SUBGAME-PERFECT PUNISHMENT FOR REPEAT OFFENDERS

SUBGAME-PERFECT PUNISHMENT FOR REPEAT OFFENDERS

WINAND EMONS*





First I show that for wealth-constrained agents who may commit an act twice the

optimal sanctions are the offender's entire wealth for the first and zero for the second

crime. Then I ask the question whether this decreasing sanction scheme is subgame

perfect (time consistent), that is, does a rent-seeking government stick to this sanction

scheme after the first crime has occurred. If the benefit and/or the harm from the crime

are not too large, this is indeed the case; otherwise, equal sanctions for both crimes are

optimal. (JEL D82, K47, K42)





I. INTRODUCTION small cost of doing so. The rational criminal

will anticipate the ex post enforcement beha-

The literature on optimal law enforcement

vior of the government. Therefore, she will

typically assumes that the government can

commit the crime because the threat of being

commit to sanction schemes.1 This means

sanctioned is not credible. Once one drops the

the government can use any set of threats to

commitment assumption, the typical deter-

penalize wrongdoers. In particular, if a crime

rence equilibria of the law enforcement litera-

occurs, the government actually sanctions the

ture between potential wrongdoers and the

wrongdoers even though, ex post, it may have

government are based on empty threats. In

no incentive to do so. Potential wrongdoers

the language of game theory, the equilibria

believe that the government will carry out

are not subgame perfect or time consistent.

the threat at any cost and, therefore, do not

I study the problem of subgame perfect

engage in the act in the first place.

sanctions using the framework of Emons

In this article I give up the assumption that

(2003). Agents may commit a crime twice.

the government can commit to whatever sanc-

The act is inefficient; the agents are thus to

tion scheme. I consider the analysis of optimal

be deterred. The agents are wealth-constrained

sanctions without the possibility to commit

so that increasing the fine for the first offense

important because judges often have a lot of

means a reduction in the possible sanction for

discretion as to the size of the penalty; they

the second offense and vice versa. The agents

may, for example, adjust sanctions to the finan-

may follow history-dependent strategies, that

cial possibilities, age, education, and so on of

is, commit the crime a second time if and only if

the wrongdoer. Accordingly, I allow only for

they were (were not) apprehended the first

sanctions that the government actually wishes

time. The government seeks to minimize the

to implement should a crime have occurred.

probability of apprehension.

Ruling out full commitment changes the

Ignoring the government's commitment

optimal enforcement schemes. Suppose, for

problem, it is optimal to set the sanction for

example, the government does not care about

the first offense equal to the entire wealth of the

the sanction, as is typically assumed in the lit-

agents while the sanction for the second offense

erature. Then it will not enforce the penalty if

equals zero. The intuition is as follows. A

a crime has happened given that there is, say, a

money penalty imposed for the second offense

reduces the amount a person can pay for the

*I thank Nuno Garoupa, Manfred Holler, Thomas first offense, because the wealth available to

Liebi, Francois Salanie, and an anonymous referee for

Ë Â pay penalties is assumed to be fixed over the

helpful comments. two periods. For that reason, a higher prob-

Emons: Professor, University of Bern, Department of ability eventÐnamely, a first offense that is

Economics, Gesellschaftsstrasse 49, CH-3012 Bern, detectedÐwill be more effective use of the

Switzerland. Phone 41-31-631 3922, Fax 41-31-631

3992, E-mail winand.emons@vwi.unibe.ch scarce money penalty resource than a lower

