sE2i[U3i] + δE2i[U3i] (6)
Plugging in (5) yields the following expression:
U2i = −cei+ (s + δ)E2i[φθ[αei+ (1 − α)e−i] + F ] (7)
Period 2 expected utility depends on the effort choice and on both the anticipation of the future salary (via s) and the discounted expectation of the future salary.
An agent will only choose to put in effort (ei = 1) if their expected utility of doing so
exceeds the expected utility of not putting in effort (ei = 0), this results in the condition
given in (8).
−c + (s + δ)E2i[φθα + φθ(1 − α)e−i+ F ] ≥ (s + δ)E2i[φθ(1 − α)e−i+ F ] (8)
The effort decision of other agents and the fixed fee is not affected by the effort choice of agent i. Since all parameters except for the productivity parameter (θ) are certain, they can be taken outside the expectation brackets. The expression above, therefore, simplifies to:
(s + δ)φαE2i[θ] ≥ c (9)
Proposition 1. Threshold values φ • If Ei
2[θ] = θH, agents will put in effort if:
φ ≥ c
(s + δ)αθH
≡ φH (10)
• If Ei
2[θ] = qθH + (1 − q)θL, agents act on their prior.4 Agents will put in effort if:
φ ≥ c
(s + δ)α(qθH + (1 − q)θL)
≡ φprior (11)
• If Ei
2[θ] = θL, it will never be optimal to put in effort if θL < 0.5 If θL > 0, however,
agents will put in effort if:
φ ≥ c
(s + δ)αθL
≡ φL (12)
Since θH > qθH + (1 − q)θL> θL, φH < φprior < φL. An higher expected productivity
level makes putting in effort more attractive, which lowers the threshold for φ. For all φ such that 0 < φ < φprior agents acting on their prior will not put in effort at t = 2. And for all φ such that φH < φ < φprior agents acting on their prior will not put in effort, but agents acting on a high signal will put in effort.
4.2
Period 1
In period 1, agents receive a signal and have to decide on a cognitive strategy. Period 1 discounted utility of pay-offs is given by (13).
4I assume this expectation to be greater than 0, which is an assumption that B´enabou (2012) also
makes. If this would not hold, the ex ante expected productivity of the project would be negative.
5Technically, the firm could induce effort in this case by setting a negative φ, which corresponds to
U1i = −Mi+ δE1i[−cei+ sE2i[U3i]] + δ2E1i[U3i] (13)
In this expression Mi represent the date 1 costs of the chosen cognitive strategy. If an agent engages in denial, Mi = m, and Mi = 0 in case of realism. The second and third term are the discounted period 1 expectations about (6).
Since agents will not have an incentive to misinterpret a high signal, high signals will always be realistically encoded in the mind. If an agent receives a low signal, anticipatory feelings create an incentive to engage in denial. A couple of cases need to be distinguished in case of a low signal, as depending on the value of φ agents engaging in denial or realism might make different effort choices in period 2. These different effort choices may result in different optimal cognitive strategies at t = 1. More specifically, agents choosing to engage in denial know that they will act on their prior in the next period. This might mean that they will put in effort or not depending on the value of φ. I will search for the optimal cognitive strategy for different values of φ 6
In this analysis, I will follow B´enabou (2012) and first impose some arbitrary level of realism λ−i ∈ [0, 1] for all other agents and look for a best response level of realism λi.
This best response cognitive strategy is a personal equilibrium.
In discussing each separate case outlined in proposition 1, my approach will be similar. If an agent receives a low signal, this agent can engage in realism or in denial. I will calculate the expected utilities associated with both choices. An agent’s incentive to engage in denial is given by the difference between both expected utilities. Next, I will evaluate for which values of φ realism or denial is a personal equilibrium. I will only focus
6If φ < φH
on situations in which pure realism or denial is an equilibrium. In a later section, I will come back to the possibility of mixed strategy equilibria and to the possibility of multiple equilibria.
After discussing the personal equilibria in all separate cases, I will move to solve for a social equilibrium in cognitive strategies. A realistic social equilibrium entails that all agents have an incentive to be realistic, given that all other agents are realistic, and vice versa for a denial social equilibrium.
