Punishment, Compliance, and Anger in Equilibrium

36 Pages·2010·0.29 MB·English

Punishment, Compliance, and Anger
in Equilibrium
JOB MARKET PAPER
Robert J. Akerlof
∗
November 18, 2010
Abstract
This paper develops an alternative to a repeated-game approach to thinking about
norms. It instead conceives of norms as views regarding how people should behave.
Norms matter because they determine what people consider to be fair, and when in-
dividuals feel unfairly treated, they become angry. Norms are (potentially) followed
because a failure to do so may provoke anger. The paper considers a two-period
psychological game in which a first player chooses whether to “comply” and a sec-
ond player potentially punishes noncompliance, where the motivation for punishment
is anger. Because anger depends upon the expected level of compliance, there may
be multiple equilibria. This gives an explanation of why some organizations, despite
professed disapproval of corruption, have high levels of corruption and punishment of
corruptionisrelativelymild,whileotherorganizationshavelowlevelsofcorruptionand
severe punishment of corruption when it occurs. Because norms are contextual, the
paperexplainswhyinmarketcontextsitisoftenviewedasfairforasellertosetaprice
based upon economic self interest while transacting according to economic self-interest
frequently provokes anger within a firm/organization. The paper gives foundations for
Hart and Moore’s (2008) model of aggrievement since signing a contract can be viewed
as establishing norms. An extension to the basic model shows that “institutionalizing
punishment”–thatis,creatingnormsregardinghownoncomplianceshouldbepunished
andwhoshoulddothepunishing–canincreasetheprovisionofpunishment,leadingto
greater compliance. (JEL: D02, D03, D74.)
∗MassachusettsInstitueofTechnology,[email protected]. IwouldliketothankRobertGibbons,PhilippeAghion,
Oliver Hart, Richard Holden, George Akerlof, and seminar participants at Berkeley and MIT for helpful comments
and suggestions.
1 Introduction
This paper develops an alternative to a repeated-game approach to thinking about
norms. Itinsteadconceivesofnormsasviewsregardinghowpeopleshouldbehave. Norms
matter because they determine what people consider to be fair, and when individuals feel
unfairly treated, they become angry. Norms are (potentially) followed because a failure to
do so may provoke anger.1
Consider one relevant example: a firm in which a manager gives orders to employees.
If an employee fails to follow orders—shirks—her coworkers might be angry with her if they
are inconvenienced and there is a sense among the coworkers (a norm) that the manager’s
orders should be followed. The norm is crucial to generating the anger: if instead the
coworkers felt that the employee was entitled to violate the manager’s orders they would
not feel angry. Anger may lead the coworkers to punish the shirking worker themselves or
alternatively report the shirking to the manager (giving the manager the ability to inflict
punishment). Hence, whenamanagerisunabletoobservewhetheremployeesfolloworders
directly, the ability to provide incentives to follow orders will depend crucially on whether
a norm exists that orders should be followed.
The paper considers a two-period psychological game. A first player chooses whether
to “comply” at a cost. A second player, who values compliance, potentially punishes
noncompliance out of anger.
Both players have views as to whether there is a duty to comply: we will refer to these
views as “norms.” The norms play two roles: (i) if player 1 feels a sense of duty to comply,
this motivates her to comply; (ii) player 2’s view as to whether player 1 has a duty to
comply plays a role in determining whether player 2 will be angry over noncompliance.
Thekeyassumptionofthepaperregardswhatmakespeoplefeelangry. We assumethat
anger arises when a person feels she has been harmed because someone lacks an appropriate
sense of duty. Hence, in the model, player 2 feels angry if she thinks player 1 failed to
1See Baker, Gibbons, and Murphy (1999, 2002), or Kandori (1992) for examples of repeated-game ap-
proaches to norms.
1
comply, but a person with an appropriate sense of duty would have complied.
