Promotion Tournament
(Slide for UST Organization Study Group)
Kong-Pin Chen
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1 Introduction
 Promising young ‘star’ slump in mid-career. It is one who
was obscure (or not highly regarded) in early career that
eventually wins.
 Examples
─ Zhao Ziyang, Hu Yaobang (politics)
─ Mario Cuomo, Clinton (politics)
─ Levine vs Nicholas (business)
─ Negative campaign (politics)
 Why?
 More than a matter of luck
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 Fact: Promotion is all-or-nothing, based on relative,
rather than absolute, performance.
 As a result, negative effort (sabotage) is a valuable
instrument to compete.
 In order to compete for promotion, the contestants
engage in both productive and unproductive (sabotage)
activities.
 When the number of contestants is large enough, the
ablest person might become the ‘focal point’ of attack so
that his performance might fall behind less able people.
 Relation to tradition tournament model or all-pay-auction:
In these models, the ablest contestant (or the one with
highest valuation of the good) always has the greatest
chance to win. This is no longer true when they can
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engage in negative activities.
 Relation to the literature on ‘influence activity’ (Milgrom,
1998): The contestants not only engage in influence
activity to increase promotion chance, but also actively
destroy opponents; performance.
 This phenomenon is not only common in promotion
tournament, but also between competing firms. Many
firms file perverse antitrust litigation against IBM, Kodak,
Microsoft (Brenner, 1987), just as a way of competition.
2 Model
 n contestants, one promotion.
 e i : level of productive activity by i .
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 a ij : level of attack by i against j .
 e i and a ij have different nature: The former only helps
person i . The latter not only helps i but also k  i, j .
As a result, a ij has a flavor of being a ‘public good’.
 t i : ability of i in productive activity.
 si : ability of i in sabotage.
 ri  t i / si . The comparative ability of i in productive
activity.
 If ri  r j , then we say i has greater comparative ability
in productive activity than
j.
 Performance (or output) of i  t i ei  g ( j i s j a ji )   i ;
where

j i
s j a ji is the total attack person i receives.
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 g (0)  0, g '  0, g "  0.

 i and  j are IID.  ~ f () ; singled-peaked, symmetric
around 0: Luck is ‘fair’.
 Abilities observable among contestants, but not to
superior.
 Wi  t i ei  g ( j i s j a ji ) , the expected performance of i .
 The utility of i , ui (e, a)  Pr(i is promoted )u  v(ei 

j i
aij ) ; where
u is the utility of promotion, and v the
disutility of effort. The utility of not being promoted is
 v'  0, v"  0.
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0.
ui (e, a)  Pr (Wi   i  W j   j , j )u  v(ei   aij )
j i

 i W ji


 [  f ( i )( 
j i
f ( j )d j )d i ]u  v(ei  aij ).
 where W ji  W j  Wi .
 Contestant i chooses the values of e i and aij ( j  i )
to maximize u i (e, a) .
 We are interested in the Nash equilibrium of the game.
 Theorem 1 If
ri  r j ,
then

k i
s k a ki  k  j s k a kj .
Contestant with higher comparative ability in productive
activity receives more total attack.
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 Intuition: Other things equal, if i has high value of t i ,
then opponents need to attack him more at the margin.
However, attacking him will force him to revenge, which
is not worthwhile the higher is the value of s i .
 Special case: If si  s j , i, j , then abler contestant is
subject to more total attack.
 (l  k sl alk ) / si  0 . A person with more talent in
negative activity receives less total attack.
 (l  k sl alk ) / si  0 (i  k ) . If a person becomes abler
in sabotage, then everyone else will be subject to more
total attack.
 A person ablest in productive activity probably does not
have greatest promotion chance.
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 For example: a person very talented in negative activity
( s i large), but bad in productive activity (low t i ) will beat
all others.
 (l  k sl alk ) / t k  0 . A contestant receives more total
attack when he becomes abler in productive activity.
 (l  k sl alk ) / ti  0 (i  k ) . A person diverts from
sabotage as he becomes more productive.
 If there is a new member added into the organization
(call him person n  1 ), then
n 1

