Post on 19-Jul-2020
TOURNAMENTS: THEORY AND EVIDENCE
ANAND J. SHUKLA
Introduction
In this paper, I synthesize the literature in tournaments and present essential
theory and evidence. A tournament can be described as a game where there are
prizes and the participants are measured according to their relative rank among
other participants and the prizes are awarded accordingly. A simple example from
a personal experience is the case of a clothing store having a contest among its
sales representatives to sell pants and the one who sells the highest number is
awarded a prize. Of course, the applications of tournaments spans far beyond
just selling pants and has some very important bene�ts.
In this paper, I study the e�ciency of tournaments as pay schemes compared
to piece rates (under di�erent settings) and also as mechanisms to increase e�ort
among agents. Both of these pay schemes come from a root problem and that
is costly monitoring. The problem is that workers may shirk and if monitoring
is relatively inexpensive then the best pay scheme is an input-based pay such as
periodic wage. In many settings this may not be viable and so we must consider
piece rates or tournaments, which are output-based pay schemes.
The principal question: Are tournament based pay schemes e�cient and under
what conditions? This question was �rst studied by Lazear and Rosen (1981),
which has provided the theoretical framework for most of the work that has been1
TOURNAMENTS: THEORY AND EVIDENCE 2
done in this subject. Over the years, there has been much progress on the empir-
ical side of these questions and the results have yielded some interesting policy
implications. I will cover extensively evidence on the basic theory and uneven
tournaments. I will also brie�y cover self-selection, information (or feedback),
risk-taking, and moral hazard, and how these environments a�ect the e�ciency
and performance of tournaments.
Theoretical Framework
The seminal paper by Lazear and Rosen (1981) provides the general framework
for the tournament theory that has been studied in its original settings or vari-
ations of it over the past few decades. They study tournaments and piece rates
(pay based on per unit of output/action) as pay schemes and determine their
e�ciency under di�erent settings (risks and shocks).
Risk-neutral agents
First, consider the case where there are two risk-neutral agents and no common
shocks. There are two cases studied here, one where the workers are paid on a
piece rate, and the other where workers are paid on their relative rank, in prizes.
On the �rm's side, the production is additively separable in workers' outputs and
the manager is risk-neutral. Also, we will assume that the markets are competitive
so we have a �xed price V per unit. The model looks like the following:
The output agent j produces
qj = µj + εj
where µj can be thought of as the individual e�ort, or investment, or a measure
of skill, and εj is the random shock the agent j gets, which is independently
TOURNAMENTS: THEORY AND EVIDENCE 3
distributed from the shocks that other agents get, as mentioned before. The prize
for highest output is W1, while the second place prize is W2.
Proposition 1: Under risk-neutral agents and no common shocks, piece rates
and tournaments both yield pareto e�cient outcomes.
The proof is given in the Appendix section, but it is rather simple to understand.
The agent and the �rm will maximze their ex-ante utility function and pro�t
function, respectively. It is easy to see that under competitive markets, the price of
output equals the marginal product of labor (this is the piece rate), which is equal
to the marginal cost. Under the tournament case, since the prizes (W1 > W2) are
predetermined, the investment by each agent is also predetermined. The �rm must
set W1−W2 such that the agents play a Nash-Cournot game. The agents simply
maximize their expected payo�s using P as their probability of winning. Also,
since the shocks are identically distributed, the players play a Nash-Cournot game
where each of their investment is maximized at the intersection of their reaction
functions. This intersection corresponds to both of their investment being the
same and therefore the probability of winning for each player to be the same as
well. As mentioned before, the �rm must set the prizes optimally so that such
investment occurs (C ′(µi) = (W1 −W2)g(0) ). Again we have price equal to the
marginal cost.
Risk-averse agents
The above conclusion doesn't hold true under the case of risk-averse agents.
I will not provide an extensive proof. The piece rates do provide a slight im-
provement over the tournaments when there are no common shocks. Intuitively,
TOURNAMENTS: THEORY AND EVIDENCE 4
risk-averse people generally don't like the bimodal nature of tournaments, espe-
cially when the spread of the prize is large. However, the previous statement does
not apply under certain conditions such as when initial wealth is high and/or
there are common shocks, where relative pay may in fact yield greater e�ort than
piece rates. I will not go into great detail as these results are not fully proved.