1. See Garoupa (1997) or Polinsky and Shavell (2000a) probability eventÐnamely, a second detected

for surveys. offense. Why is the probability of detection



496

Economic Inquiry

(ISSN 0095-2583) DOI: 10.1093/ei/cbh076

Vol. 42, No. 3, July 2004, 496±502 # Western Economic Association International

EMONS: SUBGAME-PERFECT PUNISHMENT 497





lower for the second rather than for the first If the benefit and/or the harm of the second

crime? Simply because an agent faces the pos- crime are large, the decreasing sanction scheme

sibility of being sanctioned for the second crime is no longer time consistent. The government

if and only if he or she has already been sanc- prefers to deter the second crime should the

tioned the first time. For further results it is first crime have occurred. Accordingly, only

important to note that the optimal probability sanction schemes where each sanction by

of apprehension increases with the benefit from itself deters the corresponding crime are time

the crimes. consistent. In this case the optimal subgame-

This decreasing sanction scheme raises of perfect sanction scheme entails equal sanctions

course the issue of time consistency. Will the in both periods. Enforcement costs are higher

government really charge the agent the entire than with the decreasing sanction scheme.

wealth when she was apprehended for the first The only article I am aware of that deals

crime, knowing that then she will commit the with the problem of time-consistent sanctions

second act for surec Isn't it better for the gov- is Boadway and Keen (1998). They consider a

ernment to renege and charge little for the first government choosing a capital income tax rate

act so that the agent still has sufficient wealth to and an enforcement policy. The government

pay a sanction that deters the second crimec can commit to the enforcement policy but

Given that the first act has been committed not to the tax rate. Ex ante the government

anyway, that way the government can at wishes to announce a low tax rate to induce

least deter the second act. savings; ex post, when savings have been

To study this problem I consider a rent- made, it will renege and apply a high tax

seeking government. The sanctions paid by rate. Boadway and Keen show that by commit-

the criminals enter the government's welfare ting to a lax enforcement policy the govern-

function. Our government, therefore, has an ment can alleviate the welfare loss implied by

ex post incentive to collect fines. The govern- its inability to commit to the tax rate.

ment can commit to a probability of apprehen- In the next section I describe the model.

sion but not to sanctions. Our basic result is In section III I derive the optimal sanctions

that if the agent's benefit and/or the harm from for a government that can commit and in

the crime are not too large, then the scheme section IV for a government that cannot

where the sanction for the first crime is the commit. Section V concludes.

entire wealth and the sanction for the second

crime is zero is indeed subgame perfect.

To see this, consider the government after II. THE MODEL

the agent has been apprehended for the first

crime. If it implements the decreasing sanction Consider a set of potential wrongdoers,

scheme, it appropriates the entire wealth yet which has measure 1. Individuals live for two

incurs the harm of the second crime. Thus, periods. In each period the agents can engage in

the lower the harm of the second crime, the an illegal activity, such as illegal parking, illeg-

more attractive this option. ally raising prices, polluting the environment,

The alternative is to set the sanction for the or evading taxes. If an agent commits the act in

second crime to a level that deters the act. With either period, she receives a monetary benefit

this option the government doesn't incur the b40. I consider crimes without social gains.

harm of the second crime, yet forgoes the sanc- Using the language of Polinsky and Rubinfeld

tion for the second crime because it is deterred. (1991), b is the illicit gain and the crime creates

If the benefit from the crime goes up, the opti- no acceptable gain.2 The act causes a monetary

mal probability of apprehension increases, yet harm h to society, which is borne by the gov-

by more than the benefit; therefore, the actual ernment. Because h 4 0, the act is not socially

sanction necessary to deter the second crime desirable. The individuals are thus to be

falls. Because a low sanction for the second deterred from the activity.

crime means a high amount the government

can charge for the first crime, a high benefit 2. See also Chu et al. (2000) for an analysis of crimes

of the second crime makes this option attrac- without social gains. They argue that the gains to the offen-

tive. Accordingly, only for low benefits the der are not considered because the crime is not socially

acceptable or because the gains of offenders (such as

government sticks to the decreasing sanction theft or other zero-sum crimes) offset with the victims'

scheme. losses.