l 1,l  k
sl alk  ()
n
s a
l 1,l  k
l
lk
if rn 1 is small (large): Adding a dove (hawk) into the
organization decrease (increases) the total attack
inflicted on everybody. (Also Lazear, 1989).
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3 Two-Person Case
 If t i  t j , then ei  aij  e j  a ji ; that is, i exerts more
total effort. This, however, does not mean that i has
more chance to win.
 If the two persons have the same ability in sabotage,
then the one with higher value of t is more likely to win.
Reason: He can mimic the effort level of opponent and
guarantees a greater chance to win.
 Some interesting comparative statics results:
ei / u  0, (i  1, 2) . One works harder in productive
activity when prize increases.
eij / u  0 . Negative effort level does not depend on
prize.
ei / t j
does not have definite sign: Income and
substitution effects.
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4 Three-Person Case
 In 2-person case, a person abler in productive activity
are more likely to win, when they are equally talented in
sabotage. This is no longer true in 3-person case.
 To contrast the difference. Assume that s i  1 for all i .
 The ablest person cannot have the lowest chance to win,
that is, he is at least No2 in ranking. But he probably
does not have the greatest chance to be promoted.
 Example: r1  5, r2  4, r3  1. v(0)  0, v(1)  1, v(2)  3 , and
v (3)  8 . g (0)  0, g (1)  2.5 , and g ( 2)  4 .   1 or  1 ,
each with probability 1 / 2 . Assume that the contestants
have equal chance of being promoted if they have the
same performance.
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 Tables 2, 3 and 4 show that the ablest person ends up
having the second highest chance of being promoted.
 Note that this is impossible in 2-person case even for
discrete specification.
5 Identical Contestants
 This case is of interests if contestants’ ability are
unknown.
 The contestants not only exert less productive effort
levels (than when they can only engage in productive
activities), but also that some of the outputs are
destroyed by opponents: Double inefficiency.
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 An increase in number of contestants will decrease level
of negative effort: Negative effort is directed to a specific
opponent. As they # of contestants increases, the return
of negative activity decreases.
6 Alleviating Impact of Negative Activities
 Pay equality: reducing the value of u reduces the return
of negative activity, and thus its level. However, it also
reduces the return (and level) of productive effort.
(Lazear, 1989. Industrial Politics).
 Seniority promotion system:
In our model, it adds a
term related to seniority in Wi , so that the influence of
a ij
on Wi
decreases. Example: Japanese firms.
Similarly, this also decreases value (and level) of
productive effort.
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 Group compensation: If the promotion chance (or pay)
of a member depends also on the performance of the
group he belongs to, then the level of negative activity
decreases. Example: NBA players. Problem: Free-riding
incentive.
 Early designation of successor: Announcing the winner
well in advance, so that negative effort is worthless.
Example: Throne succession in Imperial China. Problem:
1. Commitment needed (Kangxi story). 2. Hurt the
productive incentives.
 External recruiting: Since an inside contestant cannot
sabotage outsiders, the return of negative effort
decreases when there is outside recruitment. Example:
Picking
presidents
in
AT&T
from
presidents
in
subsidiaries rather than from headquarter. That means,
contrary to literature, external recruitment also has an
incentive role to pay (Chen, hopefully before Y2K).
Problem: Same old problem.
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 If it is difficult to decompose the performance of a
contestant into how much is form his own effort, and how
much is destroyed by others, then it seems difficult to
completely eliminate negative activity in an organization.
 Whether one wants to use a particular system depends
on relative benefit and cost of it.
7 Extension
 Dynamic model: The contestants’ abilities are unknown,
but can be learned from past performance. In this case
there will be double jeopardy to efficiency: Since a
person performing well earlier in career will be inferred as
having higher ability and subject to more attack later,
every contestant will hide their ability by exerting even
less productive effort than the static model.
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 In reality, people do not compete as single individuals.
They form factions (coalition). This is common especially
in politics.
 Reason for forming factions:
1. Forming factions essentially breaks the all-or-nothing
nature of promotion: Even if one loses in promotion, as
long as his alliance wins, he can still share some of the
gains from promotion. Risk sharing.
2. There is synergy in forming factions. Anyone who
refuses to join a faction has no chance.
 Question: What is the structure of coalition in promotion
tournament, and what is its consequence?
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e1
a12
a13
W21
W31
v(e1  a1 )
u1 (a1 , e1 , a*1 , e*1 )
1
1
0
0.5
-1
3
3
u 3
16
1
1
1
0.5
-3.5
8
1
u 8
4
1
0
1
3
-3.5
3
-3
1
0
0
3
-1
1
-1
0
1
0
5.5
4
1
-1
0
1
1
5.5
1.5
3
-3
0
0
1
8
1.5
1
-1
0
0
0
8
4
0
0
e2
a21
a23
W12
W32
v(e2  a2 )
u2 (a2 , e2 , a* 2 , e* 2 )
1
1
0
0.5
-1
3
9
u 3
16
1
1
1
0.5
-3.5
8
3
u 8
4
1
0
1
3
-3.5
3
1
u 3
4
1
0
0
3
-1
1
3
u 1
16
0
1
0
5.5
4
1
-1
0
1
1
5.5
1.5
3
-3
0
0
1
8
1.5
1
-1
0
0
0
8
4
0
0
17
e3
a31
a32
W13
W23
v(e3  a3 )
u 3 ( a3 , e3 , a * 3 , e* 3 )
0
1
0
1
1.5
1
1
u 1
16
0
1
1
1
0
3
1
u 3
8
0
0
1
2.5
0
1
-1
0
0
0
2.5
1.5
0
0
1
1
0
0
0.5
3
1
u 3
8
1
1
1
0
-1
8
3
u 8
8
1
0
1
1.5
-1
3
3
u 3
16
1
0
0
1.5
0.5
1
1
u 1
16
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