Adverse selection
Consider the simple case of two di�erent types of agents, who know their type,
but the principal doesn't:
There are two leagues, a, which yields the most e�cient outcome given the high
ability people, and league b, which yields the highest outcome given low ability
people. The problem is league a is strictly preferred since the revenue function
for league a yields a strictly higher payo�. This leads to the lower type b contam-
inating the league a, which results in a mixed bag of agents competing against
each other. To be precise, these agents don't sort themselves into their particular
leagues. It is intuitive to see why such mixing would lead to ine�ciencies if the
proportion of agents in each league is unequal. One type overinvests and the other
type underinvests.
Remarks and Extensions
In sum, since it may be less costly to measure the relative performance than
individual output, tournaments yield an e�cient solution, where wages are given
as prizes, and not necessarily in terms of the agents' marginal products. There
is one behavioral concern and that is, depending on the risk aversion, the agents
may well be satis�ed with the lower prize under common shocks, discouraged by
their relative chances of winning. The question here is how risk-averse are these
TOURNAMENTS: THEORY AND EVIDENCE 5
agents and how does it change their percieved costs. This would only occur if
agents didn't fully understand the fact that other agents are of the same type.
Well, it's a bad day outside, I'm not going to be able to sell much, I might as well
not work today and just get the lower prize. By symmetry of both players, we
may actually have a worse outcome than the piece rates.
Another crucial remark is that the tournament is a strategic game that involves
the agents maximizing expected values and �nding Nash solutions. Generally
speaking, this may not be robust in real settings as most people do not think as
strategically as conjectured.
Evidence
Testing the Theory
One of the �rst papers to test Lazear and Rosen's theory was by Bull, Schotter,
and Weigelt (1987). Since the theory required some restrictive assumptions (risk-
neutrality, independent random shocks, etc.), the test was done as a laboratory
experiment. The authors tested both the piece rate scheme and the tournament
scheme using the original model, where the cost function took this form:
C(e) = e2
cwhere c was some positive value that the authors decided upon (2000
for the piece rate, and 10,000 for the tournament for example).
So the parameters chosen by the authors are: c, M, m, and a, where M refers
to the large prize and m refers to the small prize; a is the bound on the random
shock, ε ∈ [−a, a]. Given these parameters, the authors calculate the predicted
e�ort levels (decision numbers) by the theoretical equilibriums. Table 1 in the
Appendix shows the parameters chosen.
TOURNAMENTS: THEORY AND EVIDENCE 6
The authors did ten experiments with one piece rate scheme and others being
variations of the tournament game. In the tournaments, participants were paired
with each other (but were not told whom they were paired up with), and were
asked to provide a decision number (which can be viewed as a e�ort level) between
0 and 100. After the decision number is chosen, the administrator goes around
with a basket of balls with numbers on them representing the random shock.
That is, the random ball picked by the participant has a number on it between
−a and a, inclusive. The participants then note this number down, put back the
ball in the basket and add the number to their decision number to get the total
output. In the case of the piece rate, the experimenter calculated the exact piece
rate needed to get an average decision number of 37. The experiments are divided
as follows: the �rst three experiments study the tournament setting with di�erent
cost and prize structure; Experiment 1 is the base case with 37 as the predicted
e�ort level. Experiment 2 and 3 study the variations in the costs and prizes to
check for the robustness of the tournament setting itself. Experiment 4 goes over
the asymmetric cost function, where one agent is given a higher cost than the
other Experiment 5 through 8 basically test how the the players use information
(the opponent's e�ort levels) to maximize their payo�s, instead of using strategy
to uncover the opponents e�ort levels (they are playing the �eld in a sense and
not the other players); experiment 10 is the piece rate case and experiment 9 is
simply the experiment 1 repeated 25 times instead of 12 rounds to see if it reduces
the variance.
The results are given in Table 2 in the Appendix. Looking at the piece rate
(experiment 10), one can see that the average is pretty close to the predicted value
TOURNAMENTS: THEORY AND EVIDENCE 7
of 37, which tells us that the subjects are maximizing their payo�s given the par-
ticular cost function. Under the even tournaments, where the cost functions are
the same for the paired agents, the results show the averages are on par with the
predicted theoretical values. The variance of the tournaments is quiet high, even
under full information (experiment 6,7, and 8), though still statistically insignif-
icant from the predicted value. The full information case gave the participants
full information about the other player's decision number to see if there was any
strategic di�culty in getting the predicted value, but the reduction in variance
was not much, which says this needs further explanation. In the case of the un-
even tournaments, where the cost of one agent is higher than the other's, we see
that the theory underestimates the e�ort level. Both the disadvantaged and the
advantaged exerted higher e�ort than what was predicted. This is another area
of further exploration.