498 ECONOMIC INQUIRY





To achieve deterrence, the government the sanction. With such a sequencing, the

chooses sanctions and a probability of appre- rational government will not impose the fine:

hension. The government cannot tell whether It does not care about the fine anyway and it

an agent is in the first or second period of life. can save the cost e. If one anticipates this ex

The government only observes whether the post behavior of the government, the threat of

crime is the first or the second one. Accord- being sanctioned is not credible and the agent

ingly, the government uses fines s1 , s2 ! 0, will commit the act in the first place. To put it in

where s1 applies to first-time and s2 to second- the language of game theory: The equilibrium

time observed offenders. in the game between the offender and the gov-

I assume that the government cannot com- ernment is not subgame perfect.

mit to sanctions. This means that the govern- If one wants to take the issue of subgame

ment can choose a different sanction from the perfection (or time consistency) seriously, one

one announced at the outset once a crime must give the government an incentive to actu-

occurred. Typically, a judge always finds good ally collect the fines. I do so by including the

reasons to reduce or increase sanctions. In sanctions in the government's payoffs.6 Our

addition to sanctions, the government chooses government maximizes revenues from sanc-

a probability of apprehension p. This probab- tions minus the harms minus the enforcement

ility is the same for first- and second-time expenditure and thus has an incentive to collect

offenses.3 It is irrevocably fixed before the the fine should a crime have occurred. To

agents take their actions. The government save on notation, I take the probability of

cannot easily change the amounts spent on, apprehension p as an indicator of the enforce-

say, training the police. Accordingly, I assume ment expenditure.

that the government can commit to p while it This approach can be motivated in several

cannot commit to sanctions.4 ways. Garoupa and Klerman (2002) take the

In the law enforcement literature, the opti- public choice perspective of a self-interested,

mal policy is derived by maximizing the sum rent-seeking government that maximizes rev-

of the offenders' benefits minus the harm enues minus the harm borne by the government

caused by the offenses minus law enforcement minus expenditure on law enforcement.7

expenditures. Sanctions do not enter the Polinsky and Shavell (2000b) consider the stan-

benevolent government's objective function dard benevolent welfare function and add a

because they are a mere transfer of money.5 term reflecting individuals' fairness-related uti-

Within this framework the literature derives lity. If this fairness-related utility equals the

the results on optimal fines and optimal prob- actual sanction, their government maximizes

abilities of apprehension. See, for example, the same welfare function as ours.8

Garoupa (1997) or Polinsky and Shavell Individuals are risk-neutral and maximize

(2000a). expected income. They have initial wealth

Nevertheless, these results hold true if and W 40. Think of W as the value of the privately

only if the government can fully commit to owned house or assets with a long maturity.

the probability of apprehension and to the The agents hold on to their wealth over both

announced sanction. To see this, suppose the periods unless the government interferes with

government incurs a small cost e 4 0 of collect- sanctions. Any additional income they receive

ing the fine. Suppose the agent has been appre- in both periods, be it through legal or illegal

hended for the crime and then the government activities, is consumed immediately. Accord-

strategically decides whether or not to impose ingly, all the government can confiscate is W.

If the fine exceeds the agent's wealth, she goes



3. I thus rule out the case where agents with a criminal

record are more closely monitored than agents without a

record. See Landsberger and Meilijson (1982) for an ana- 6. In terms of the explicit welfare function given in

lysis of optimal detection probabilities. the preceding note, I simply exclude the criminal's utility

4. Boadway and Keen (1998) use the same commitment (benefit minus expected sanction).

structure when studying the time consistency problem in 7. Dittmann (2001) uses a similar approach.

the taxation of capital income. 8. In Rubinstein (1979) the government's payoffs also

5. In the explicit formulation, welfare is the criminal's depend on whether or not it punishes the offender. Unlike

utility (benefit minus expected sanction) plus the govern- the other studies, Rubinstein's government is worse off if it

ment's utility (expected sanction minus harm) minus enfor- punishes the offender, independently of whether the act was

cement costs. committed intentionally or not.

