Experimental Design
Predictions: There are two stages of experimental study. The aim of the first stage is to
capture effect of cultural factors such as grid and group on individual as well as group
performance. In a first stage of experiments we test following hypothesis: H1: high
group individuals contribute more than the low-group individuals; H2: high-grid
individuals will react more radically to initial contribution by others, rewarding high
contributions and punishing low contributions; H3: high-group individuals will anticipate
higher cooperation among others than low-group individuals will; H4: high-grid
individuals will anticipate greater adherence among others to strong reciprocity among
others than low- group individuals will; H5: high-grid individual will punish more than
the low-grid individuals; H6: individuals contribute more with institutions that support
cooperation than without; H7: high gridness individuals, when placed in the receiver role,
will be more likely to reject low offers than others. H8: high groupness individuals, when
placed in the offerer role, will be more likely to make high offers than others. H9: in the
absence of credible threat of punishment framing may increase contributions in a team
with many high-group individuals; framing reduces contribution with many low-group
individuals. In general framing will tend to reduce contributions if punishment is not
available. H10: with punishment framing has no effect on contributions. H11: framing in
convex ultimatum game improves negotiation.
The second stage tests the role-assignment algorithm that improves team performance. In
particular, algorithm suggests optimal composition of a team that incorporates cultural
factors such as grid and group. We show a significant positive difference in mean
performance of algorithm-assigned group compared to randomly-assigned control group.
In particular, we test following hypothesis in stage 2:
H1: under no institution condition clustering of high-group individuals with high-group
individuals and clustering low-group individuals in other teams produces higher
performance than the mixed combination of teams.
H2: under established norms and punishment condition concentrating high-grid
individuals with low-group individuals yields higher overall performance.
H3: under no institutions condition partial visibility of high-group individual’s actions
(contributions) enhances performance.
H4: under established norms and punishment condition specialization of high-grid
individuals into punisher roles improves overall performance.
H5: clustering of high-grid individuals in one team improves team performance due to
more coordinative nature of particular type.
H6: high-group individuals, when placed in the trustor role, will be more likely to trust
others than others
H7: high-group and high-grid individuals, when placed in the trustee role, will be more
likely to send more dollars than others if they get chance
H8: high-group individuals, when placed in the divider role, will be more likely to make
high offers (% of share) than others
H9: high-group and high-grid individuals, when placed in the designator role, will be
more likely to divide more dollars than others the more the divider proposes to share with
designator
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Stage 2
There are twelve treatments in four designs (See Table 3).
Design 1 consists of four treatments in 24 periods: (i) iterated voluntary contribution
mechanism (VCM) with no punishment (NP) with sorting; (ii) iterated VCM with
punishment (P) and sorting; (iii) Trust game; (iv) Convex ultimatum game.
Design 2 contains four treatments in 24 periods: (i) iterated VCM with no punishment
(NP) and no sorting; (ii) P-condition without sorting; (iii) Trust game; (iv) Convex
ultimatum game.
Design 3 has four treatments in 24 periods: (i) NP-condition-differentiated group role
with sorting; (ii) P-condition-differentiated group role with sorting; (iii) 4-person
Assurance game; (iv) 2-person Assurance game.
Lastly, Design 4 comprised of four treatments in 24 periods: (i) NP-conditiondifferentiated grid role with sorting; (ii) P-condition-differentiated grid role with sorting;
(iii) 4-person Assurance game; (iv) 2-person Assurance game.
Random assignment treatments serve as a control for the pre-specified algorithm
treatments with sorting.
DESIGN 1:
(1-1) Collective compensation with sorting (NPA)
Game Setup: partner VCM with no punishment (NP), 10 periods, teams of four
Assignment Rule: high group individuals are concentrated with other high group
individuals as much as possible, leaving the low group individuals in other teams.
NP-condition reproduces linear public good game where the number of people in the
group is set to four. This treatment maximizes team performance based on idea that highgroup individuals tend to cooperate; at the same time there are many conditional
cooperator who will induce high effort if others will exert high effort. Conditional
cooperators tend to deviate from cooperation when other free ride and exert low effort.
