In criminal law, when a conflict is solved by plea bargaining, the negotiation is mainly made between the prosecutor and the lawyer. Adopting a complete information framework about his type (selfish or altruistic), this paper compares two lawyer payment systems: flat fees and hourly-wage fees. We identify the system of fees in which the sentence is the lowest. We first show that under flat fees the prosecutor provides less effort when he faces an altruistic lawyer. Second, we show that under some conditions an altruistic lawyer may accept a higher sentence than a selfish lawyer.plea bargaining, lawyer's selfishness, system of fees

Lydie Ancelot

Philippe Delacote

English

Research Papers in Economics

     
 
 
  
  
Volume 29, Issue 3 
  
Prosecutor and lawyers in plea bargaining with complete information 
  
 
 
Philippe Delacote  
INRA, AgroParisTech, LEF 
Lydie Ancelot  
Beta, BETA-CNRS, Université de Nancy
Abstract 
In criminal law, when a conflict is solved by plea bargaining, the negotiation is mainly made between the prosecutor 
and the lawyer. Adopting a complete information framework about his type (selfish or altruistic), this paper compares 
two lawyer payment systems: flat fees and hourly-wage fees. We identify the system of fees in which the sentence is 
the lowest. We first show that under flat fees the prosecutor provides less effort when he faces an altruistic lawyer. 
Second, we show that under some conditions an altruistic lawyer may accept a higher sentence than a selfish lawyer.
We thank warmly Myriam Doriat-Duban, Yannick Gabuthy, Nuno Garoupa, Sandrine Spaeter and an anonymous reviewer for their helpful 
advice. 
Citation: Philippe Delacote and Lydie Ancelot, (2009) ''Prosecutor and lawyers in plea bargaining with complete information'', Economics 
Bulletin, Vol. 29 no.3 pp. 1925-1932. 
Submitted: Mar 16 2009.   Published: August 13, 2009. 
 
