Group Cooperation
Under Uncertainty
Min Gong
Advisors: Jonathan Baron
Howard Kunreuther
Outline


Introduction and Motivation
Major Finding on Group Cooperation Under
Uncertainty


Why do Groups Cooperate More than
Individuals Under Uncertainty?




Study 1: Group-Individual Cooperation Difference in
Deterministic and Stochastic PD
Study 2: Group-Individual Risk Preference Difference
Study 3: 3-Option Stochastic PD
Study 4: A Survey Study
Generality Discussion and Future Research


When does uncertainty reduce inter-group competition
and encourage inter-group cooperation?
Future research on group factors and game factors
Key Finding
Groups are less cooperative than individuals in a
prisoner’s dilemma, but more cooperative than
individuals in a stochastic version of the game.
Group and Uncertainty Interaction
Deterministic
Prisoner's Dilemma
Stochastic Prisoner's
Dilemma
Cooperation Rate
100%
78%
75%
50%
25%
52%
32%
22%
0%
Group
Individual
Player Type
Motivation – Why Study Group
Cooperation Under Uncertainty

In many real-life situations, the decision makers
are nations, firms, or families

Groups behave differently from individuals with
regard to
 cooperation
and competition (Insko et al. 1987;
Bornstein et al., 2002 ; Wildschut 2003)
 uncertainty (Marquis 1962; Sniezek 1992)
Outline


Introduction and Motivation
Major Finding on Group Cooperation Under
Uncertainty


Why do Groups Cooperate More than
Individuals Under Uncertainty?




Study 1: Group-Individual Cooperation Difference in
Deterministic and Stochastic PD
Study 2: Group-Individual Risk Preference Difference
Study 3: 3-Option Stochastic PD
Study 4: A Survey Study
Generality Discussion and Future Research


When does uncertainty reduce inter-group competition
and encourage inter-group cooperation?
Future research on group factors and game factor
Experiment Design--Subjects &
Processes

2 Types of players
 Individual
OR group player
 Group Player





3 members in each group
A group makes one collective decision
All members share the outcome equally
Unanimous decisions or majority rule
Subjects:
 202
subjects
 Between-subject 2X2 design (2 games X 2
player types)
Experiment Design
– the Deterministic Prisoner’s Dilemma



Negative numbers represent costs or losses
The dominant strategy is Not Invest (always better
off by defecting no matter what the other party does)
Nash Equilibrium is (NI, NI)
Table 1: the DPD game
Player 2
Player
1
Invest
Not
Invest
Invest
-45;- 45
-65;- 40
Not
Invest
-40;- 65
-52;- 52
Experiment Design
– the Stochastic Prisoner’s Dilemma




In the SPD, each player decides whether or not to invest at a
cost of 45 to reduce his or her own risk of losing 100.
If one player invests, both players’ risks are reduced.
Joint cooperation eliminates uncertainty.
Substituting the outcomes with the expected values the DPD.
Table 2: the SPD game
Table 1: the DPD game
Player 2
Invest
Player
1
Invest
Not Invest
-45; -45
20% lose 145,
80% lose 45;
40% lose 100,
60% lose 0
Not
Invest
40% lose 100,
60% lose 0;
52% lose 100,
48% lose 0;
20% lose 145,
80% lose 45
52% lose 100,
48% lose 0
Player 2
Player
1
Invest
Not
Invest
Invest
-45;- 45
-65;- 40
Not
Invest
-40;- 65
-52;- 52
A Example of the SPD game

SPD is a special case of the Interdependent
Security Game (Kunreuther and Heal, 2003)

A Scenario : Baggage transfer security Pre-911
 An airline has to determine whether it wants to
invest in baggage security
 Investing reduces its risk to be attacked by
terrorists
 But even if it invests, it may face a security risk
from a dangerous bag loaded onto its plane by
another airline, as in the Pan Am 103 crash.
Key Finding
Groups are less cooperative than individuals in the
DPD, but more cooperative than individuals in the
SPD.
Group and Uncertainty Interaction
Deterministic
Prisoner's Dilemma
Stochastic Prisoner's
Dilemma
Cooperation Rate
100%
78%
75%
50%
25%
52%
32%
22%
0%
Group
Individual
Player Type
What is Known and What is New
Replicated the “discontinuity effect”:
groups cooperate less than individuals in
DPD (Insko, et al 1987; Wildschut et al 2003
for a review)
 Discovered a “reversed discontinuity
effect”: groups cooperate more than
individuals in SPD.
 Survey data and recorded discussion
provide explanations for both the
discontinuity effect in DPD and the
reversed discontinuity effect in SPD.