Remarks and Extensions
The case of the high variance in this model is reduced dramatically when sorting
is allowed as we will see later. The high e�ort exerted by the disadvantaged group
in the uneven tournament is still under debate. A possible explanation is that
this type of setting (lab experiment given a utility function) may not be the best
at determining worker e�ort when there is cost asymmetry. There might be some
di�culty calculating the cost. A real-work experiment would perhaps yield better
results to this situation.
Uneven Tournaments
This section goes over the particular importance of uneven and unfair tour-
naments. Since most real-life cases are uneven, the results from Schotter and
TOURNAMENTS: THEORY AND EVIDENCE 8
Weigelt (1992) have much to o�er for policy-making. The authors try to answer
the question: Is there an equity-e�ciency trade o�? That is, by handicapping
the disadvantaged and equalizing the playing �eld, is there any loss to e�ciency?
They found that for the most part there is not a trade-o�.
The authors did lab experiments in the same sense as Bull, Schotter, and
Weigelt (1981). The participants had to choose a decision number between 0 and
100. The uneven tournaments are de�ned as follows:
Ui(p, e) = u(p)− c(e), where p is simply the payment
Uj(p, e) = u(p)− αc(e), where α >1
The payment to agent i is M , if yi > yj + k, and m < M o.w.
where k is a constant that indicates that j is favored if k > 0.
Three cases were studied in the experiments:
Unfair tournaments- α = 1 and k > 0; this can be thought of as prejudice in
the work place, where one person is favored over another.
Uneven tournaments- α > 1 and k = 0;
A�rmative action- α > 1 and k > 0; In this case, we are helping the disadvan-
taged (the high cost agent) by favoring him.
The authors �nd that under unfair tournaments, the mean of the e�ort is higher
than what is predicted for both agents. The pro�ts of the administrator are also
higher, but still less than the symmetric case, when there is no favoring. In the
case of uneven tournaments, where costs are asymmetric (α = 2 and α = 4),
the means are on par with the the theory, though there is a higher variation
among the disadvantaged in the case when α = 4. The later part is particularly
interesting because agents either gave too much e�ort or dropped out completely.
TOURNAMENTS: THEORY AND EVIDENCE 9
In real settings, the dropping out case is often noted as one of the selling points
for a�rmative action.
These results are then put into the format of a policy. Equal opportunity: In
the case where one agent is favored, this policy aims to reduce such discrimination.
In this case, as shown in Table 3 (in Appendix), tournament output is increased
as equal opportunity laws are imposed. Notice if the discrimination is very high,
then the favored worker exerts a lot less e�ort, which is the main reason for the
lack of e�ciency.
A�rmative action: The case where one agent has a higher cost, the policy
aims to level the competition by favoring the disadvantaged (the high cost). The
results, shown in Table 4 (in Appendix), indicate that the e�ort level actually
decreases for both agents if a�rmitive action is placed, when the cost di�erences
are small (α = 2). These results are statistically not di�erent from the predicted
results. However, in the case when there is a big di�erence among the two agents
(α = 4), the results indicate an increase in e�ort in both agents. In the earlier
analysis, we saw that when there is a huge cost di�erence, many agents tend to
drop out. These results indicate the a�rmative action policy will reduce or even
eliminate this behavior for the disadvantaged.
Remarks and Extensions
There is clear evidence that decreasing favoring in the tournament setting in-
creases overall e�ort and output. Similarly, for the case when there is a huge
di�erence among the agents, a�rmative action laws do provide a substantial gain
in output and e�ciency. The authors do not mention it, but it would be interest-
ing to see why the e�ort of the advantaged agents increased in the case of high
TOURNAMENTS: THEORY AND EVIDENCE 10
cost di�erences, but not in the case of low cost di�erence, when a�rmative action
was put in place.
Self-selection
We learned in the paper by Lazear and Rosen that there is a problem of adverse
selection when agents allowed to choose between two leagues of tournaments.
