Group Cooperation Under Uncertainty

Min Gong

Advisors: Jonathan Baron Howard Kunreuther

Outline Introduction and Motivation Major Finding on Group Cooperation Under

Uncertainty Study 1: Group-Individual Cooperation Difference in

Deterministic and Stochastic PD Why do Groups Cooperate More than

Individuals Under Uncertainty? 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

Group and Uncertai nty I nteracti on

32%

78%

52%

22%

0%

25%

50%

75%

100%

Group I ndi vi dual

Pl ayer Type

Coop

erat

ion

Rate

Determi ni sti cPri soner' s Di l emmaStochasti c Pri soner' sDi l emma

Groups are less cooperative than individuals in a prisoner’s dilemma, but more cooperative than individuals in a stochastic version of the game.

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 Study 1: Group-Individual Cooperation Difference in

Deterministic and Stochastic PD Why do Groups Cooperate More than

Individuals Under Uncertainty? 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)

Player 2

Invest Not Invest

Player 1

Invest -45;- 45 -65;- 40

Not Invest

-40;- 65 -52;- 52

Table 1: the DPD game

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.

Player 2

Invest Not Invest

Player 1

Invest -45; -45 20% lose 145,80% lose 45;

40% lose 100,60% lose 0

NotInvest

40% lose 100,60% lose 0;

20% lose 145,80% lose 45

52% lose 100,48% lose 0;

52% lose 100,48% lose 0

Player 2

Invest Not Invest

Player 1

Invest -45;- 45 -65;- 40

Not Invest

-40;- 65 -52;- 52

Table 1: the DPD gameTable 2: the SPD game

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

Group and Uncertai nty I nteracti on

32%

78%

52%

22%

0%

25%

50%

75%

100%

Group I ndi vi dual

Pl ayer Type

Coop

erat

ion

Rate

Determi ni sti cPri soner' s Di l emmaStochasti c Pri soner' sDi l emma

Groups are less cooperative than individuals in the DPD, but more cooperative than individuals in the SPD.

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

Defection in the name of group interest

Out-group schema on intergroup competition

At least one member identifies the dominant strategy and persuades others

Identifiability Explanation

Social Support Explanation

Schema-Based Distrust

Explanation

Smart-strategy persuasion

Explanation

Discontinuity Effect

Greater greed

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 Study 1: Group-Individual Cooperation Difference in

Deterministic and Stochastic PD Why do Groups Cooperate More than

Individuals Under Uncertainty? 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

0%

10%

20%

30%

40%

50%

60%

70%

1 2 3 4 5 6 7 8 9 10Round

Inve

stme

nt D

ecis

ion

ComputerI ndi vi dual sGroups

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 Study 1: Group-Individual Cooperation Difference in

Deterministic and Stochastic PD Why do Groups Cooperate More than

Individuals Under Uncertainty? 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 InvestOne or both players withdrew both

received a certain outcomeNo one withdrew SPD game in Table 2

Table 9: Possible outcomes in the 3-option SPD game

Player 2

Withdraw Invest Not Invest

Player 1

Withdraw -50,-50 -50,-50 -50,-50

Invest -50,-50 -45; -4520% lose 145,80% lose 45;40% lose 100,60% lose 0

Not Invest -50,-5040% lose 100,60% lose 0;20% lose 145,80% lose 45

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) Not Invest (Distrust)

Risk Preference of Player 1

Risk Seeking

Preference: Paying 50 <Paying 45 < 40% losing 100

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

22%

59%

19%

14%

34%

52%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Groups I ndi vi dual s

Not I nvest (Ri skSeeki ng)Wi thdraw (Di strust)

I nvest (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 Study 1: Group-Individual Cooperation Difference in

Deterministic and Stochastic PD Why do Groups Cooperate More than

Individuals Under Uncertainty? 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.

Table 13: Reasons for Not Suggesting Defection

Niceness Norm 4%

Guilt Aversion 47%

Blame Avoidance 55%

Persuasion Concern 29%

Does Not Care Enough 23%

Guilt Aversion, Blame Avoidance, and Social Norm

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