EMONS: SUBGAME-PERFECT PUNISHMENT 499





bankrupt and the government seizes the strategy defines the agents' binding incentive

remaining assets. This implies that the fines constraint for the optimal sanctions.10

s1 and s2 have to satisfy the ``budget constraint'' Before I start deriving optimal sanctions,

s1 ‡ s2 ˆ W .9 I have to ensure that the government indeed

To save on notation, let the interest rate be wants complete deterrence. I achieve this by

zero. An agent can choose between the follow- assuming W À 2h 5 À1. If the government

ing strategies: completely deters, there is neither harm nor

 She can choose not to commit the act at revenue, and the maximum possible expendi-

all. I call this strategy (0, 0), which gives rise to ture for deterrence is 1 (recall that I take the

utility U…0, 0† ˆ W . This is the strategy I wish probability of apprehension as a measure for

to implement. enforcement cost). If the government doesn't

 She can choose to commit the act in per- deter at all, enforcement costs are zero, the

iod 1 and not in period 2. Call this strategy government incurs the harm twice, and the

(1, 0); here we have U…1, 0† ˆ W ‡ b À ps1 . The maximal revenue it can obtain is the agents'

act generates benefit b; with probability p the wealth W. Accordingly, if the harm is suffi-

agent is apprehended and pays the sanction s1 . ciently large, the rent-seeking government

 The agent can opt to commit the crime in wants complete deterrence.

period 2 but not in period 1. Call this strategy Let us now analyze sanctions that give the

(0, 1) generating utility U…0, 1† ˆ W ‡ b À ps1 . agents proper incentives not to engage in

With strategy (0,1) the agent has the same the activity in either period. I first derive

utility as with strategy (1, 0) because the gov- the cost-minimizing sanction scheme that

ernment observes only one offense. achieves perfect deterrence ignoring the gov-

 Moreover, the agent can commit the act in ernment's commitment problem. This is the

both periods, which I denote by (1, 1) and standard approach found in the literature.

U…1, 1† ˆ W ‡ b À ps1 ‡b À p…‰1 À pŠs1 ‡ ps2 †. The literature does not further discuss why

The second crime is detected with probability p. the government is able to commit. One argu-

With probability p the agent has a criminal ment coming to mind in favor of commitment

record in the second period and thus is fined is that the government plays repeated games

s2 ; with probability …1 À p† she has no record with potential wrongdoers and, therefore,

and pays s1 if apprehended. wants to build up a reputation of being

 Finally, the agent can choose two history- tough. The analysis of the commitment sce-

dependent strategies. First, she commits the act nario follows Emons (2003). I will then con-

in period 1. If she is not apprehended, she also sider the government's incentives to actually

commits the act in period 2; however, if she implement this penalty scheme without com-

is apprehended in period 1, she does not mitment in section IV.

commit the act in period 2. Call this strategy

(1, (1 j no record;0 j otherwise)) with U(1,(1 j no

record; 0 j otherwise)) ˆ W ‡ b À ps1 ‡ …1À p† III. OPTIMAL SANCTIONS IF THE

…b À ps1 †. Because the agent stops her criminal GOVERNMENT CAN COMMIT

activities if she is apprehended once, she is

never sanctioned with s2 . I assume that agents have enough wealth so

 Second, she commits the act in period 1. that deterrence is always possible, that is,

If she is not apprehended, she does not commit 2b5W . The agent does not follow strategy

theactinperiod2;however,ifsheisapprehended (1, 0), if U…1, 0† U…0, 0†, she does not follow

in period 1, she commits the act in period 2. strategy (0,1), if U…0, 1† U…0, 0†, and so on.

Callthisstrategy(1,(0 j norecord;1 j otherwise)) Straightforward computations confirm that

with U(1,(0 j record; 1 j otherwise)) ˆ W ‡ b the agent does not engage in strategies (1, 0),

Àps1 ‡ p…b À ps2 †. It turns out that this (0,1), and (1,(1 j no record;0 j otherwise)), if



9. This assumption distinguishes our approach from …1† s1 ! bap;

Polinsky and Shavell (1998) who work with a maximum

per period sanction sm . Accordingly, they may set

s1 ˆ s2 ˆ sm , which is typically the optimal enforcement

scheme. In their framework sm is like a per period income 10. These history-dependent strategies distinguish my

that cannot be transferred into the next period. Burnovski work from Burnovski and Safra (1994), where individuals

and Safra (1994) use the same budget constraint as we do. decide ex ante simply on the number of crimes.