There are sometimes multiple equilibria. There might be one equilibrium in which
the degree of compliance is high and there is considerable anger over and punishment of
noncompliance; and there might be another equilibrium in which the degree of compliance
is low and there is only mild anger over and punishment of noncompliance. This explains
why some organizations, despite professed disapproval of corruption, have high levels of
corruption and punishment of corruption is relatively mild, while other organizations have
low levels of corruption and severe punishment of corruption when it occurs.2
The theory captures the finding of many researchers that fairness attitudes—what makes
people angry—differ greatly across contexts (see especially Elster (1992), Walzer (1983),
Kahneman, Knetsch, and Thaler (1986), and Young (1994)).3 These contextual differences
are accounted for by the presence of different norms. Consider one example of the impor-
tance of context. In markets it is often considered fair or appropriate for buyers and sellers
to act according to their self interest. In contrast, within firms and other organizations,
transacting according to self interest is rarely seen as fair or appropriate.
The paper gives foundations for Hart and Moore’s (2008) model of aggrievement, in
which the contracts that parties sign ex ante determine what makes the parties angry (or
“aggrieved”) ex post. Hart and Moore (2008) can be interpreted as follows to relate it
to this paper: when parties in their model sign a contract, this establishes a norm. It
establishes a norm that the parties should meet the terms of the contract. Hart and Moore
(2008) have shown that anger is important for organizational economics, since it is a key
reasonforexpostinefficienciessuchashaggling, rentseeking, andshadingofperformance.4
Inanextensiontothebasicmodel,wewillshowthattheprovisionofpunishmentcanpo-
tentiallybegreatlyincreased(andcomplianceobtained)by“institutionalizingpunishment”—
2Thereareotherpapersthat,takingverydifferentapproachesfromtheapproachofthispaper,obtainas
a result the existence of high corruption and low corruption equilibria. See, especially, Andvig and Moene
(1990), Andvig (1991), Tirole (1996), and Cadot (1987). For a review of the corruption literature, see
Bardhan (1997). Also see Shleifer and Vishny (1993).
3For a review of the literature on fairness and justice, see Konow (2003).
4SeeGibbons(2005),Williamson(1971,1979,1985),andKleinetal. (1978)forfurtherdiscussionofthe
importance of ex post inefficiencies for organization theory. See also Hart and Moore (2007).
2
thatis,bycreatingnormsregardinghownoncomplianceshouldbepunishedandwhoshould
do the punishing. We will show that the key condition for institutionalization to be helpful
is that a punishment of size p can be inflicted at a cost to the punisher of less than p (a
condition which would seem to hold in many circumstances).
This paper is related to several other papers that have developed psychological game
models of fairness: Rabin (1993), Dufwenberg and Kirchsteiger (2004), and Falk and Fis-
chbacher (2006). These papers, like this one, all recognize the importance of beliefs others’
intentions/motivations in the formation of fairness attitudes. For this reason, they all sim-
ilarly employ psychological game models.5 Indeed, there is a great deal of evidence that
beliefsregardingothers’intentions/motivationmattercruciallytowhetheronefeelsonehas
been treated fairly (see, for example, Falk, Fehr, and Fischbacher, 2008).
But there are three important respects in which this paper differs from Rabin (1993),
Dufwenberg and Kirchsteiger (2004), and Falk and Fischbacher (2006). First, this paper
accountsforOstrom’s(1990)findingthatinmostcontextsthereare“graduatedsanctions”:
there is more punishment for repeat offenders. The previous models cannot explain this
fact because anger depends upon the type of strategy an actor follows but not upon the
type of the actor.
Second, these other papers do not explore contextual differences in what is considered
fair. Followinguponthepreviousexample, theydonotexplainwhyitmightbeacceptable
to act in a self-interested manner in a market but unacceptable within a firm.
Finally, Rabin (1993), Dufwenberg and Kirchsteiger (2004), and Falk and Fischbacher
(2006) model both negative and positive reciprocity, treating them as flip sides of the same
thing. This paper, in contrast, focuses on negative reciprocity: anger and punishment
rather than gratitude and reward. Section 5 explains the reason for treating positive
reciprocity separately and hints at how it might be modeled.
It is important to point out that this paper examines what makes people angry, taking
norms as exogenous. It does not explain why certain norms prevail in certain contexts.