4.2.1 Case 1: φH ≤ φ < φprior
If φH ≤ φ < φprior, agents engaging in denial and acting on their prior will not put in
effort at t = 2. Agents receiving a low signal will thus know that regardless of their cognitive strategy, no agent will put in effort in the next period. This means that agents will only receive their fixed salary at t = 3.
Hence, in case of realism, agent’s expected utility can be found by plugging in ei = 0, Mi = 0, Ui
3 = F in (13), which results in period 1 expected utility of realism:
U1,R1i = δ(δ + s)F (14)
In case of denial, agents have cognitive costs associated with denial, and agents know that their own level of effort will be zero. This results in the following expected utility of denial:
U1,D1i = −m + δE1i[sE2i[((1 − a)e−i)φθ + F ]] + δ2E1i[[(1 − α)e−i]φθ + F ] (15)
An agent engaging in denial knows that in the next period they will assign probability r(λi) to being in state H with productivity θ
exerting effort. They will assign probability 1 − r(λi) to being in state L, where no one puts in effort.7 Expected utility in case of denial,15, simplifies to:
= −m + δs[F + r(λi)λ−i(1 − α)φθH] + δ2[F ] (16)
Which can be rewritten as:
= −m + δ(δ + s)F + δsr(λi)λ−i(1 − α)φθH (17)
Agent’s incentive to deny reality is given by the difference between (17) and (14):
U1,D1i − Ui
1,R1= −m + δsr(λ i)λ−i
(1 − α)φθH (18)
I denote the RHS of (18) as Ψ1(λi, φ|λ−i). Since r(λi) and thus Ψ1(λi, φ|λ−i) are
increasing in λi, realism (λi = 1) is a personal equilibrium if Ψ1(1, φ|λ−i) ≤ 0, which
corresponds to:
φ ≤ m/δ
s(1 − α)λ−iθ H
≡ φ1 (19)
Denial (λi = 0) is a personal equilibrium if Ψ1(0, φ|λ−i) ≥ 0, which corresponds to:
φ ≥ m/δ
sq(1 − α)λ−iθ H
≡ ¯φ1 (20)
λi ∈ (0, 1) is the unique solution to Ψ1(λi, φ|λ−i) = 0 for Ψ1(0, φ|λ−i) < 0 <
Ψ1(1, φ|λ−i).
7Since agents engage in denial, their period 1 expectation about their salary differs from their period
4.2.2 Case 2: φ ≥ φprior
In this section, I will assume that agents engaging in realism who receive a low signal will not have an incentive to put in effort. I will address the alternative in the next subsection. When φ ≥ φprior, agents engaging in denial will put in effort at t = 2. This also means that agents know that other agents that engage in denial will put in effort at t = 2. Expected utility of engaging in realism is:
U1,R2i = δ(δ + s)[(1 − α)(1 − λ−i)φθL+ F ] (21)
Expected utility of engaging in denial is:
U1,D2i = −m + δE1[−cei+ sE2[(αei+ (1 − a)e−i)φθ + F ]] (22)
+ δ2E1[[(αei) + (1 − α)e−i]φθ + F ]
If the agent engages in denial, they will, in the next period, assign probability r(λi)
to being in state H with productivity θH and everyone exerting effort, and probability
1 − r(λi) to being in state L where only agents that engage in denial put in effort. The incentive to engage in denial in this case is given by:
U1,D2i − Ui
1,R2= −m − δ(c − (δ + s)αφθL) + δsφr(λi)[(1 − α)λ−iθL+ ∆θ] (23)
if Ψ2(1, φ|λ−i) ≤ 0, which corresponds to:8
φ ≤ m/δ + c
sθH + δαθL− (1 − λ−i)sθL
≡ φ2 (24)
Denial (λi = 0) is an personal equilibrium if Ψ2(0, s|λ−i) ≥ 0, which corresponds to:
φ ≥ m/δ + c
(s + δ)αθL+ sq∆θ + sq(1 − α)λ−iθL
≡ ¯φ2 (25)
λi ∈ (0, 1) is the unique solution to Ψ2(λi, φ|λ−i) = 0 for Ψ2(0, φ|λ−i) < 0 < Ψ2(1, φ|λ−i).