There has been much research done in terms of entry decisions into tournaments:
Camerer and Lovallo (1989) found that there is excessive entry when they studied
MBA students and asked them to choose between relative pay and piece rate.
Given the sample of MBA students, it's no surprise that they are more competitve
and overcon�dent (and might I add, male dominated). Niederle and Vesterlund
(2007) study the gender di�erences in the entry decisions; they �nd that men
exhibit more con�dence given their abilities, and women tend to opt for piece
rates rather than tournaments.
Perhaps more important and de�nitely more relevant to our previous topics is
the paper by Eriksson, Teyssier and Villevel (2008). Bull et al. (1987) found that
there was large variance in tournament settings in the e�ort levels, and despite
introducing more information such as the opponent's e�ort levels, there was still
much variance (Table 2, experiment 5 and 6). Eriksson et al. has similar setup
to that of Bull et al. except that the participants are allowed to choose between
piece rates and relative-pay. They �nd that those who choose the tournament
provide, on average, higher e�ort. After running the experiments, they also did
a questionaire with a bunch of lottery decisions to elicit the risk aversion of each
participant. They found that risk averse agents tend to choose the piece rate
TOURNAMENTS: THEORY AND EVIDENCE 11
scheme. This sorting lead to two homogeneous groups, reducing the between-
subject variance dramatically (577 in Bull et al. (Table 2) to 101 in Erikkson et
al., Table 5) in the tournaments.
Remarks
One note on these results is that even though the piece rate and tournament
was designed to yield the same e�ort level and expected payo�, the tournament
yielded a higher e�ort level. It is understood that these subjects are less risk
averse than those who chose piece rate, but what is the explanation for choosing
higher e�ort levels?
Information (feedback)
Theory has shown us that the agents choose e�ort levels ex-ante by the amount
of payment, the randomness, and the cost function, but a revelation of the other
agent's e�ort should not have any e�ect on the decision of e�ort. In this section,
I consider the interim case, when information or feedback is given to one agent
about the other agent's performance. Eriksson, Poulsen, and Villeval (2008) do
an experiment in the lab with similar setup as Niederle and Vesterlund (2007),
where they give agents a simple task to perform, which actually requires some
e�ort. They study three levels of feedback: no feedback, halfway (discrete), and
continuous. They �nd that there is no e�ect on both piece rate and tournament,
when there is feedback (discrete) given, but they do �nd that when continuous
feedback is given, the underdog (the agent lagging behind) actually reduces e�ort.
Gill and Prowse (2009) �nd similar results. They also study in a lab using
a real-e�ort game (on the computer), but the di�erence here is that the two
agents did not go simultaneously, but one agent went �rst and then the e�ort
TOURNAMENTS: THEORY AND EVIDENCE 12
level given by this agent was shown to the second mover who then decided how
much e�ort to exert. They �nd agents who feel behind exert less e�ort, and call
it disappointment aversion. The opposite is found by Berger and Pope (2009).
They study basketball teams that are behind during half-time and �nd that they
actually exert more e�ort and increase their probability of winning. They also
use a lab experiment to back up this claim.
Remarks and Extensions
It is confusing to see how we can end up with both of these conclusions given
lab experiments, but there are crucial di�erences between the two studies and
their methods. As we learned in Eriksson et al. that the timing and the amount
of di�erence matters. Berger and Pope use the halfway time to give feedback (and
study only when teams lag behind a point or two), while suppose the feedback is
given at the last two minutes of the basketball game, and the di�erence between
winning team and losing team is a lot. Again from Eriksson et al. it is shown that
peer e�ects matter when there is continuous feedback, it is easy to see NBA games
have continuous feedback. Also, just the fact that one is in a team should have
some within team peer e�ect, this may be a key di�erence between the results
compared with Gill and Prowse (2009). Lastly, the nature of the tournament
matters: Gill and Prowse study a sequential game, while most studies are done in
a simultaneous format. From personal experience (selling clothes), I can say that
the Gill and Prowse result de�nitely holds, but then again timing, peer e�ects,
and the nature of the tournament matter, not to mention the sample itself (we
have seen risk-averse agents tend to drop out of tournaments).