500 ECONOMIC INQUIRY





she does not pick strategy (1, 1), if FIGURE 1

The Set of Incentive-Compatible

…2† s2 ! …2bap2 † À s1 …‰2apŠ À 1†; Sanctions and the Optimal Sanction

Scheme …sà , sà † ˆ …W , 0† and

1 2

and she does not pick strategy (1,(0 j no pà ˆ ba…W À b†

record;1 j otherwise)), if



…3† s2 ! …b‰1 ‡ pŠap2 † À s1 apX





Accordingly, with all sanction schemes

…s1 , s2 † to the right of the bold line in Figures 1

and 2, the agent has proper incentives and

commits no crime. For example, the scheme

s1 ˆ s2 ˆ bap induces no crimes.

Next I minimize the enforcement costs, as

given by p, while providing incentives not to

commit any crime.11 I will minimize p taking

the incentive constraint (3) into account. Then I

show that the optimal ” also satisfies the incen-

p

tive constraints (1) and (2). FIGURE 2

Obviously, Becker's (1968) maximum fine

The Set of Incentive-Compatible

result applies here, meaning that to minimize

p the government will use the agent's entire Sanctions and the Optimal Sanction

wealth for sanctions.12 Accordingly, plugging Scheme …sà , sà † ˆ …W a2, W a2† and pà ˆ

1 2

the budget constraint s1 ‡ s2 ˆ W into (3) and 2baW

differentiating the equality yields



dpads1 ˆ …p À p2 †a…b À s1 À 2p‰W À s1 Š† 5 0



for b 5 s1 W . Consequently,

”1 ˆ W , ”2 ˆ 0,

s s and ” ˆ ba…W À b†X

p



Because bap52bap…1 À p†5b…1 ‡ p†ap Vp P

…0, 1†, the incentive constraints (1) and (2)

are also satisfied.

I thus find that the optimal sanction scheme

sets ”1 ˆ W and ”2 ˆ 0. First-time offenders

s s

are punished with the maximal possible sanc-

tion, and second-time offenders are not pun-

ished at all. The sanction s1 is high enough that Consequently, p is minimized by putting all the

it not only deters first-time offenses but also scarce resources into s1 .

second-time offenses even though they come It is perhaps somewhat surprising that strat-

for free. egy (1,(0 j no record;1 j otherwise)) and not

The intuition for this result follows immedi- strategy (1,(1 j no record;0 j otherwise)) defines

ately from the incentive constraint (3). The the binding incentive constraint in the optimal

agent pays the sanction s1 with probability p penalty structure. Given that the optimal

and the sanction s2 only with probability p2 . To penalties are declining, an agent who was not

put it differently: The agent is charged s2

with probability p if and only if he has paid 11. Because in my setup the harm of the crime exceeds

already s1 . Because paying the fine s1 is its acceptable benefit, maximizing social welfare boils down

to minimizing enforcement costs.

more likely than paying s2 , shifting resources 12. If s1 ‡ s2 5 W , sanctions can be raised and p low-

from s2 to s1 increases deterrence for given p. ered so as to keep deterrence constant.

EMONS: SUBGAME-PERFECT PUNISHMENT 501





apprehended for the first crime has a strong for the first act. If the government wants to

incentive not to commit the act a second deter the second act, it will set s2 ˆ bap. It

time: If she is apprehended, she pays the high chooses the minimal sanction ensuring deter-

sanction s1 . If the agent was, however, appre- rence because it will not get the money. This

hended for the first crime, the second crime way it can collect the maximum amount s1 ˆ

comes for free. The sanction s1 has to be W À bap for the first act from the agent.

high enough so that she doesn't commit the In contrast, the government may wish to

first crime in the first place. induce the second crime. It does so by setting

s2 5bap. The government collects s2 only with

probability p; it collects s1 for sure because we

IV. OPTIMAL SANCTIONS IF THE

GOVERNMENT CANNOT COMMIT

are in the node where the government has just

apprehended the agent for the first crime.