4.2.3 Case 3: φ ≥ φL
This case is only a possibility if θL > 0. In this case both agents engaging in denial and
agents engaging in realism will put in effort in case of a low signal. Expected utility of engaging in realism when receiving a low signal is:
U1,R3i = −δc + δ(δ + s)[φθL+ F ] (26)
All agents will exert effort in all possible states. Expected utility of engaging in denial is:
U1,D3i = −m + δE1[−c + sE2[φθ + F ]] + δ2E1[φθ + F ] (27)
If the agent engages in denial, they will assign probability r(λi) to being in state H with
high productivity and 1 − r(λi) to being in the low productivity state. Expected utility
8When θ
L> 0, the denominator will always be positive regardless of the exact value of the parameters.
I assume here that the denominator is also positive when θL < 0, which comes down to assuming that
becomes:
U1,D3i = −m − δc + δ(δ + s)F + r(λi)δsφθH + (1 − r(λi))δsφθL+ δ2φθL (28)
The incentive to engage in denial is given by:
U1,D3i − Ui
1,R3= −m + r(λ
i)δsφ∆θ (29)
The benefit of engaging in denial is that in the next period an agent believes to be in the high state with probability r(λi), which increases anticipatory feeling by the difference between θH and θL. On the other hand, the cognitive costs of denial are m.
Realism is a personal equilibrium (λi = 1) if:
φ ≤ m/δ
s∆θ ≡ φ3 (30)
Denial is a personal equilibrium (λi = 0) if
φ ≥ m/δ
qδs∆θ ≡ ¯φ3 (31)
4.2.4 Social equilibrium
I will first discuss the first case. By plugging in 1 for λ−i in (19), the threshold for φ becomes:
φ1 = m/δ
s(1 − α)θH
(32)
A pure denial social equilibrium does not exists. Looking at (18), the second term will become zero if λ−i = 0, and the expression will simplify to: −m, which is always negative. Hence, an agent will not have an incentive to engage in denial if all other agents engage in denial. Intuitively, if all other agents engage in denial, they will not put in effort in case of a high signal, which removes the benefit from engaging in denial.
Now, I will move to the second case. By plugging in 1 for λ−i in (24), the threshold for φ becomes: φ 2 = m/δ + c sθH + δαθL (33)
Similarly, the threshold for denial in case all agents engage in denial becomes:
¯ φ2 =
m/δ + c
sqθH + δαθL− s(q − α)θL
(34)
The thresholds for the different cases are summarized in Proposition 2. 9 Proposition 2. Social equilibrium
The social equilbria in the different cases are:
9For all threshold values for realism and denial, I cannot be certain whether these thresholds lay within
- Case 1: φH ≤ φ < φprior
• Realism is a social equilibrium if: φ ≤ s(1−α)θm/δ H
• Denial is never a social equilibrium - Case 2: φ > φprior
• Realism is a social equilibrium if: φ ≤ sθm/δ+c H+δαθL
• Denial is a social equilibrium if: φ ≥ sqθ m/δ+c H+δαθL−s(q−α)θL
- Case 3: φ > φL
• Realism is a social equilibrium if: φ ≤ m/δs∆θ • Denial is a social equilibrium if: φ ≥ qδs∆θm/δ
4.3
Multiple and mixed equilibriums
The thresholds for φ in the previous sections were constructed to ensure that realism or denial was a social equilibrium. These equilibriums, however, where not necessarily unique, there may be some overlap, and different equilibria might result for a certain φ. If I assume the worst, and assume that agents will ’choose’ the equilibrium that is least favourable for the firm, the thresholds need to be adjusted. These thresholds need to be adjusted to ensure that the equilibrium that the firm wants to stimulate is the only social equilibrium. I showed in the previous section that expected profits for a certain equilibrium do not depend on the specific value of φ. Hence, adjusting the thresholds will not affect expected profits.
is no overlap for the thresholds for case 3 in proposition 1. For case 2, the thresholds depend on the cognitive strategy of other players. For realism to be a social equilibrium, realism should be a best response to all other agents engaging in realism. However, for realism to be the only possible equilibrium, realism should even be a best response if all other agents engage in denial. The reverse holds in case of denial. This requires a small adjustment of the equations given in (34). The new thresholds become:
φ 22= m/δ + c s∆θ + δαθL ¯ φ22= m/δ + c sqθH + δαθL+ (1 − q)sαθL (35)
These thresholds also ensure that there is no mixed equilibrium. Since revenues are linear in effort choices, firms either want to stimulate or prevent effort in case of a low signal. Thus, it is not profit maximizing to have agents engaging in a mixed strategy.