Risk-taking and Moral Hazard
TOURNAMENTS: THEORY AND EVIDENCE 13
Bronars (1986) �nds that leading agents choose a low-risk strategies, while those
that are behind choose a high-risk strategy in a sequential. This is quite intuitive,
if one was to think about race car drivers who are in the lead, they tend not to
take any risky moves. This theory is supported by quite a few papers in the lab.
Nieken and Sliwka (2008), however, �nd the opposite, that leading agents do no
play it safe, instead they tend to imitate their opponents. There are explanations
I can think of that could determine most of the di�erence in these two results.
First, there is di�erence between a sequential game and a simultaneous game. The
leading agent again doesn't know the e�ort of the second mover in a sequential
game and therefore could play it safe. If one was to see that the there is a car
very close behind him, then he would drive a bit faster and more recklessly, and
so the distance between the two competitors also matters. Charness and Kuhn
(2009) suggest one application of the Nieken and Sliwka prediction would be on
mutual fund managers, who invest in the same risky assets.
Moral hazard in tournaments is studied mainly in the terms when reducing
the relative performance of the peers increases one's own probability of winning
(sabotage). Sabotaging is a big issue in tournaments, when monitoring is rela-
tively expensive. Due to the negative nature of this subject, it has mainly been
studied in the lab. One exception, however, is Carpenter, Matthews, and Schirm
(forthcoming); they do a real-work experiment where participants are asked to
type and print a paper, stu� it in an envelope, write the name and address, and
then put it in the output box. The sabotaging comes into play when everyone
is asked to do a peer review (how many envelopes? the quality?, etc.). They
�nd that participants do �miscount� the envelopes and do report negatively (all
TOURNAMENTS: THEORY AND EVIDENCE 14
evaluations were done by administrators also to cross reference). As a result,
there was actually a decrease in the e�ort and the envelopes produced among the
participants because heck, they were being miscounted anyways. In peer review
case, the piece rate performed much better than the tournaments, with far less
sabotage.
Remarks
In the beginning of the last paragraph, I mentioned sabotage as the main moral
hazard, but an additional case (and to the contrary) is collusion. If the workers
collude then again we may have an ine�cient outcome. The collusion can occur
as a way to equalize e�orts and reduce any large penalties to participants. One
example of this is by Bandiera, Barankay, and Rasul (2005); they study a �eld
experiment on a UK farm. The farm originally has the tournament-based pay
scheme and then switches to a piece rate. The fruit pickers who know each other
well tend to pick less fruit so as to not raise the average of the group. The result
was even more severe among the groups, where there was a strong friendship
among the fruit pickers. Collusion, however, is not a big issue as some other
papers point out, when participants don't know each other.
Conclusion
In sum, the theory and evidence are pretty close, however, there are a few
irregularities and concerns yet to be answered. One problem that we got from
our empirical evidence is that there is a huge variance among participants in a
tournament. Introducing information such as the opponent's e�ort level reduces
the strategic di�culty and makes the problem a maximization problem. This
reduces the variance a bit, but not much. Eriksson et al. show that when self
TOURNAMENTS: THEORY AND EVIDENCE 15
sorting is allowed there is a more homogeneous group and so variance decreases
immensely.
Uneven tournaments can be improved by a�rmative action, but only in the case
when there is a huge di�erence between the costs of the two agents. Equal oppor-
tunity laws are de�nitely welfare improving (favoring any agent is unproductive
and something that �rms should consider anyways).
Entering tournaments is relatively similar to what the theory predicts except
the case when we have overcon�dence (Camerer and Lovallo 1989), which is quite
common among men (Niederle and Vesturland 2007). Risk-averse people tend
to opt of tournaments (this is intuitive) and prefer piece rates. Thus, it is not
surprising that tournaments increase risk-taking (by nature of the game, it induces
agents to take high risk) even for those who are in the lead and have a high
probability of winning (Nieken and Sliwka 2008). The e�ects of information
(feedback) of other player's performance is contradictory. We have that agents
lagging behind lose motivation and reduce their e�orts and we also have the result
that agents increase their e�orts given this feedback. Many things are at play here
and we have identi�ed timing, peer e�ects, and the nature of the game as being
possible solutions to the di�erence in outcomes.