Hence to ensure that conditional reciprocators would not retaliate seeing other free riding
we separate low group individuals from high group individuals. This way we maximize
the overall welfare of the society /community that consists of several units/ teams. In this
treatment subjects assignment schedule follows as:
1. All subjects will be ranked according the grid/group characteristics. We run
survey before each design to obtain the cultural characteristics. We quantify the
cultural characteristics of each individual based on answers they pursue during the
survey that consists of 29 questions. First 5 questions identify nationality of the
participants, the rest of questions quantify the subjects value and belief system.
First, we calculate grid/group indexes in line with formula:
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grid=((4-Answer[10])/3+(3-Answer[13])/2+(3-Answer[14])/2+(3-Answer[17])/2+(2Answer[18])/1+(3-Answer[22])/2+(Answer[25]-1)/9+(10-Answer[26])/9+(10Answer[27])/9+(10-Answer[28])/9+(10-Answer[29])/9)/11;
group=((4-Answer[8])/3+(4-Answer[9])/3+(2-Answer[11])/1+(2Answer[12])/1+(Answer[15]-1)/1+(Answer[16]-1)/3+(3-Answer[19])/2+(3Answer[20])/2+(Answer[21]-1)/2+(Answer[23]-1)/9+(10-Answer[24])/9)/11;
The Answer[1], Answer[2]…. are the numbers that quantify and identify the exact
answers provided by subjects in the survey.
2. Given the gird/group score for each subject, calculate the average of the scores
present in the session (N=20). If the score that belongs to one individual is above
the average define it as high and if the score is below define it as low.
3. Now rank all subjects in terms of group score.
4. Assign first highest ranked high-group four subjects (ranked 1-4) in a first team,
then assign next four individuals (ranked 5-8) with highest group score into
second team; assign next four highest group scored bundle of subjects (ranked 912) into third team, etc.
Assignment schedule generates relatively homogeneous teams to maximize overall
system performance.
Note: In addition to creating a control treatment in which individuals are assigned at
random to groups, we can compare the performance of those teams with high average
groupness to those with low average groupness. This would actually be a test of the
additional hypothesis that collective compensation regimes (which is basically the nature
of a VCM without punishment) work better with high-group members in them.
(2-1) Enforced compensation regime with sorting (PA)
Game Setup: partner VCM with punishment, 10 periods, teams of four.
Assignment Rule: high grid individuals are distributed in higher numbers in those groups
which have low numbers of high group individuals
P-condition differs from NP-condition by punishment stage. Here to ensure that
punishment mechanism (social norms) followed by everyone, we assign enough number
of high-grid individuals (strong reciprocators) to each team. Strong reciprocators are
willing to enforce the rules of the team and hence they are helpful to sustain cooperation
and high performance1.
P-condition has different assignment rule as follows:
“The essential feature of strong reciprocity is a willingness to sacrifice resources for
rewarding fair and punishing unfair behavior even if this is costly and provides neither
present nor future material rewards for the reciprocator”(Fehr, Fischbacher and Gachter,
2002).
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3
1.
All subjects are ranked according their group score and grid score. Average of
the session grid scores and group scores will serve as a threshold for the definition
of high/low group, or high/low grid categories. Hence, if the person’s score is
above the session’s average score, then we count person as having high score and
if it’s below the average score, then the score is categorized as low as before.
2. We rank all subjects according the groups score and take half of subjects with
lowest group scores within the session2 as a target. Then we rank the rest of
population according the grid score. In the next step of algorithm two highestgrid scored subjects are matched with two lowest-group scored subjects in teams
of four. This way we ensure that al low group scored subjects would not cluster in
one team and other types of individuals have opportunity to discipline low-group
types.
Here assignment allows obtaining high performance in a team with mixed cultural types.
(1-3) Sequential Action-Trust Game (TG)
Game Setup: Trust game, 2 rounds (simultaneous “reflection”, shuffle), one each as
trustor and trustee. Either trustor either keeps $3 for self or can entrust $10 to trustee.
Trustee observes trustor's action, then allocates any portion of this amount to trustor. In
case trustor decides to keep $3 for self, trustee also gets $3.