I now check under which conditions the Because W ˆ s1 ‡ s2 , the revenue maximizing

sanction scheme ”1 ˆ W , ”2 ˆ 0 together

s s government sets s1 ˆ W and s2 ˆ 0 if it wants

with the minimal enforcement probability ” ˆ p to induce the second crime. This generates a

ba…W À b† is subgame perfect. This means: payoff of W À 2h À p for the government.

Does the government really implement these The government prefers the strategy of

sanctions once the agent has committed a inducing the second crime to optimally deter-

crimec To do so, consider the subgame starting ring the second crime if W À 2h À p4

when the agent has been apprehended for the W À h À bap À p D bap4h. Deterring the

first crime. second crime has the cost of the forgone rev-

If the government sticks to the penalty enue s2 ˆ bap; encouraging the second crime

scheme ”1 ˆ W , ”2 ˆ 0, the agent will commit

s s has the cost of the harm h.

the second offense for sure because it comes The left-hand side of the inequality bap 4 h

for free. The government's payoff then is is decreasing in p. Therefore, if it is not satisfied

W À 2h À ”. It incurs the harm twice and seizes

p for the minimal probability of apprehension

the agent's entire wealth with s1 . inducing no crimes ” ˆ ba…W À b†, it does

p

The alternative is to lower s1 and at the same not hold for any p deterring both crimes.

time increase s2 such that the agent doesn't p

Thus, if ba” 5 h D W À h 5 b, the govern-

commit the second act. Obviously, the rent- ment prefers to deter the second crime and

seeking government will set s2 ˆ ba”, the p does so optimally by setting sà ˆ sà ˆ W a2

1 2

minimal sanction-achieving deterrence. The and pà ˆ 2baW (see Figure 2).

government goes for the minimal sanction A low probability of apprehension increases

guaranteeing deterrence because, by its very bap, the sanction that is necessary to deter the

nature, the government will not get this second crime. Deterring a second crime thus

money; that way, s1 is as large as possible. becomes unattractive. By choosing a low p, the

Using ” ˆ ba…W À b†, I find s2 ˆ W À b and

p government commits not to raise s2 to a level

s1 ˆ b. If the government follows this strategy, that deters. This result is similar to Boadway

its payoffs are Àh ‡ b À ”. It incurs the harm

p and Keen (1998) where the government com-

from the first crime, collects s1 ˆ b, and there is mits to a lax enforcement not to raise tax rates

no more crime. after savings decisions have been made.

Comparing the two payoffs, obviously the I summarize the preceding observations

government prefers to stick to”1 ˆ W ,”2 ˆ 0 if

s s with the following proposition.

W À h ! b. The government gets the entire

wealth less the harm by sticking to the optimal PROPOSITION 1. If W À h ! b, the optimal

incentive scheme, whereas it gets s1 ˆ b if it subgame-perfect sanction scheme is given by

chooses to deter the second offense. One sà ˆ W , sà ˆ 0 and pà ˆ ba…W À b†.

1 2

may, therefore, conclude that sà ˆ W , sà ˆ 0

1 2 If W À h5b, the optimal subgame-perfect

is subgame perfect if the agent's benefit b and/ sanction scheme is given by sà ˆ sà ˆ W a2

1 2

or the harm are not too large (see Figure 1). and pà ˆ 2baW .

I now determine the optimal subgame-

perfect sanction scheme together with the prob- Obviously, the government is better off in

ability of detection p if W À h 5 b. Consider the first case, where it uses the decreasing sanc-

again the government deciding on sanctions tion scheme. In both cases crime is completely

after the wrongdoer has been apprehended deterred. With the decreasing sanction scheme

502 ECONOMIC INQUIRY





the probability of apprehension and hence REFERENCES

enforcement cost is lower than in the second Becker, G. ``Crime and Punishment: An Economic

case of constant sanctions. Approach.'' Journal of Political Economy, 76(2),

1968, 169±217.