5Psychological games were first discussed by Geanakoplos, Pearce, and Stacchetti (1989). These papers
and this one use variants of their equilibrium concept.
3
As we will see, just understanding what will be regarded as fair taking norms as exogenous
is not a trivial problem. That said, it is important to endogenize the norms: understand
how they form and change. This is a topic that I have explored in other work that is
complementary with this paper.6
The paper will proceed as follows. Section 2 develops the setup of the model and
defines a punishment-compliance equilibrium of the game. Section 3 gives the main results
ofthepaper,describingthepunishment-complianceequilibria. Section4extendsthemodel
developedinsection2toshowthatinstitutionalizingpunishmentcanimprovetheprovision
of punishment and make it easier to obtain compliance. Section 5 relates the theory
developed in this paper to Hart and Moore (2008) as well as Rabin (1993), Dufwenberg and
Kirchsteiger (2004), and Falk and Fischbacher (2006). Section 6 concludes.
2 The Model
We will consider a two-period game with two players, player 1 and player 2. At time
1, player 1 chooses an action a 0,1 .7 We will refer to a=1 as “compliance” and a=0
∈{ }
as “noncompliance.” At time 2, after observing a, player 2 chooses how much to punish
player 1, p [0, ).
∈ ∞
We will proceed as follows. We will begin by discussing player 1’s choice of action
a. Then, we will discuss player 2’s choice of p. In discussing player 2’s choice, we will
introduce the concept of mistreatment. Anger is caused by a feeling on player 2’s part that
she has been mistreated by player 1, and anger is what motivates player 2 to punish player
1. Finally, we will define an equilibrium concept for the game, which will be similar to the
equilibrium concept developed by Battigalli and Dufwenberg (2009).
6For an overview of my ideas on norm formation and change, see my “Research Statement” (Akerlof
(2010c)). See also Akerlof (2008), Akerlof (2010a), and Akerlof (2010b).
7The results of the model look similar when individual 1 can choose any action a [0, ). We will
∈ ∞
discussthiscasebelow. Thereasonformaking1’schoicediscreteforthetimebeingistosimplifyanalysis.
4
2.1 Player 1’s Choice
Player 1 maximizes:
U = p˙(a) Ca Dmax(I a,0)
1 1
− − − −
For simplicity, we assume that a =1 if player 1 is otherwise indifferent.
The first term of the utility function is the disutility associated with player 2’s punish-
ment, where p˙(a) [0, ) is individual 1’s belief concerning the punishment action a will
∈ ∞
receive. The second term reflects a cost C > 0 of compliance (choosing a = 1 rather than
a =0). The final term reflects a disutility to player 1 of D >0 if player 1 feels that she has
failed to do her duty. We assume I 0,1 . If I =1, player 1 feels that she has a duty
1 1
∈{ }
to comply (choose action a=1) and loses D if she chooses fails to comply. If I =0, player
1
1 does not feel it is her duty to comply (choose action a = 1) and does not lose utility D
from taking either action. Put another way, player 1 feels entitled to take whichever action
she wants to take. Observe that we can think of I as a norm.
1
Let a (C,I ,p˙()) denote the optimal choice of action.8 If player 1 does not feel a sense
∗ 1
·
of duty to comply (I =0), player 1 will only comply if the cost C of complying is less than
1
the punishment associated with failure to comply. That is, if I = 0, a = 1 if and only if
1 ∗
C p˙(0) p˙(1). Similarly, if player 1 feels a sense of duty to comply (I = 1), player 1
1
≤ −
will only comply if the cost C is less than the punishment associated with failure to comply
plus the benefit to player 1 from doing her duty, D. That is, if I = 1, a = 1 if and only
1 ∗
if C D+[p˙(0) p˙(1)].
≤ −
The following table summarizes:
I =0 I =1
1 1
a (C,I ,p˙( ))=0 C >p˙(0) p˙(1) C >D+[p˙(0) p˙(1)]
∗ 1
· − −
a (C,I ,p˙( ))=1 C p˙(0) p˙(1) C D+[p˙(0) p˙(1)]
∗ 1
· ≤ − ≤ −
8We choose not to write a as a function of D because, in the analysis that follows, D will have a fixed
∗
value whereas the values of C, I , and p˙(a) may vary.
