Management Compensation System:

-- Adding Tournament to Tournament: The Interactive Effect of Individual and Team IncentivesYu TianKenneth G. Dixon School of AccountingUniversity of Central Florida

IMA Carolinas Winter Conference

February 17, 2012

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.

2

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

Background: Incentive Systems

Individual compensation (within-team)

Tournament (No)

Tournament

(Yes)

Team

Com

pens

atio

n (b

etw

een -

team

)

Tournament

(No)

Low Effort

Uncooperative& Collusion

Tournament

(Yes)

Free riding

???

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?

Figure 1

Individual compensation (within-team)

Tournament (No)

Tournament

(Yes)

Team

Com

pens

atio

n (b

etw

een -

team

)

Tournament

(No)

NONE

WITHIN

Tournament

(Yes)

BETWEEN

BOTH

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 .ijijindividual cxxfOutput

i

n

j ij

n

j ijteam cxcxxfOutput ii 11

ijx is effort level of member j in team i.

The Model – Group Contest

(1)

otherwise 2/1

0,max if ......

2121

xxxx

x

xpi

iji

0ijx

.1

in

j iji xx

: probability that team i wins the contest and receives both group and individual rewards

: the effort contribution of member j in team i

: total effort in team i

ip

Step 1: Inter-team contest success function:

The Model – Individual Share

(2)

otherwise 1

0......max if 1

1

i

ijii

ij

ij

n

xnx

x

q

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”

ijq

Step 2: Distribution of individual reward ( ) within a teamIV

The Nitzan’s Model - Payoff

Total reward ( )

= Group reward ( ) + Individual reward ( )

ijIijiGi

iijij xVqpVn

px 1

......

ii n

j ij

n

j Iijii

Giiii xVqpn

Vpnx11

)1

(......

V

GV IV

The payoff function of individual j in group i is:

Expected group reward

Expected individual reward

Cost of individual

effort

Expected team payoff

Expected individual

payoff

Model Prediction (Baseline)(maximizing joint payoff: joint NE)

Model Prediction (Baseline)(maximizing individual payoff: symmetric NE)

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

SIT Prediction (Hypotheses)

Within: NO Within: YES

Effort Between: NO

Between: YES

Between: between team tournament Within: within team tournament

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

ProcedureRandomly assign participants into a team.

Assign to one combination of incentive systems

Communicate & make decisions (10 periods)

Participants are mixed up and

randomly assigned to new teams.

Decide a team name.

Part I

Notify individual payoff after each period

Forced manipulation check (quiz)

Instructions

Part II

Calculate payoff and pay participants.

Z-tree: Welcome

Z-tree: Chat

Z-tree: Decision

Z-tree: Feedback

Average Effort LevelsTable 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

Effort Levels: Comparisons

22

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 Individual Incentive (within-team tournament)

with vs. without 72 11.24 2.48 0.017 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 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.

H1

H2

H3

Actual Effort (Figure)

Actual Effort (Figure)

Effort – TSCS Analysis

25

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 Individual (within-team) Tournament 1 11.24 < 0.0001 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 BOTH 1 -6.87 0.0045 Period 1 -0.62 0.0155 Number of observations: 2880. Dependent variable: Individual effort in each period.

H1H2

H3

Actual Effort (Within-subject Comparison)

26

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.

Free-riding (zero effort)

Free-riding (< 1/3 endowment)

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.

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.

Messages: categoriesTable 6 Analysis of Communication

Panel A: Categories for coding messages

Category Description Relative frequency of coding "1"

NONE WITHIN BETWEEN BOTH

Cooperation

C1

Ask for the opinions of other team members (may or may not specifically refer to an effort level) 0.188 0.333 0.379 0.396

C2

Proposal to choose high efforts within team or state own choice of high efforts 0.129 0.167 0.654 0.692

C3 Agree on team members’ proposals (high effort) 0.058 0.075 0.554 0.571

C4 Give reasons why need to choose high efforts 0.025 0.008 0.104 0.146

Overall cooperation 0.263 0.413 0.725 0.750

Collusion

C5

Proposal to choose low efforts within team or state own choice of low efforts

0.529

0.558

0.221

0.129

C6 Agree on team members’ proposals (low effort) 0.371 0.392 0.146 0.063

C7 Proposal to take turns in winning the tournament 0 0.142 0 0.021

C8 Give reasons why need to choose 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 period are taken as one observation unit for coding, resulting in 960 observations in total. Within each observation, each category is coded as “one” if present and “zero” otherwise.

Messages: p-valuesTable 4.6 Analysis of Communication (continued) Panel B: Cooperation and collusion

Category Description Pairwise comparisons between condition coefficients from logistic regressions (p-values)

NO

NE

vs.

BO

TH

WIT

HIN

vs.

BO

TH

BE

TW

EE

N

vs.

BO

TH

NO

NE

vs.

BE

TW

EE

N

WIT

HIN

vs.

BE

TW

EE

N

NO

NE

vs.

WIT

HIN

Cooperation C1

Ask for the opinions of other team members

***

0.131

0.690

*** 0.266

**

C2

Proposal to choose (or state own choice) high efforts within team

*** *** 0.371

*** ***

0.242

C3

Agree on team members’ proposals (high effort)

*** *** 0.637

*** ***

0.463

C4

Give reasons why need to choose high efforts

*** *** 0.157

**

**

0.173

Overall cooperation

***

*** 0.519 *** *** **

Collusion

C5

Proposal to choose (or state own choice of) low efforts within team

***

***

*

***

***

0.517

C6

Agree on team members’ proposals (low effort)

***

***

*

***

***

0.636

C7

Proposal to take turns in winning the tournament

N/A

***

N/A

N/A

N/A

N/A

C8

Give reasons why need to choose low efforts

***

***

0.504

***

***

0.067

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

Overall cooperation

Overall collusion

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

Thank you !