Boadway, R., and M. Keen. ``Evasion and Time Consis-

V. CONCLUSIONS tency in the Taxation of Capital Income.'' Interna-

tional Economic Review, 39(2), 1998, 461±76.

The purpose of this article is to analyze Burnovski, M., and Z. Safra. ``Deterrence Effects of

subgame-perfect sanction schemes, that is, Sequential Punishment Policies: Should Repeat

sanctions the government indeed wants to Offenders Be More Severely Punishedc'' International

Review of Law and Economics, 14(3), 1994, 341±50.

implement should a crime have occurred. I con-

Chu, C. Y., Cyrus, Sheng-cheng Hu, and Ting-yuan

sider the problem of time consistency impor- Huang. ``Punishing Repeat Offenders More

tant because judges tend to have a lot of Severely.'' International Review of Law and Econom-

discretion as to the size of the penalty. They ics, 20(3), 2000, 127±40.

anticipate that a high penalty now may reduce Dittmann, I. ``The Optimal Use of Fines and Imprisonment

if Governments Don't Maximize Welfare.'' Discus-

the potential for future sanctions. Rational a

sion Paper, Humboldt-Universitt Berlin, 2001.

criminals will anticipate this and thus not be Available online at http://papers.ssrn.com/sol3/

deterred by empty threats. papers.cfmcabstract id ˆ 274449.

A rent-seeking government will stick to the Emons, W. ``A Note on the Optimal Punishment for

optimal decreasing sanction scheme if it gets Repeat Offenders.'' International Review of Law and

Economics, 23, 2003, 253±59.

more money by allowing the second crime Garoupa, N. ``The Theory of Optimal Law Enforcement.''

and cashing in the agent's entire wealth with Journal of Economic Surveys, 11(3), 1997, 267±95.

the first sanction than by deterring the second Garoupa, N., and D. Klerman. ``Optimal Law Enforce-

crime. In the opposite case the government pre- ment with a Rent-Seeking Government.'' American

fers to deter the second crime. It does so with Law and Economics Review, 4(1), 2002, 116±40.

Landsberger, M., and I. Meilijson. ``Incentive Generating

equal sanctions for both crimes. State Dependent Penalty System, The Case of Income

Accordingly, the constraint of time consis- Tax Evasion.'' Journal of Public Economics, 19(3),

tency has bite. If the government can commit, 1982, 333±52.

decreasing sanctions are always optimal; if the Polinsky, M., and D. Rubinfeld. ``A Model of Fines for

government cannot commit, decreasing sanc- Repeat Offenders.'' Journal of Public Economics,

46(3), 1991, 291±306.

tions may still be optimal but so may be equal Polinsky, M., and S. Shavell. ``On Offense History and the

sanctions. I haven't explained escalating sanc- Theory of Deterrence.'' International Review of Law

tions based on offense history, which are and Economics, 18(3), 1998, 305±24.

embedded in many penal codes and sentencing ÐÐÐ. ``The Economic Theory of Public Enforcement of

guidelines. Explaining escalating sanctions Law.'' Journal of Economic Literature, 38(1), 2000a,

45±76.

seems to be fairly difficult for the law enforce- ÐÐÐ. ``The Fairness of Sanctions: Some Implications for

ment literature.13 Nevertheless, in my set-up Optimal Enforcement Policy.'' American Law and

the commitment issue ruled out decreasing Economics Review, 2(2), 2000b, 223±37.

sanction schemes in some cases. Perhaps the Rubinstein, A. ``An Optimal Conviction Policy for

problem of time consistency is a fruitful Offenses that May Have Been Committed by Acci-

dent,'' in Applied Game Theory, edited by S. Brams, A.

track for future research to explain escalating È

Schotter, and G. Schwoodiauer. W urzburg: u

sanction schemes. Physica-Verlag, 1979, 406±13.









13. See Emons (2003) for a discussion of the problems

the law enforcement has in explaining escalating sanctions.