1
5
What Player 2 Knows About Player 1 Player2knowsthevalueofD. However,
player 2 does not know the cost of compliance C or whether player 1 has a sense of duty,
I . 2’s prior is that C is distributed according to distribution F with support S = (0, ).
1
∞
2’s prior is that I =1 with probability q and I =0 with probability 1 q. Let 0,1
1 1
− I ⊆{ }
be the support of I . We assume that, if q =1, = 1 and if q =0, = 0 .9 2 believes
1
I { } I { }
that the values of I and C are independent.
1
2.2 Player 2’s Choice
In this section, we will derive p (a,I ,p¨( )), the optimal choice of punishment. The
∗ 2
·
optimal punishment will depend upon whether player 1 complies, a. It will also depend
upon I , player 2’s view regarding what player 1’s duty is. If I = 1, player 2 feels that
2 2
player 1 has a duty to comply. If I = 0, player 2 feels that player 1 is entitled to take
2
whichever action she wants to take. Player 2’s view regarding player 1’s duty might differ
from player 1’s own view (I ). I and I are the two norms present in the model.
1 1 2
Finally, the optimal choice of punishment depends upon p¨(), where p¨(a) [0, ) is
· ∈ ∞
player 2’s belief regarding p˙(a). When player 2 believes player 1 expects noncompliance
to be punished harshly, she will take a different view of noncompliance from the view she
would have taken if she believed that player 1 expected mild punishment. This final term
will capture the idea, as discussed in the introduction, that there will be less anger (and
hence less punishment) if the level of compliance is expected to be low.
To preview the equilibrium concept, which wewill discussformally in Section 2.3, itwill
be roughly as follows: p (a,I ,p¨()) = p˙(a) = p¨(a). In other words, in equilibrium, there
∗ 2
·
will be a convergence of belief.
9This assumption implies that, if I = 1 (I = 0) almost surely—with probability 1—I = 1 (I = 0) for
1 1 1 1
sure.
6
2.2.1 Player 2’s choice
We assume that player 2 cannot commit ex ante to punish player 1. Player 2 chooses
p to maximize:
U =va κ(p) Φ(M(a,I ,p¨()),p)
2 2
− − ·
The first term of the utility function reflects a benefit v 0 received when player 1 chooses
≥
to comply. The second term is a cost associated with punishing player 1. The third term
is the disutility associated with feeling mistreated by player 1. M, which we will discuss
more presently, denotes player 2’s view of how much player 1 has mistreated her. We will
assume that the disutility associated with mistreatment is lower when player 2 punishes
player 1. Hence, the third term captures player 2’s anger and the corresponding desire to
punish player 1 in the event that player 2 feels mistreated.
We will use the following convenient functional forms for κ and Φ for the remainder of
paper:
p
κ(p) =
θ
kM
Φ(M,p) = Mlog
p
µ ¶
10θ > 0 parameterizes the ability to punish player 1 (higher θ implies a greater ability or
lower cost of punishing). k is a positive constant.11
The amount of punishment player 2 will choose to administer will be:
p (a,I ,p¨())=θM(a,I ,p¨( ))
∗ 2 2
· ·
Higherθ (agreaterabilitytopunishplayer1)leadstomorepunishment. Greaterperceived
mistreatment by 1 leads to more punishment. When player 2 feels fairly treated by player
1 (M =0), player 2 will not punish player 1.
10Mlog kM istechnicallyundefinedwhenM =0. WewillassumeΦ(0,p)=lim Mlog kM =0.
p M 0+ p
→
11Theva(cid:19)lueo(cid:20)fkwillhavenoeffectontheamountofpunishmentpthatplayer2willadminister.(cid:19)How(cid:20)ever,
wemightwanttoassumethatk θe 1,whichensuresthatanincreaseinM willdecreaseplayer2’sutility.