Other extensions include studying risk-averse agents when the distribution of
the agent types is unknown. That is, we may have risk-averse agents being overly
satis�ed with the lower prize money and simply not even competing. The strategic
nature of tournaments in real life can lead to these types of results, where agents
don't necessarily know all the information or simply don't understand how to
use such information. We have seen the e�ciency gains from tournaments and
TOURNAMENTS: THEORY AND EVIDENCE 16
possible problems such as adverse selection or moral hazard, but it would be
interesting to see how we can having small teams could reduce these problems
while preserving the gains from a tournament system.
TOURNAMENTS: THEORY AND EVIDENCE 17
References
[1] Bandiera, Oriana, Iwan Barankay and Imran Rasul. �Social Connections and Incentives in
the Workplace: Evidence from Personnel Data� Econometrica, Vol. 77, No. 4 (July 2009a),
1047� 1094.
[2] Berger, Jonah, and Devin G. Pope. �Can Losing Lead to Winning?� unpublished paper,
The Wharton School, University of Pennsylvania, August 2009.
[3] Bronars, S. (1986): �Strategic Behavior in Tournaments� Texas A&M University.
[4] Bull, Clive, Andrew Schotter and Keith Weigelt (1987), �Tournaments and Piece Rates:
An Experimental Study�, Journal of Political Economy 95(1): 1-33. (February)
[5] Camerer, C. and D. Lovallo. �Overcon�dence and Excess Entry� American Economic Re-
view 89 (1999): 306-318.
[6] Carpenter, Je�rey, Peter Matthews and John Schirm. �Tournaments and O�ce Politics:
Evidence from a real e�ort experiment� American Economic Review forthcoming (available
as IZA DP No. 2972)
[7] Charness, G., and Peter Kuhn (2010), "Lab Labor: What Can Labor Economists Learn
from the Lab?" University of California Santa Barbara.
[8] Eriksson, Tor, Anders Poulsen and Marie-Claire Villeval (2008), �Feedback and Incentives:
Experimental Evidence� IZA Discussion Paper No. 3440.
[9] Eriksson, Tor, Sabrina Teyssier and Marie-Claire Villeval (2008), �Self-selection and the
E�ciency of Tournaments�, Economic Inquiry (47): 530-548.
[10] Gill, David and Victoria L. Prowse. �A Structural Analysis of Disappointment Aversion in
a Real E�ort Competition� IZA working paper no. 4356, October 2009.
[11] Lazear, E. and S. Rosen, "Rank-Order Tournaments as Optimum Labor Contracts", Jour-
nal of Political Economy, Oct. 1981.
[12] Niederle, Muriel and Lise Vesterlund (2007), �Do Women Shy Away from Competition? Do
Men Compete Too Much?�, Quarterly Journal of Economics 122(3): 1067- 1101. (August)
[13] Nieken, Petra and Dirk Sliwka (2010), �Risk-taking Tournaments: Theory and Experimen-
tal Evidence�, Journal of Economic Psychology.
TOURNAMENTS: THEORY AND EVIDENCE 18
[14] Schotter, Andrew and Keith Weigelt (1992), �Asymmetric Tournaments, Equal Oppor-
tunity Laws and A�rmative Action: Some Experimental Results�, Quarterly Journal of
Economics 107(2): 511- 539. (May)
TOURNAMENTS: THEORY AND EVIDENCE 19
Appendix
Proposition 1: Under risk-neutral agents and no common shocks, piece rates
and tournaments both yield Pareto e�cient outcomes.
Proof. qj = µj + εjwhere µj is the level of investment, a measure of skill and εj is mean zero i.i.d.Under Piece Rate:Worker maximizes:E[rq − C(µ)] = rµ− C(µ)r = C ′(µ), Similarly for �rm V = C ′(µ)Tournaments:Worker maximizes:(P )[W1 − C(µ)] + (1− P )[W2 − C(µ)] = PW1 + (1− P )W2 − C(µ)Assuming Nash-Cournot, symmetry: µj = µk
C ′(µi) = (W1 −W2)g(0),Firms (zero pro�t condition):V µ = (W1 +W2)/2P = 1
2implies the expected utility is V µ− C(µ)
Again marginal cost equals marginal social return V = C ′(µ)
�
TOURNAMENTS: THEORY AND EVIDENCE 20
TOURNAMENTS: THEORY AND EVIDENCE 21
TOURNAMENTS: THEORY AND EVIDENCE 22
TABLE 3
TABLE 4
TABLE 5