     1 Introduction
In the United States, more than 95% of all criminal cases are solved by plea bargaining.
This process consists in reducing the defendant’s sentence if he recognize his guiltiness.
After the common law countries, civil law countries (Italy, Poland, France) have applied this
widely discussed process (see Alschuler, (1968), (1975), (1976), Schulhofer (1988)) with same
objectives as American plea bargaining, mainly decreasing legal costs.
Focusing on criminal law1, the economic theory of plea bargaining usually considers that
the prosecutor oﬀers a contract to the defendant, who accepts or rejects it2. However, in plea
bargaining the relationship is mainly between the prosecutor and the lawyer. This paper thus
analyzes plea bargaining by focusing on the prosecutor and lawyer relationship, considering
diﬀerent degrees of lawyer’s altruism. Moreover, the system of fees in plea bargaining is a
crucial element determining the ﬁnal outcome. We thus compare ﬂat fee and hourly wage,
when the level of lawyer’s altruism known by the prosecutor.
In the next section, we analyze plea bargaining as a two step game. We analyze the
impact of the fee system on the sentence, ﬁrst when the case goes to court, and then when
it is concluded by plea bargaining. So, this paper allows to compare the systems of payment
and their impact on the sentence against the defendant.
2 Plea bargaining as a two-stage game
We consider a two-stage game between the prosecutor and the lawyer. We assume that the
lawyer may be more or less altruistic. The degree of altruism of lawyer i is assumed to be
public knowledge, which may be explained by reputation. In the ﬁrst stage, the prosecutor
oﬀers a reduced sentence qi, as a take-it-or-leave-it oﬀer, to the lawyer so that his client
accepts to plea guilty3. The game ends if the oﬀer is accepted. In the second stage, if the
oﬀer is refused, the case goes to court. At this point, both players choose how much time
to spent on the case4. ei and a are thus the number of worked hours by the lawyer and
prosecutor, respectively, which result in expected sentence q(ei,a). The game is solved by
backward induction, invoking the concept of subgame perfect Nash equilibria.
2.1 The lawyer
The lawyer is endowed with available time e. If the case goes to court, the lawyer chooses
the number of hours to spend on the case, ei, to maximize his expected payoﬀ, which is a
weighted sum of his net private payoﬀ and the ﬁnal sentence5.
1In civil law, the literature mainly explores the agency problems in settlement between the lawyer and his
client (Miller (1987), Gravelle and Waterson (1993, Gilson and Mnookin (1997), Hay (1997)). The agency
issue between the two parties may arise because of diverging interests coming from the fee system.
2For a survey see Ancelot and Doriat-Duban (2008).
3We implicitly assume that the lawyer is able to inﬂuence the client’s decision (Gravelle and Waterson
(1993)).
4We assume here that time spent on the case can be perfectly monitored by the defendant. We avoid
thus the potentially interesting case of moral hazard between the lawyer and his client.
5The following expected payoﬀ function is equivalent to the more conventional weighted payoﬀs:
αi(Ω(ei) − cei) − (1 − αi)λiq(ei,a), with αi ∈ (0,1] and λi = αi
1−αi. αi = 1(αi = 0) corresponds to a
fully selﬁsh (altruistic) lawyer. This speciﬁcation brings similar but more straightforward analytical results.
1max
ei
Πi = λi(Ω(ei) − cei) − q(ei,a) (1)
The lawyer may be more or less altruistic. A more altruistic (equivalently less selﬁsh)
lawyer acts with a perspective of professional ethic, that is in the best interest of his client,
i.e. to reduce the most the sentence. A more selﬁsh lawyer thus puts more weight on his net
private payoﬀ. A smaller λi thus describes a more altruistic lawyer.
The lawyer’s private payoﬀ Ω(ei) may either be hourly wage or ﬂat fee. In the case of
hourly-wage system, we have: Ω(ei) = wei, with w being the hourly wage. Conversely, in
the ﬂat-fee system, the lawyer receives a ﬂat sum, whatever the time spent on the case:
Ω(ei) = w. c is the unit cost of a worked hour.
q(ei,a) is the expected sentence received by the client and depends on both time spent
by the attorney and the prosecutor. We take the standard assumption that more time spent
on the case by the lawyer decreases the expected sentence, at a decreasing rate:
∂q(ei,a)
∂ei < 0,
∂2q(ei,a)
∂e2
i > 0.
2.2 The prosecutor
The prosecutor chooses the number of hours spent on the case, to maximize the severity