5
Period 0: Contract setting and profit maximization
When offering a contract, the firm will take into account that workers need to accept the contract, and how the contract will influence the realism/denial decision of agents at t = 1, and how the contract will affect the effort decision of agents at t = 2, and how this affects their profits.
Total revenues depend on the state of the world (high or low) and the effort decision by agents. For different values of φ, there are different social equilibria at t = 1, hence there are multiple cases at t = 0.
maximize firm profits. If productivity in case of a low signal is expected to be positive (θL > 0), the firm wants agents to exert effort in both states of the world, if it is not too
costly. This may result in an incentive structure that encourages groupthink or wishfull thinking. Similarly, if θL < 0, the firm wants agents not to exert effort in the low state
of the world, which would result in an incentive structure that encourages realism, while preserving the incentive to put in effort in the high state of the world.
5.1
Profits
Third period profits are given by (5), which I copied below for convenience:
Π3 = θV N X i ei− N X i U3i
Agents will only accept the contract if their expected utility exceeds the utility they can get from their outside option. This is presented in the individual rationality constraint in (1) and states that Ui
0 ≥ O. The fixed fee does not affect any incentives. Since the firm has
all the bargaining power the fixed fee will be set to ensure that the IR-constraint is exactly binding. Since agents do not make any costs at t = 0, nor get any payment in this period, expected period 0 utility is the discounted expected period 1 utility (U0i = δE0i[U1i]). Plugging expected period 1 discounted utility, given in (13), into the IR-constraint yields the following: δE0i − Mi+ δEi 1[−ce i+ (s + δ)Ei 2[U i 3]] = O (36)
Plugging in the salary (U3i), given in (4), yields:
Since the fixed fee (F ) is known in advance it can be taken outside the expectation. Solving the above expression for F gives:
F =
O − δEi 0
− Mi+ δEi
1[−cei+ (s + δ)E2i[φθ αei+ (1 − α)e −i]]
δ2(s + δ) (38)
Period 3 salary for an agent can be found by plugging (38) into (4):
U3i = φθ[αei+ (1 − α)e−i] +
O − δEi 0
− Mi+ δEi
1[−cei+ (s + δ)E2i[φθ αei+ (1 − α)e −i]]
δ2(s + δ)
(39)
Lowering the variable part of the salary via φ has two direct effects on the payments to workers at t = 3. On the one hand it lowers the payments in terms of part of the revenue that has to be paid to the workers. On the other hand, it increases the fixed fee the firm has to set to compensate for this.
The firm does not have anticipatory utility and only cares about maximizing profits. Period 0 expected profits are equal to the discounted expected profits at the third period (δ3E
0[Π3]). Expected profits at t = 0, taking into account agent’s salary given in (39),
become: δ3E0[Π3] = δ3E0 θV N X i ei− N X i
φθ[αei+ (1 − α)e−i] (40)
+
O − δEi 0
− Mi+ δEi
1[−cei+ (s + δ)E2i[φθ αei+ (1 − α)e −i]]
δ2(s + δ)
how for different values of φ associated profits will differ. Next, I consider what φ will maximize profits.
5.1.1 φH ≤ φ < φprior
Realism (φ ≤ φ
1): Suppose the firm would set the contract to induce pure realism. This
would mean that no worker would put in effort in case of a low signal and all workers put in effort in case of a high signal. Expected revenue at t = 0 is equal to:
δ3E0[θV N
X
i
ei] = V N [qθH ∗ 1 + (1 − q)θL∗ 0] = N qθHV (41)
All N agents put in effort (e = 1) in case of a high signal (θH), which happens with
probability q.