In this treatment we test grid and group characteristics in the following manner: highgroup individuals suppose to trust more and will transfer all $x to the partner in the hope
to maximize social surplus and triple initial investment while low group ones trust less
and will not transfer money to the partner and the game ends with the payoff of x,x. In
turn high-grid individuals might punish bad behavior in the next round. If the trustee
receives money then as reward for kind behavior, high-grid ones will return substantial
amount of tripled money to the trustor. More generous trustors in the position of
reciprocators will send back also large proportion of raised money. This game differs
from ultimatum game by letting to see action of social welfare maximizers (altruist) by
sharing not a fixed amount of money and also allows heterogeneity in reciprocal behavior
by trustees.
(1-4) Ultimatum Game
Game Setup: Convex ultimatum game, 2 rounds (simultaneous “reflection”, shuffle), one
each as divider and designator. Divider decides the dividing rule, namely decides how to
split $x and percent of share that goes to him and other party from $x. Designator not
knowing the divider’s decision submits his/her decision for each possible dividing rule a
divider possibly could choose. Strategy method is used to elicit preferences.
Immediately after the trust game subjects experience convex ultimatum game (Andreoni
et al. 2003). UG-condition allows us to test group, grid, and role effects at the same time.
Therefore, by assigning each subject into two different roles in one period we capture
task effect. The role of a divider identifies group characteristic while the role of a
2
All sessions are held with 20 subjects except session 3.
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designator isolates grid characteristic of the individual. This condition tests two-person
interaction in role assignment. Consider bargaining game where total amount of M
money has to be divided among two persons. The divider specifies the proportion of the
money that he/she offers to the designator. The designator then determines how much
money to divide, from zero to $x dollars. The divider faces a punishment threat from the
designator such that at worst case the offer may be rejected and both players will get zero
dollars. Thus punishment threat makes the divider to be inclined to social norms or
fairness. At the same time convexity of the game (the choice of designator is non-binary
and wider) allows us to see the increments at which rejections may occur from designator
side. Again high-group individuals placed in the roles of Divider will provide more
percent of share to counterpart than the low-group persons. High-grid individuals placed
in the Designator roles will reciprocate kind behavior by splitting more dollars, and
punishing bad behavior by splitting fewer dollars.
DESIGN 2:
(2-1) Collective compensation without sorting (NPR)
Game Setup: partner VCM with no punishment, 10 periods, teams of four.
Assignment Rule: random assignment.
(2-2) Enforced compensation regime without sorting (PR)
Game Setup: partner VCM with punishment, 10 periods, teams of four.
Assignment Rule: random assignment.
(2-3) Trust Game
Game Setup: Trust game, 2 rounds (simultaneous “reflection”, partner pairs), and teams of two.
Trustor can dictate 50/50 split of 6 tokens (3 tokens each), or can entrust $10 to trustee. Trustee
can then allocate any portion of this amount to trustor.
Assignment Rule: random
(2-4) Ultimatum Game
Game Setup: Ultimatum Convex Game, 2 rounds (simultaneous "reflection", partner pairs)
Assignment Rule: random
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DESIGN 3:
(3-1) Collective compensation-partial visibility-with sorting (NPPA)
Game Setup: Shuffle VCM with no punishment, 10 periods, teams of four. 1 individual's
contribution is visible to everyone in periods 1-5, rest not visible, identity individuals who
are visible is not announced. 2 individual's contributions are visible to everyone in
periods 6-10. Total payoff cannot be seen until end.
Assignment Rule: Assign individuals with highest groupness in each team to be visible
(except to individual herself, who sees next highest groupness individual's contribution).
Collective actions suffer from free rider problem since not all actions are observable by
others. Hence certain types of individual tend to free ride on other by exerting less effort.
To prevent this situation we assign particular high-group individuals in positions/tasks
where the action taken by individual is observable to others. This transparent role would
serve as role model for the rest of team. This treatment allows differentiating roles within
the team.
Therefore, we rank individuals by group score within the team and the contribution of
highest-group individual will be displayed to others in period 1-5. The person with
highest group scores observes the contribution of the second highest person within the
group. In the next five periods starting from period 6, everyone observes the contribution
of the two highest-group scored subjects. The highest-group scored person does see the
second and third highest-group ranked subjects’ contributions. The second high-group
ranked person observes the first highest groupness and third highest groupness
individual’s contributions.