Why Groups Cooperate Less than
Individuals (Discontinuity Effect) in DPD
Anonymity in a group
shields social sanction
from the other group
Identifiability
Explanation
Greater greed
Defection in the name of
group interest
Out-group schema on
intergroup competition
At least one member
identifies the dominant
strategy and persuades
others
Social Support
Explanation
Schema-Based
Distrust
Explanation
Smart-strategy
persuasion
Explanation
Discontinuity
Effect
Greater fear
Why Discontinuity Effect Disappears in SPD




Identifiability is the same in both games.
Social support for defection is reduced in the SPD than
in DPD, because some members may consider
defection too risky and not in the group interest.
Schema-based distrust is reduced in the SPD than in
DPD, because group members observe reduced
tendency for their own group to defect and infer that the
other group is less likely to defect as well.
Smart-Strategy Persuasion power to defect is reduced
in the SPD than in DPD, because with uncertainty it is
harder to figure out that defect is the smart strategy and
convince other members.
Why Groups Cooperate More
than Individuals in SPD
- Safety Oriented to Avoid Guilt and Blame

People take less risk when their decisions affect

others (Charness and Jackson 2008)
In DPD
 Defection
is always better off
 No ex post guilt or blame

In SPD
 Defection
has a higher expected payoff, but also a
higher probability of suffering a loss.
 If a large loss follows defection ex post guilt and ex
post blame for the one who suggested defection
 Group members favor safety-oriented strategy
(cooperation) to avoid ex post guilt and blame
Reversed discontinuity effect
Why Groups Cooperate More than Individuals in SPD
-Social Pressure to Conform to Certain Norms



Three norms are most relevant in PD games: Being
pro-group, Being smart, and Being nice
Similar to the group morality and individual morality
argument (Cohen 2006; Pinter 2007)
In DPD
 Both
pro-group (group morality) and smart norm
clearly indicate defection
 Niceness (individual morality) is clouded

In SPD
 Unclear
what strategy is pro-group and smart
 Being nice is socially desirable and more salient than
in DPD.
Major Findings of Study 1
Replicated the discontinuity effect in the DPD
game.
 Four explanations were offered to explain the
discontinuity effect.
 Found a reversed discontinuity effect when
uncertainty existed: groups were more
cooperative than individuals in the SPD game.
 Two explanations are proposed to explain the
reversed discontinuity effect: safety oriented
behavior and social pressure to be nice.

Outline


Introduction and Motivation
Major Finding on Group Cooperation Under
Uncertainty


Why do Groups Cooperate More than
Individuals Under Uncertainty?




Study 1: Group-Individual Cooperation Difference in
Deterministic and Stochastic PD
Study 2: Group-Individual Risk Preference Difference
Study 3: 3-Option Stochastic PD
Study 4: A Survey Study
Generality Discussion and Future Research


When does uncertainty reduce inter-group competition
and encourage inter-group cooperation?
Future research on group factors and game factor
Experiment Design

2 Types of players
 36
Individuals and 50 groups
 Between-subject design

Play against a computer player in a SPD:
 The
same payoff table as in Table 2
 The probability of computer investing is known
Table 8: Invest Probabilities of the Computer Player in Study 2
Round Number
1
2
3
4
5
6
7
8
9
10
Probability of
Investing
60
%
55
%
54
%
53
%
50
%
49
%
47
%
42
%
31
%
17
%
Rationale and Hypothesis

Rationale




This design removed any interactive motivations for cooperation
The only benefit from one player’s investment was to reduce her
own risk of suffering a loss
The investment difference between groups and individuals in
Study 2 is determined by their difference in risk preference.
Hypothesis


Guilt aversion and blame avoidance indicate more risk aversion
and/or less risk seeking
H1: Groups are more risk concerned and invest more often than
individuals in Study 2
Results at Study 2
70%
Investment Decision
60%
50%
Computer
Individuals
Groups
40%
30%
20%
10%
0%
1
2
3
4
5
6
Round
7
8
9
10
Major Finding and Limitations



Supporting H1, groups invested more frequently
than individuals in Study 2
Cannot distinguish between group risk aversion
and individual risk seeking
Group-individuals difference is smaller than in
Study 1
 Other reasons besides risk preference difference
 Groups who had similar risk preference to individuals
might invest more frequently because they had higher
cooperation expectation than individuals
Outline


Introduction and Motivation
Major Finding on Group Cooperation Under
Uncertainty


Why do Groups Cooperate More than
Individuals Under Uncertainty?