of the expected sentence with respect to the cost of a worked hour. This assumption is
consistent with the literature that speciﬁes conviction maximization as an objective function
of the prosecutor (Ramseyer and Rasmusen (1999)). Furthermore, one part of the economic
analysis of plea bargaining considers this assumption as fair (Grossman and Katz (1983),
Reinganum (1988), Baker and Mezzetti (2001)). In the American system, this assumption
is even more justiﬁed by the fact that the prosecutor acts in a re-election perspective. In
fact, the electorate and politician tends to evaluate the prosecutor’s quality by the severity
of sentences obtained (Garoupa and Stephen (2008)).
If the case goes to court, the prosecutor chooses to spend a hours on the case, in order
to maximize his expected payoﬀ6:
max
a
I = q(ei,a) − ka (2)
Time spent on the case increases the penalty at a decreasing rate:
∂q(ei,a)
∂a > 0,
∂2q(ei,a)
∂a2 < 0.
k is the prosecutor’s unit cost of a worked hour.
Note here that if the case goes to court, the ﬁnal sentence depends on both levels of
worked hours: q(ei,a). A crucial question here is the impact of the lawyer’s eﬀort on the
prosecutor’s eﬀort marginal eﬀect and vice versa. Both players have opposite objectives
about the ﬁnal sentence. It is thus likely that a player’s eﬀort decreases the other player
marginal productivity:
∂2q(ei,a)
∂a∂ei < 0. We will thus keep this assumption for the remaining of
the paper.
6Maximizing expected sentence means that the prosecutor aims at maximizing the probability of convic-
tion and/or the sentence if the defendant is convicted.
22.3 Going to court
If the reduced sentence oﬀered by the prosecutor is refused, the case goes to court. In this
case, both the prosecutor and the lawyer choose their optimal level of worked hours.
The lawyer’s ﬁrst order condition gives its optimal working time level. e∗
i is implicitly
deﬁned by:
λi(
∂Ω(e∗
i)
∂ei
− c) =
∂q(e∗
i,a)
∂ei
(3)
Hourly-wage system: If the lawyer is paid proportionally to the provided hours level,
equation (3) gives: λi(w − c) =
∂q(e∗
i ,a)
∂ei . Since additional spent time reduces the expected
sentence (
∂q(ei,a)
∂ei < 0), this condition is not met as long as w > c, which is the most likely
case. Under an hourly-wage system, the lawyer optimization thus leads to a corner solution,
in which the lawyer spend all his available time on the case, whatever his type.
Flat-fees system: If the lawyer receives a ﬂat fee, equation (3) gives: λic = −
∂q(e∗
i ,a)
∂ei .
A selﬁsh lawyer thus puts extra weight on its private net payoﬀ, while an altruistic lawyer
puts more weight on the sentence.
Proposition 1:
• In a hourly-wage framework, so long as the hourly wage exceeds the lawyer’s hourly cost,
the lawyer spends all his available time on the case, whatever his degrees of altruism :
e∗
i = e, ∀i.
• In a ﬂat-fee framework, a more altruistic lawyer spends more time on a case than a
less altruistic one:
∂e∗
i
∂λi < 0.
Proof: from the implicit function theorem:
∂e∗
i
∂λi = −c
∂2q(ei,a)
∂e2
i
< 0.
Similarly, the prosecutor maximizes equation (2). The ﬁrst-order condition implicitly
gives the prosecutor equilibrium worked hours:
∂q(ei,a∗)
∂a
= k (4)
Relying on the assumptions above (
∂2q(ei,a)
∂a2 < 0,
∂2q(ei,a)
∂e2
i < 0 and
∂q(ei,a)
∂a∂ei < 0), we
can conclude from equation (3) and (4) that a prosecutor spends more time on a case if
the lawyer is paid through hourly wage than with a ﬁxed-fee mechanism: a∗(ei) > a∗(e),
∀i. Moreover, in the case of a ﬂat-fee payment, the prosecutor spends less time if he
is confronted to a more altruistic lawyer:
∂a∗(ei)
∂λi > 0, ∀i. This results comes from the
prosecutor’s trade oﬀ between the expected sentence and his cost of worked hours. Indeed,
the expected sentence meets the marginal cost earlier if the lawyers works longer.
3Proposition 2:
• When going to court, the defendant can expect a larger sentence if his lawyer is
paid through a ﬂat-fee mechanism than if he receives an hourly-wage: q(e,a∗(e)) <
q(e∗
i,a∗(e∗
i)), ∀i.
• Moreover, if the lawyer receives a ﬂat fee, the sentence is smaller if the lawyer is more
altruistic:
∂q(e∗
i ,a∗(e∗
i ))
∂λi > 0.
Proof: from the implicit function theorem:
∂a∗(e∗
i )
∂λi =
∂a∗(e∗
i )
∂ei
∂e∗
i
∂λi = −
∂q(e∗
i ,a∗(e∗
i ))/∂a
∂q(e∗
i ,a∗(e∗
i ))/∂ei
∂e∗
i
∂λi > 0.
Moreover, as shown before,
∂e∗
i
∂λi < 0. Since
∂q(ei,a)
∂a > 0 and
∂q(ei,a)
∂ei < 0, it follows that
∂q(e∗
i ,a∗(e∗
i ))
∂λi > 0.
Our results thus gives the intuition that, when the case is solved by trial, a two-speed
