Explicit versus Implicit Contracts
for Dividing the Benefits of
Cooperation
Marco Casari and Timothy Cason
Purdue University
A Partnership Game
• As in most experimental labor markets, in this
game two individuals interact and must
cooperate to generate a divisible joint surplus
• The standard environment (e.g., Fehr & coauthors) is sequential, with payments sometimes
before and sometimes after effort
• By contrast, in our game efforts are simultaneous, and must be incurred by both parties
• As in earlier research, however, the relationship
is still hierarchical, with one “strong” agent
responsible for dividing the surplus
– Example: Senior partners at a law firm
Parameters and Treatments
Weak Agent
1 (high effort) 2 (low effort)
Strong
Agent
1 (high effort)
A, B
(A+B=60)
0, 10
2 (low effort)
10, 0
10, 10
• Baseline: Strong agent selects A & B after effort choices
• Bonus: Like Baseline, except strong agent makes an
unenforceable “promise” of A & B pre-effort (implicit
contract)
• Explicit Commitment: Strong agent announces a
committed level of A & B pre-effort (explicit contract)
• 144 subjects (48 per treatment)
Design & Predictions Summary
• 3 preliminary measurements without feedback
– lottery choices, ultimatum & trust games (strategy meth)
• 10 rounds of partnership game, with 1 round paid
– perfect strangers re-matching
• Baseline and Bonus:
– low effort equilibrium, but high effort can occur in
equilibrium for some distributions of social pref. types
• Explicit Commitment:
– multiple equilibria, including high effort equilibrium
(commitment can turn effort choice into a stag hunt)
Results:
Pooled Effort Choices Summary
Panel A: Baseline
Strong
Agent
Panel B: Bonus
Weak Agent
High
Effort
Low
Effort
Totals
High
Effort
17.9%
36.7%
54.6%
Low
Effort
14.6%
30.8%
Totals
32.5%
67.5%
Weak Agent
High
Effort
Low
Effort
Totals
High
Effort
35.8%
36.7%
72.5%
45.4%
Low
Effort
10.4%
17.1%
27.5%
100.0%
N=480
Totals
46.3%
53.8%
100.0%
N=480
Strong
Agent
Panel C: Explicit Commitment
Strong
Agent
Weak Agent
High
Effort
Low
Effort
Totals
High
Effort
59.6%
28.3%
87.9%
Low
Effort
5.0%
7.1%
12.1%
Totals
64.6%
35.4%
100.0%
N=480
Time Series of Mutual Cooperation
100%
Baseline
90%
Bonus
80%
Explicit Commitment
70%
60%
50%
40%
30%
20%
10%
0%
1
2
3
4
5
6
7
8
9
10
perio
Earnings, Average Bonuses, and
Efficiency
Baseline
Bonus
Explicit Commitment
All
Periods
Last 3
Periods
All
Periods
Last 3
Periods
All
Periods
Last 3
Periods
Overall frequency of high
effort choices
43.5%
25.0%
59.4%
47.9%
76.3%
81.3%
Frequency of mutual high
effort outcome
17.9%
5.6%
35.8%
25.0%
59.6%
68.1%
Actual bonus paid by
strong agents
choosing high effort
10.8
Ave. earnings strong agent
13.6
9.4
19.8
15.8
21.8
24.5
Ave. earnings weak agent
8.4
9.0
9.9
9.7
18.7
20.1
Share of earnings of
strong agent
61.8%
51.1%
66.7%
62.0%
53.8%
54.9%
Efficiency (possible range
from 16.7% to 100%)
36.7%
30.7%
49.5%
42.5%
67.5%
74.3%
11.9
21.4
Promised and Actual Bonus
60
50
Actual bonus
40
30
20
10
0
0
10
20
30
-10
Promised bonus
40
50
60
Implicit and Explicit Bonus Offers to
Coordinate Efforts
100%
80%
high payoff outcome (1,1)
60%
low payoff outcome (2,2)
40%
Explicit Commitment
20%
0%
10 or below
above 10, below
30
30
Am ount prom ised
Bonus Treatment
above 30, below
60
60
100%
80%
high payoff outcome (1,1)
60%
low payoff outcome (2,2)
40%
20%
0%
10 or below
above 10, below
30
30
Am ount prom ised
above 30, below
60
60
Measurements of Risk Aversion
and Social Preferences
• A majority (70%) of our subjects appear risk
averse on the lottery choices
– Most of the others appear risk neutral
• Average ultimatum offer was 28.2 francs (out of
60), average 27.0 francs demanded
• 63% of trustors trusted, but 60% of trustees kept
all 60 francs and only 26% provided a positive
return to the trustor
• “Fair-minded” strong agents who offered at least
30 francs in the ultimatum game were more
trustworthy on average
• But “Fair-minded” weak agents who demand at
least 25 of 60 francs were not less likely to trust
Measured Preferences Help Partnership
Behavior (stable types across games)
• Strong agents who are more risk averse tend to
exert lower effort
• In the Bonus treatment, risk-seeking strong
agents offer higher bonuses but pay lower actual
bonuses
• Trusting weak agents were more likely to exert
high effort in the Baseline and Bonus treatments
• Untrustworthy strong agents were less likely to
exert high effort in the Baseline treatment but
more likely to exert high effort in the Explicit
Commitment treatment
The Last Slide
• While our results are consistent with some
agents having social preferences, explicit
contracts—which do not rely on social
preferences to achieve efficiency—clearly
perform better than implicit contracts in this
partnership setting
• Similar behavior is exhibited by other primates
– Non-kin capuchin monkeys choose low effort when
dominant member of pair can’t commit to sharing
• Perhaps implicit contracts in this environment
require repeated interaction?
• Would implicit contracting work better if explicit
contracting required costly verification and
strong agents had a choice between implicit and
explicit contracting?
Implicit Contracts and Social
Preferences
• Recent research has documented superior
performance of implicit (“bonus”) contracts in
some laboratory labor markets
– Fehr, Klein & Schmidt (2007) show that principals
prefer to offer an unenforceable bonus over an explicit
incentive contract that relies on costly verification of
agent effort
– An efficiency wage “trust” contract does worse,
however than an explicit contract
• Social preferences, such as simple inequity
aversion, are consistent with these results
• How general is this “failure” of contract theory?
Equilibrium Predictions (Self-Regarding
and Inequity-Averse Preferences)
• Baseline and Bonus treatments:
– Unique equilibrium of low effort for standard, selfinterested preferences
– For certain type distributions of social preferences
(e.g., inequity aversion), high effort outcome can
occur in equilibrium
– Promised bonus could provide a type signal
• Explicit Commitment treatment:
– Multiple equilibria exist, including both high and low
effort equilibria, for self-interested and other-regarding
preferences
– Commitment can turn effort choice into a stag hunt
game
Patterns Expected by Different
Types of Subjects
• In Baseline and Bonus treatments, fair-minded
strong agents may pay positive bonuses
• Strong agents have more to gain from
cooperation than weak agents, implying higher
average effort from strong agents
• Self-regarding strong agents have more to gain
from cooperation than fair-minded strong
agents, implying higher effort from them
• Fair-minded weak agents fear the asymmetric
(0, 60) payoffs more than self-regarding weak
agents, so they should exert less effort and
exhibit less trust