Plugging all information into (40), yields the following expression for profits:
δ3 N qθHV − N φqθH[α + (1 − α)] + O − δ δ[−cq + (s + δ)[φqθH α + (1 − α)]] δ2(s + δ) (42)
Next, I got N outside the brackets, I noted that α + (1 − α) = 1 and I worked away some brackets in the final term. This results in:
δ3N qθHV − φqθH − O + δ2cq δ2(s + δ)+ δ2[(s + δ)φqθH]] δ2(s + δ) (43)
Which simplifies to:
From (44) it becomes clear that profits in this case do not depend on φ. Hence, every φ ∈ [φH, φ
1] will result in the same expected profits. Lowering φ has two opposing effects:
at the one hand it lowers the variable part of the salary, but on the other hand it does increase the fixed payment. Both effects cancel out exactly.
Looking at these profits, profits are increasing in the probability that the high state occurs (q) if θHV > s+δc , which I assume to hold. Higher costs of effort lower the expected
utility of agents, and hence increase the required payment to them. An higher value of the anticipatory utility parameter s implies that agents’ utility, ceteris paribus, will increase, which allows the firm to pay them a lower fixed fee.
Denial: Denial is never a social equilibrium in this case.
5.1.2 φ > φprior Realism (φ ≤ φ
22): If the firm would induce workers to be realistic, no worker would
put in effort in case of a low signal and all workers put in effort in case of a high signal. In terms of further analysis, this is completely equivalent to the analysis for realism in the previous section, and hence profits will be given by (44).
Denial (φ ≥ ¯φ22): Suppose the firm is inducing workers to be in denial. If all workers
are in denial, they will all put in effort in case of both a low and a high signal. Agents receiving a low signal will engage in denial, which entails cognitive costs. I put this information into (40). Profits become:
Which simplifies to: δ3E[Π3] = δ3N (qθH + (1 − q)θL)V − O + δ(1 − q)m + δ2c δ2(s + δ) (46)
Also, in this profit function no φ appears. Compared to the case of realism, revenue’s are changed by (1 − q)θLV , since also effort is exerted in the low state. In terms of costs,
agents now engage in costly signal distortion, for which they need to be compensated. Similarly, since agents now also exert effort in the low state, they incur extra expected costs for which they need to get compensated.
Comparing both cases, realism should be preferred if the difference between (44) and (46) is positive: δ3N qθHV − O + δ2cq δ2(s + δ) − δ3N (qθH + (1 − q)θL)V − O + δ(1 − q)m + δ2c δ2(s + δ) ≥ 0 (47)
Revenues in case of a high signal are present in both parts, which cancels out. The same holds for the outside option. Simplifying the remainder of the equation yields:
m + δc
δ(s + δ) ≥ θLV (48)
The left hand side of (48) only consists of positive components and hence will be positive. The sign of the right hand side depends on the sign of θL. If θL < 0, the RHS
will always be negative, and it will always be optimal to induce realism. If θL > 0, it
is optimal to induce denial, provided that θLV is sufficiently high. Since effort in the
low state is beneficial for the project, denial and effort in case of a low signal should be stimulated instead of prevented.
LHS represents the increase in costs associated with this. Since agents engaging in denial have cognitive costs and costs of effort in case of a low signal, which they do not have in case of realism, they need to be paid more to cover these costs.
5.1.3 φ > φ
L
This last case is only a possibility for θL > 0.
Realism (φ ≤ φ
3): All agents will put in effort in both the low and the high state of
the world. Expected profits become:
δ3E[Π3] = δ3E0 θV N − N φθ + O − δEi 0 δEi 1[−c + (s + δ)E2i[φθ]] δ2(s + δ) (49)
Which simplifies to:
= δ3N (qθH + (1 − q)θL)V − O + δ2c δ2(s + δ) (50)
Denial (φ ≥ ¯φ3): In this case, expected profits will be equal to the denial case in the
previous section. Profits are given in (46).
Profits in case of realism are higher. In case of both realism and denial agents will always put in effort and hence the firm’s expected revenues are not affected by a choice for realism or denial. However, in case of denial agents have to incur cognitive costs of denial, for which they need to be compensated, which lowers profits.
5.2
Profit maximization
both profit levels is given in 48.
A firm has a third option when θL > 0, given by (50). In the previous section, I
showed that when φ > φ
L, profits in case of realism are higher than profits in case of
denial, which also means that those profits are higher than profits in case of denial for φ
prior< φ < φL.