justice is developed: defendants (and often poorer) with ﬂat-fee lawyers can expect a larger
sentence than with hourly-wage lawyers.
2.4 Take-it-or-leave-it oﬀer
The prosecutor may oﬀer a reduced sentence qi to the defendant if he decides to plea guilty.
We consider that the defendant is relatively ignorant, which implies that the lawyer is able
to inﬂuence his decision to conclude a arrangement. Thus we implicitly consider that the
lawyer has suﬃcient bargaining power to persuade his client to accept any oﬀer. If the
defendant accepts the oﬀer, the prosecutor and the lawyer save the time they would spend if
the case goes to court. Moreover, the lawyer gets a private payoﬀ of Ω(0). Remember that
the lawyer’s type is public knowledge because of the lawyers reputation.
2.4.1 Participation constraints
In order to have any interest in the plea bargaining process, both players need to get at least
the expected payoﬀ they would get if the game would have gone to court.
Prosecutor Participation Constraint: The prosecutor’s participation constraint is:
qi ≥ q(a
∗(e
∗
i),e
∗
i) − ka
∗(e
∗
i) ≡ qpi (5)
Thus he will never oﬀer a reduced sentence below qpi to the lawyer. The prosecutor has
a smaller participation constraint when he is confronted to an more altruistic lawyer if his
cost of one worked hour is suﬃciently small:
∂qpi
∂λi
= (
∂q(e∗
i,a∗(e∗
i))
∂a
− k)
∂a∗(e∗
i)
∂λi
+
∂q(e∗
i,a∗(e∗
i))
∂ei
∂e∗
i
∂λi
> 0 (6)
4Lawyer Participation Constraint: The participation constraint of a type i lawyer is:
qi ≤ λi(Ω(0) − Ω(e
∗
i) + ce
∗
i) + q(a
∗(e
∗
i),e
∗
i) ≡ qli (7)
The lawyer only accepts the prosecutor’s oﬀer if it is smaller than qli. Considering hourly
wage, the lawyer looses the whole income he would have had if the game has gone to court:
Ω(0) = 0. In this context, a more altruistic lawyer thus accepts a worse oﬀer (larger qli) than
a more selﬁsh lawyer. Indeed, the lawyer looses his wage if the reduced sentence is accepted,
and a selﬁsh lawyer puts more weight on his private payoﬀ. Selﬁshness thus creates an
incentive to refuse an oﬀer in order to go to court and receive a larger private payoﬀ.
Considering ﬂat-fee: Ω(0) = w. Thus a lawyer paid through a ﬂat-fee system accepts a
worse oﬀer (larger qli) than a lawyer with an hourly-wage system. Indeed, in this case, the
lawyer reduces his level of eﬀort without reducing his wage.
Proposition 3:
• In an hourly-wage system, a more altruistic lawyer accepts a worse oﬀer than a less
altruistic one:
∂qli
∂λi = (−w + c)e < 0.
• In a ﬂat-fee framework, a more selﬁsh lawyer accepts a worse oﬀer than a more al-
truistic lawyer if the marginal productivity of a worked hour is large or if the cost a
worked hour is small:
∂qli
∂λi = c(e∗
i + λi) +
∂q(e∗
i ,a∗(e∗
i ))
∂ei +
∂q(e∗
i ,a∗(e∗
i ))
∂a
∂a∗(e∗
i )
∂ei > 0.
The system of fee is also crucial in the plea bargaining stage. The ﬂat-fee system plays
as an incentive for the lawyer to accept a worst oﬀer than under an hourly-wage framework.
This statement is particularly relevant when considering that poorer defendants are usually
represented by lawyers paid under a ﬂat-fee framework.
2.4.2 Surplus from plea bargaining:
Overall the plea bargaining may be implemented if qli ≥ qpi, which implies:
λi ≥
ka
Ω(ei) − cei − Ω(0)
≡ λ
w (8)
Proposition 4:
• Under a ﬂat-fee framework, the surplus of a plea bargaining is always positive: λw =
−ka
cei < 0.
• Under an hourly-wage system, the surplus of a plea bargaining is larger if the lawyer
is more altruistic, if the prosecutor’s cost is large or if the lawyer’s cost is small.
As long as equation (8) is satisﬁed, and since we consider a take-it-or-leave-it framework,
the prosecutor oﬀers a reduced sentence that binds the lawyer’s participation constraint.
Therefore the lawyer does not get any extra payoﬀ from the plea bargaining. The prosecu-
tor thus gets the whole surplus S from the plea bargaining, that depends on the payment
framework:
S =
￿
ka(e) − λi(w − c)e if hourly − wage payment
ka∗(e∗
i) + λice∗
i if flat − fee payment
(9)
5Proposition 5:
• An hourly-wage framework implies a smaller prosecutor surplus than a ﬂat-fee system
framework.
• Considering a hourly-wage system (ﬂat-fee system) framework, a more selﬁsh lawyer
decreases (increases) the prosecutor surplus.
Indeed, in the ﬂat-fee framework, the plea bargaining allows the lawyer to save time,
which increases its payoﬀ. This eﬀect is increasing in selﬁshness. Conversely, in the hourly-
wage system, the plea bargaining deprives the lawyer from the positive private net payoﬀ he