Study 1: Group-Individual Cooperation Difference in
Deterministic and Stochastic PD
Study 2: Group-Individual Risk Preference Difference
Study 3: 3-Option Stochastic PD
Study 4: A Survey Study
Generality Discussion and Future Research


When does uncertainty reduce inter-group competition
and encourage inter-group cooperation?
Future research on group factors and game factor
Study 3: 3-Option Stochastic
Prisoner’s Dilemma
Subjects: 40 individual and 38 Groups
 Between-subject design
 Players had three options: Withdraw, or
Invest, or Not Invest

or both players withdrew  both
received a certain outcome
 No one withdrew  SPD game in Table 2
 One
Table 9: Possible outcomes in the 3-option SPD game
Player 2
Player
1
Withdraw
Invest
Not Invest
Withdraw
-50,-50
-50,-50
-50,-50
Invest
-50,-50
-45; -45
Not Invest
-50,-50
40% lose 100,60% lose 0;
20% lose 145,80% lose 45
20% lose 145,80% lose 45;
40% lose 100,60% lose 0
52% lose 100,48% lose 0;
52% lose 100,48% lose 0
Table 11: Player’s Decision in the 3-option SPD game
Player 1’s Expectation of Player 2
Invest (Trust)
Risk
Seeking
Risk Preference
of Player 1
Preference: Paying 50
<Paying 45 < 40%
losing 100
Not Invest (Distrust)
Preference: Paying 50 < 20%
losing 100, plus paying 45 <
52% losing 100
Behavior: Not Invest
Risk
Averse or
Risk
Neutral
Preference: 40% losing
100 < paying 50<
paying 45
Preference: 52% losing 100 <
20% losing 100, plus paying 45
< paying 50
Behavior: Invest
Behavior: Withdraw
Table 12: Implications of Three Possible Decisions
Decisions
Risk Preference
Trust
Withdraw
Risk averse or neutral
Distrust
Invest
Risk averse or neutral
Trust
Not Invest
Risk seeking
Irrelevant
Hypotheses in Study 3
H2 (Individual Risk Seeking Hypothesis):
Individuals choose Not Invest (Risk
Seeking) more frequently than Groups do;
 H3 (Group Trust Hypothesis): For those
players who are risk averse or neutral,
groups choose Invest (Trust) more
frequently than individuals. Individuals are
more likely to Withdraw (Distrust).

Figure 5: Mean Proportions of the Three Options
100%
90%
19%
80%
52%
Not Invest (Risk
Seeking)
Withdraw (Distrust)
70%
60%
50%
59%
40%
34%
30%
20%
10%
0%
22%
Groups
14%
Individuals
Invest (Trust)
Major Findings and Limitations


H2 is confirmed: groups are less risk seeking
than individuals
H3 is rejected.
 No
evidence on groups being more trusting.
 Uncertainty did reduce the usual inter-group distrust.

Questions remain to be answered:
 Are
guilt aversion and blame avoidance underlying
group-individual risk preference difference?
 Role of social norms?
Outline


Introduction and Motivation
Major Finding on Group Cooperation Under
Uncertainty


Why do Groups Cooperate More than
Individuals Under Uncertainty?




Study 1: Group-Individual Cooperation Difference in
Deterministic and Stochastic PD
Study 2: Group-Individual Risk Preference Difference
Study 3: 3-Option Stochastic PD
Study 4: A Survey Study
Generality Discussion and Future Research


When does uncertainty reduce inter-group competition
and encourage inter-group cooperation?
Future research on group factors and game factor
Study 4: A Survey Study

Three conditions
 Individual
Survey (IS) with 32 participants;
 Group Private Survey (GPS) with 72 participants (24
groups);
 and Group Shared Survey (GSS) with 78 participants
(26 groups).


Between-subject Design
Each person finished a survey after the quiz and
before playing the SPD game
Group Identity, Inter-group
Anticipation, and Group Trust
No evidence that group membership or
anticipation of interacting with another
group had an effect on players’ choice;
 Partial evidence that groups might be
more trusting than individuals in the SPD
game, at least at the beginning of the
game.

Guilt Aversion, Blame Avoidance, and
Social Norm
Table 13: Reasons for Not Suggesting Defection
Niceness Norm
4%
Guilt Aversion
47%
Blame Avoidance
55%
Persuasion Concern
29%
Does Not Care Enough
23%
Summary: Why Groups Cooperated More
than Individuals under Uncertainty



Guilt aversion and blame avoidance drove group
members to be more cautious and less risk
seeking than individuals
Mixed evidence on whether groups had higher
cooperation expectation level on the other group
than individuals did on the other individual
No evidence of social pressure pushing groups
to be nicer and more cooperative than
individuals, at least not before the group
discussion
Discussion and Future Research


When does uncertainty encourage inter-group
cooperation and when does it reduce inter-group
competition only?
Generality Studies
 Group
factors: decision rules, leadership,
heterogeneous groups
 Game factors: gain/loss domain, length of the game,
communication between players, nature of uncertainty,
coordination game, multi-player games