Comparing profits in case of realism if φ > φ
L to profits in case of realism if φprior <
φ < φ
L, the first yields higher profits if:
δ3N (qθH + (1 − q)θL)V − O + δ2c δ2(s + δ) − δ3N qθHV − O + δ2cq δ2(s + δ) ≥ 0 (51)
Which simplifies to:
θLV ≥
c
(s + δ) (52)
Hence if the benefit of effort in case of a low signal is sufficiently large to offset the extra costs, it is optimal to stimulate realistic effort in case of a low signal.
The profit maximizing choices are summarized in proposition 3. Proposition 3. Profit maximization
- If θL < 0, realism will always be stimulated, which results in agents putting in effort
only if they receive a high signal. - If θL > 0:
• If θLV ≥ (s+δ)c , realism will be stimulated. Agents will be incentivized to put in effort
in case of both a high and a low signal.
• If θLV < (s+δ)c , also θLV < δ(s+δ)m+δc, which means that realism will be stimulated.
5.3
Paying upfront
A firm might consider paying (part) of the fixed payment in earlier periods. Assuming F would be paid at t = 0, it could be seen as a signing fee, or, if it is negative, as an investment required from the worker to be allowed to work on the project. The IR-constraint would become:
F0+ δE0i[U i
1] ≥ O (53)
Assuming this constraint to be binding again, F will be set equal to:
F0 = O − δE0i − Mi+ δEi 1[−ce i+ (s + δ)Ei 2[φθ αe i + (1 − α)e−i]] (54)
This expression is similar to the F in the case of payments at t = 3. The only difference is that this expression is not divided by δ2(δ + s). In deciding upon the optimal period to pay the fixed fee, the firm will take into account that paying at t = 3 allows the firm to discount this payment with δ3. Hence the firm would be indifferent if F
0 = δ3F3, where
F3 stands for the fixed fee being paid in period 3.
Comparing both fixed payments, we get that F in period 3:
F0 = (δ3+ δ2s)F3 (55)
Hence if F > 0, δ3F
3 < F0 and the firm is best off paying agents at the last period.
However, if F < 0, δ3F
3 > F0 and the firm is best off letting agents pay the fixed fee
immediately at the t = 0.
same sum of money (in present value) to be given to them in the future over receiving it today, as this gives them extra anticipatory utility. If agents need to pay to get a job (F < 0), than it is optimal for the firm to let agents pay today, otherwise they would need to increase F to compensate for the negative anticipatory utility associated with having to pay F.
6
Conclusion
In this thesis, I elaborated on a model of groupthink by B´enabou (2012). I added a contracting stage and gave firms the opportunity to induce or prevent groupthink from happening. I showed that if agents that neglect a low signal hurt the company, the company always has an incentive to prevent groupthink. If agents who neglect bad news benefit the firm, groupthink may not be as bad. I showed, however, that even in that situation firms can do better by ensuring that putting in effort is attractive even if the signal is low. The main reason for this last point is that engaging in denial always entails some cognitive costs, which are ’wasted’ if they do not alter the effort choice of an agent. So if these costs can be prevented, without changing effort choices, the firm can make a higher profit.
Within my model, firms can in limit groupthink lowering the variable payment via φ, which would result in a higher fixed fee (F). Looking at real-life contracts this shows that contracts involving large performance bonusses are most conductive of groupthink, where contracts with fixed payments can limit the occurance of groupthink.
should be less prevalent in countries were unemployment insurance and unemployment benefits are high, or in countries with a big social security system.
In my model, I have assumed that a rational firm sets the contracts and that the agents deciding upon accepting the contract were fully aware of their tendency to engage in groupthink. An further extension of my model could be to find out what would happen if agents are not or only partly aware of their tendency to engage in wishful thinking, as the decision to neglect signal may happen partly unconsciously. Another extension may be to introduce an incentive to engage in wishfull thinking for the principal as well. The 2008 financial crises showed, among other things, that wishfull thinking was spread quite widely throughout the financial sector and that also shareholders (the owners of a firm), may be susceptible to misinterpret signals.
Furthermore, this model might be extended by introducing heterogeneity between agents. Not all agents, for example, might derive utility from anticipation in the same way. Introducing heterogeneity would make the model more ’realistic’, but would at the same time make the job for the firm more difficult, as the same contract may induce some individuals to engage in realism, while induce other agents to engage in denial.
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