would get if the game goes to court.
3 Conclusion
Focusing on the prosecutor-lawyer relationship, this paper identiﬁes the eﬀect of the lawyer
selﬁshness and of the fee system (ﬂat fee and hourly wage) on the sentence in a plea bargaining
process. If the game goes to court, the defendant can expect a smaller sentence if his lawyer is
more altruistic or if he receive an hourly wage. However, if he receives an hourly wage, a more
altruistic lawyer accepts a worse oﬀer. In the case of a ﬂat-fee system, a plea bargaining may
always be implemented. The lawyer always tend to accept the prosecutor’s oﬀer, whatever
his type.
Overall, our results provides evidence of a two-speed justice: lawyers of poorer defendants
tends to receive ﬂat fees, while richer defendant are more able to employ business lawyers
(with hourly-wage payment). It follows that poorer defendants can expect larger sentences
on court, and to some extend worse plea bargaining oﬀers. Conversely, prosecutors tend to
experience smaller surplus when confronted to a hourly-waged lawyer.
A crucial assumption in this paper is the complete information framework. Ancelot
and Delacote (2009) relax this assumption, by imposing uncertainty on the lawyer’s type.
This extension allows to add adverse selection considerations, since the prosecutor’s eﬀort is
determined by the lawyer’s type. The plea bargaining process may in this case becomes a
screening tool for the prosecutor to infer the lawyer type.
References
Alschuler, A. (1968). The prosecutor’s Role in Plea Bargaining. University Chicago Law
review, 36, pp.105-112.
Alschuler,A. (1975). The Defense lawyer’s Role in Plea Bargaining. Yale Law Journal,
84, pp.1179-1314.
Alschuler, A. (1976). The Trial Judge’s Role in Plea Bargaining.Columbia Law Review,
76, pp.1059-1114.
Ancelot, L. and Doriat-Duban, M. (2008). Th´ eorie ´ economique du plaider coupable.
Working Paper.
Ancelot, L. and Delacote, P. (2009). Prosecutor and lawyer in plea bargaining: screening
or not screening?, Working Paper.
Baker,S. and Mezzetti, C.(2001). Prosecutorial Resources, plea bargaining, and the de-
cision to go to trial. The Journal of Law, Economics and Organization, 17(1), pp.149-167.
6Garoupa, N. and Stephen, F. (2008). Why plea bargaining fails to achieve results in
so many criminal justice systems: A new framework for assessment. Maastricht Journal of
European and Comparative Law, 15, pp.319-354.
Gilson, R. J. and Mnookin, R.H. (1994).Disputing through agents: cooperation and
conﬂict between lawyers in litigation. Columbia Law Review, 94, p. 509-537.
Gravelle, H and Waterson, M (1993). No win, no fee: some economics of contingent legal
fees. Economic Journal, 103, 2, pp.1205-1220.
Grossman, G. and Katz, M.(1983). Plea bargaining and social welfare. American Eco-
nomic Review, 73, pp.749-757.
Hay, B. L. (1997). Optimal contingent fees in a world of settlement. Journal of Legal
Studies, 26, pp.259-278.
Miller G.P (1987). Some agency problems in settlement. Journal of Legal Studies, 16,
pp.189-215.
Ramseyer M. and Rasmusen, E.(1999). Why are Japanese Conviction Rates so High?.
Working paper, University of Chicago Law School Workshop in law and Econonomics.
Reinganum, J.(1988). Plea Bargaining and Prosecutorial Discretion. American Economic
Review, 78, p. 713-728.
Schulhofer, S.J.(1988). Criminal Justice as a Regulatory System. Journal of Legal Stud-
ies, 17,pp. 42-81.
7

Criminal Justice as a Regulatory System.

No win, no fee: some economics of contingent legal fees.

Optimal contingent fees in a world of settlement.

Plea Bargaining and Prosecutorial Discretion.

Plea bargaining and social welfare.

Prosecutor and lawyer in plea bargaining: screening or not screening?, Working Paper.

Prosecutorial Resources, plea bargaining, and the decision to go to trial.

Some agency problems in settlement.

Th´ eorie ´ economique du plaider coupable. Working Paper.

The Defense lawyer’s Role in Plea Bargaining.

The prosecutor’s Role in Plea Bargaining.

The Trial Judge’s Role in

through agents: cooperation and conﬂict between lawyers in litigation.

Why are Japanese Conviction Rates so High?. Working paper,

Why plea bargaining fails to achieve results in so many criminal justice systems: A new framework for assessment.

Prosecutor and lawyers in plea bargaining with complete information

http://www.accessecon.com/Pubs/EB/2009/Volume29/EB-09-V29-I3-P40.pdf

Prosecutor and lawyers in plea bargaining with complete information

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics