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Session 2 2012 ima presentation compensation system
1. Management Compensation System:
-- Adding Tournament to Tournament:
The Interactive Effect of Individual
and Team Incentives
Yu Tian
Kenneth G. Dixon School of Accounting
University of Central Florida
IMA Carolinas Winter Conference
February 17, 2012
2. Background: Incentive Systems
Incentive systems design: an important aspect
of a management control system.
Organization can incentivize effort based on:
Individual performance
Team performance
A combination of both.
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3. Background: Incentive Systems
Individual incentive systems
Lack of cooperation
Team incentive systems
Need for cooperation Increasing use of teams
Encourage cooperation
Problem: free-riding
Tournament (RPE) used to mitigate free-
riding
Increasing use in corporate world
Problem: uncooperative & collusion
5. Research Question
Can both free-riding and collusion problems
be simultaneously mitigated, when a
combination of individual and team incentive
systems are used?
Will we get the best or the worst of both worlds?
6. Figure 1
Individual compensation (within-team)
Tournament Tournament
(No) (Yes )
Tournament
(No) NONE WITHIN
Team Compensation
(between-team)
Tournament
(Yes ) BETWEEN BOTH
7. The Model - Extension
Extend Nitzan’s (1991) nested contest model
Add a group (team) reward component
More generalizable in practice
Encourage cooperation
Introduce output functions
Output individual f xij cxij .
ni ni
Outputteam j 1
f xij j 1
cxij cxi
x ij is effort level of member j in team i.
8. The Model – Group Contest
Step 1: Inter-team contest success function:
xi
if max x1 , x2 0
pi ...xij ... x1 x2 (1)
1/ 2 otherwise
pi : probability that team i wins the contest and receives both group and
individual rewards
xij 0 : the effort contribution of member j in team i
ni
xi j 1
xij . : total effort in team i
9. The Model – Individual Share
Step 2: Distribution of individual reward ( VI ) within a team
xij 1
1 if max ...xij ... 0
xi ni
qij (2)
1
otherwise
ni
q ij is a share of individual reward that member j in team i receives.
α = 1: equal share within a team
α = 0: distribution of individual reward based on “merit”
10. The Nitzan’s Model - Payoff
Total reward ( V )
= Group reward (VG ) + Individual reward ( VI )
The payoff function of individual j in group i is:
Expected Expected Expected Cost of
individual group individual individual
payoff reward reward effort
1
ij ... xij ... pi VG pi qijVI xij
ni
1 ni ni
i ... xi ... ni ( piVG ) j 1
pi qij VI j 1
xij
ni
Expected
team payoff
13. Social Identity Theory (SIT)
A theory of the role of self-conception in group
members, group process, and intergroup
relations.
Positive distinctiveness (PD) from other teams
prevails in intergroup relations.
Promote PD to enhance self-esteem.
Optimal distinctiveness
14. SIT Prediction (Hypotheses)
Effort
Between: NO
Between: YES
Within: NO Within: YES
Between: between team tournament
Within: within team tournament
15. Design
Participants: 144 senior and graduate business
students
Multi-period 2 X 2 X 2 design
Between-subject factors: team & individual incentive
systems
Within-subject factor: 2 different incentive systems
P(4,2) = 12 ordered combinations (e.g. NONE&WITHIN,
NONE&BETWEEN, NONE&BOTH…)
Each individual participates in 2 conditions
12 team observations (6 individual decisions for 10
periods in each team observation)
Payoff: $5 participation fee + decision income
16. Procedure
Randomly assign participants into a team.
Instructions
Decide a team name.
Assign to one combination of incentive systems
Participants are
Part I mixed up and
Forced manipulation check (quiz) randomly assigned
to new teams.
Communicate & make decisions (10 periods)
Part II
Notify individual payoff after each period
Calculate payoff and pay participants.
21. Average Effort Levels
Table 1 Average Effort
Equilibrium Equilibrium Standard
effort effort Actual deviation Actual
Condition (maximize (maximize average within average
ind. payoff) joint payoff) effort condition profit
NONE (N = 36) *
(equal share between and
within teams) 0 0 9.47 7.75 110.53
WITHIN (N = 36)
(equal share between teams,
tournament within team) 20 0 25.07 7.84 94.93
BETWEEN (N = 36)
(tournament between teams,
equal share within team) 10 30 40.28 10.22 79.72
BOTH (N = 36)
(tournament between and
within teams) 30 30 47.15 4.00 72.35
22. Effort Levels: Comparisons
Table 2 Main Effect and Pairwise Comparisons (Effort)
Panel A: Main effect
Mean
Conditions N Difference t Value p-value
Team Incentive
(between-team tournament)
with vs. without 72 26.45 9.36 <0.0001 H1
Individual Incentive
(within-team tournament)
with vs. without 72 11.24 2.48 0.017 H2
Panel B: Pairwise comparisons
Mean
Conditions N Difference t Value p-value
BOTH vs. NONE 24 37.68 14.96 <0.0001
BOTH vs. WITHIN 24 22.08 8.69 <0.0001
H3
BOTH vs. BETWEEN 24 6.87 2.17 0.041
WITHIN vs. NONE 24 15.61 4.90 <0.0001
BETWEEN vs. WITHIN 24 15.21 4.09 0.0005
BETWEEN vs. NONE 24 30.82 8.32 <0.0001
The average effort of all six subjects in paired teams is considered as one independent unit of
observation.
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25. Effort – TSCS Analysis
Table 3 Time Series Cross-Sectional Regression Results
Panel A: Main Effects
Independent variables DF Coefficient p-value
Intercept (NONE) 1 15.07 < 0.0001
Team (between-team) Tournament 1 26.45 < 0.0001 H1
Individual (within-team) Tournament 1 11.24 < 0.0001 H2
Period 1 -0.62 0.0155
Panel B: Hypothesis 3 (each condition compared with BOTH condition)
Independent variables DF Coefficient p-value
Intercept (BOTH) 1 50.57 < 0.0001
NONE 1 -37.68 < 0.0001
WITHIN 1 -22.08 < 0.0001 H3
BOTH 1 -6.87 0.0045
Period 1 -0.62 0.0155
Number of observations: 2880.
Dependent variable: Individual effort in each period.
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26. Actual Effort (Within-subject Comparison)
Table 4 Within Subject Comparisons (Effort)
Mean
Differences (within subject) N Difference t Value p-value
BOTH - NONE 24 33.60 14.52 <0.0001
BOTH - WITHIN 24 25.85 7.13 <0.0001
BOTH - BETWEEN 24 13.54 5.76 <0.0001
WITHIN - NONE 24 20.94 5.60 <0.0001
BETWEEN - WITHIN 24 12.76 2.33 0.0290
BETWEEN - NONE 24 36.23 8.88 <0.0001
The average effort of all 10 periods for a subject is considered as one independent unit of
observation.
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29. Messages: descriptive
7,671 messages recorded.
Each experimental session:
NONE: 289
WITHIN: 288
BETWEEN: 350
BOTH: 353
80 messages (on average) within a single
team in each part of each experimental
session.
30. Messages: coding
For each team and each period,
“1” – if a statement or argument showed up in a
given period and chat
“0” – otherwise.
960 observations in total.
31. Messages: categories
Table 6 Analysis of Communication
Panel A: Categories for coding messages
Category Description Relative frequency of coding "1"
NONE WITHIN BETWEEN BOTH
Cooperation
Ask for the opinions of other team
C1 members (may or may not
specifically refer to an effortlevel) 0.188 0.333 0.379 0.396
Proposal to choose high efforts
C2 within team
or state own choice of high efforts 0.129 0.167 0.654 0.692
Agree on team members’ proposals
C3 (high effort) 0.058 0.075 0.554 0.571
Give reasons why need to choose
C4 high efforts 0.025 0.008 0.104 0.146
Overall cooperation 0.263 0.413 0.725 0.750
Collusion
Proposal to choose low efforts
C5 within team 0.529 0.558 0.221 0.129
or state own choice of low efforts
Agree on team members’ proposals
C6 (low effort) 0.371 0.392 0.146 0.063
Proposal to take turns in winning
C7 the tournament 0 0.142 0 0.021
Give reasons why need to choose
C8 low efforts 0.233 0.167 0.050 0.038
Overall collusion 0.567 0.600 0.221 0.146
All messages within each team in each periodre taken as one observationunit for coding, resulting in 96 observations in total.
a 0
Within each observation, each category is coded as “one” if present and “zero” otherwise.
32. Messages: p-values
Table 4.6 Analysis of Communication (continued)
Panel B: Cooperation and collusion
Pairwise comparisons between condition coefficients
Category Description from logistic regressions (p-values)
BETWEEN
BETWEEN
BETWEEN
WITHIN
WITHIN
WITHIN
NONE
NONE
NONE
BOTH
BOTH
BOTH
vs.
vs.
vs.
vs.
vs.
vs.
Cooperation
C1 Ask for the opinions of *** 0.131 0.690 *** 0.266 **
other team members
Proposal to choose (or *** *** ***
C2 state own choice) high 0.371 *** 0.242
efforts within team
Agree on team *** *** ***
C3 members’ proposals 0.637 *** 0.463
(high effort)
C4 Give reasons why need *** *** 0.157 ** ** 0.173
to choose high efforts
Overall cooperation *** *** 0.519 *** *** **
Collusion
Proposal to choose (or
C5 state own choice of) *** *** * *** *** 0.517
low efforts within team
Agree on team
C6 members’ proposals *** *** * *** *** 0.636
(low effort)
Proposal to take turns
C7 in winning the N/A *** N/A N/A N/A N/A
tournament
C8 Give reasons why need *** *** 0.504 *** *** 0.067
to choose low efforts
Overall collusion *** *** * *** *** 0.456
The p-values reported in this table are based on Wald Chi-Square statistics.
***: p-value < 0.0001 **: p-value < 0.001 *: p-value < 0.05
35. Implications
MA incentive system design: one of few studies that
examine interactive effect of individual & team
incentive systems.
Answer the call to examine incentive system combinations
(Bonner & Sprinkle 2002)
Practical implication
Management control system: mitigate moral hazard
problems.
Multi-agent setting
Extend original contest model
More generalizable in practice