−
≥
7
Having expressed the optimal punishment, p , as a function of mistreatment, we will
∗
now discuss mistreatment. We will derive an expression for M(a,I ,p¨()) in the following
2
·
section, which will in turn give us a new expression for the optimal punishment.
2.2.2 Mistreatment
A key innovation of the paper is the way in which mistreatment is modeled. Perceived
mistreatment, M, is player 2’s expectation of how much better off she would be if player 1
had an appropriate sense of duty.
To be clear about what this means, suppose that player 2 knew the value of C (the
cost of compliance). Then, player 2 would expect player 1 to choose a (C,I ,p¨( )) if
∗ 2
·
player 1 had an appropriate sense of duty. Player 2 would be better off by an amount
vmax(a (C,I ,p¨()) a,0) if player 1 had an appropriate sense of duty, where a is player
∗ 2
· −
1’s actual choice. Recall that v is the value to player 2 of compliance.
So,ifC wereknown,mistreatmentwouldbegivenby: M =vmax(a (C,I ,p¨()) a,0).
∗ 2
· −
Observe that, for a sufficiently high value of C (cost of compliance), a (C,I ,p¨()) = 0, in
∗ 2
·
which case, player 2 would not feel mistreated even if player 1 did not comply (a = 0).
Therefore, a high cost of compliance serves as an excuse for noncompliance. A nice feature
of the model is that it makes precise what it means for someone to have an excuse.
Of course, the cost of compliance C is not necessarily known. More generally:
M(a,I ,p¨())=vmax(aˆ(a,I ,p¨()) a,0)
2 2
· · −
where aˆ is player 2’s expectation of the action player 1 would have taken if player 1 had
had an appropriate sense of duty and a is the actual choice made by player 1.
The following is a formula for aˆ:
aˆ(a,I ,p¨()) = E (a (C,I ,p¨( )) a (C,I ,p¨())=a)
2 · C,I1 ∗ 2 · | ∗ 1 ·
= Pr(a (C,I ,p¨())=1 a (C,I ,p¨())=a)
∗ 2 ∗ 1
· | ·
8
aˆ is player 2’s expectation of a (C,I ,p¨( )). Player 2 conditions this expectation on her
∗ 2
·
observation of a (player 1 believes, of course, that a (C,I ,p¨( ))=a).
∗ 1
·
In the event that a (C,I ,p¨( ))=a for any C S and I , aˆ(a,I ,p¨()) is undefined.
∗ 1 1 2
· 6 ∈ ∈I ·
Otherwise, aˆ(a,I ,p¨()) is defined and, applying Bayes’ rule, we find that:
2
·
[F(D+[p¨(0) p¨(1)]) F(p¨(0) p¨(1))](1 q)
aˆ(0,1,p¨()) = − − − −
· [1 F(p¨(0) p¨(1))] q[F(D+[p¨(0) p¨(1)]) F(p¨(0) p¨(1))]
− − − − − −
aˆ(1,1,p¨()) = 1
·
12
aˆ(0,0,p¨()) = 0
·
F(p¨(0) p¨(1))
aˆ(1,0,p¨()) = −
· F(p¨(0) p¨(1))+q[F(D+[p¨(0) p¨(1)]) F(p¨(0) p¨(1))]
− − − −
13
2.2.3 The Optimal Punishment
Hence, the amount of punishment that player 2 will administer will be as follows:
p (a,I ,p¨()) = θM(a,I ,p¨( ))
∗ 2 2
· ·
= θvmax(aˆ(a,I ,p¨()) a,0)
2
· −
So,
p (0,I ,p¨()) = θvaˆ(0,I ,p¨())
∗ 2 2
· ·
p (1,I ,p¨()) = 0
∗ 2
·
As we would expect, player 1 will not be punished in the event that she chooses to
12In the event that F(p¨(0) p¨(1))=1, this is not the correct expression for aˆ(0,1,p¨()).
13In the event that F(D+−[p¨(0) p¨(1)])=1, this is not the correct expression for aˆ(1·,0,p¨()).
− ·
9