(3-2) Collective compensation - partial vision - with sorting (PPA)
Game Setup: Shuffle VCM with punishment, 10 periods, teams of 4. 2 high-gridness
individuals can see contributions of all others and able to punish, rest cannot see
anything in periods 1-6. 2 low-gridness individuals can see contributions of all others
and may punish, rest cannot see anything in periods 7-10. Total payoff cannot be seen
until end.
Assignment Rule: Assign individuals with highest gridness to see contributions of others.
Certain tasks and actions taken by team members in real life may turn difficult to
observe. This creates a free rider problem where particular tasks can’t be accomplished
well. However, with some level of monitoring either random or on regular basis we could
prevent “slack” in jobs. Therefore, we introduce a situation where common goal within a
team is achieved by combination of different roles. In particular, high-grid individuals by
nature follow the norms established within a team and tend to require similar response
from others. Thus, high-grid individuals inclined to monitor others and engage in
inspection activity on regular basis while low grid individuals do not. Hence, high-grid
individuals at their own cost reveal unobservable actions and make it available to others.
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So, we assign high-grid individuals to roles where the actions of others can be seen. This
way we strengthen the position of high-grid individuals who take care about social norms
and withdraw from others information on free riding behavior. These way only high-grid
ones are specialized in monitoring since others can’t observe others actions. This
treatment allows us to see whether high-grid ones really are enforcers and not. Also, we
eliminate the selfish-purpose punishment, where in order to benefit in future period
individuals other than high-grid may punish others.
We inform subjects that there are different roles assigned to everyone and some of roles
could observe actions of others.
(3-3) Coordinative compensation with sorting 4-person (4AGA)
(3-3a)
Game Setup: N-person Assurance Game, 1 period, teams of four.
Choice A (norm): 5 if everyone chooses A, or 0 otherwise
Choice B (non-norm): 3 regardless of what other players choose
Assignment Rule: Concentrate high-grid individuals with one another
(3-3b)
Game Setup: N-person Assurance Game, 1 period, teams of four.
Choice A (norm): 5 if everyone chooses A, or 0 otherwise
Choice B (non-norm): (3-number of people chosen (A)) regardless of what other players
choose
Assignment Rule: Concentrate high-grid individuals with one another
(3-4) Coordinative Compensation with sorting 2-person (2AGA)
(3-4a)
Game Setup: N-person Assurance Game, 1 period, teams of two
Choice A (norm): 5 if both choose A, or 0 otherwise
Choice B (non-norm): 4 regardless of what other player chooses
Assignment Rule: Concentrate high-grid individuals with one another
(3-4b)
Game Setup: N-person Assurance Game, 1 period, teams of two
Choice A (norm): 5 if both choose A, or 0 otherwise
Choice B (non-norm): 4 if both players choose (B) and 2 if other player chooses (A)
Assignment Rule: Concentrate high-grid individuals with one another
Assurance game is a coordination situation where two or more players better off if they
coordinate on their decisions rather not. There are two equilibria in this game: one is
Pareto dominant that produces higher payoff; Risk dominant equilibrium generates lower
payoff but not that low as the risky case. So no matter what the other players have chosen
you ensure non-risky payoff for yourself (but lower then Pareto optimal) by choosing
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the second available choice rather than first available choice. On the other hand there is
an incentive to maximize your payoff by coordinating with others in your team.
In the 4-person game, participant will be divided into groups of four. Both the grouping
and the role assignment will be anonymous, meaning that no one will know which of the
other people they are playing with at any time, and no one will know any other person’s
role at any time. In the game, each player separately and independently choose one of
two options: (A) or (B). All players will make their choices at the same time without
knowing the other’s choice.
In part (3-3a) all four players will accumulate points based on the combined choices that
Players make. At the end of the experiment, the points that each player accumulates will
be converted to money at the rate of (1) dollars per point.
If all players coordinate on their decisions and choose A, they all get 5 each.
If all players fail to coordinate and choose B, they all get 3 points each.
In case of mismatch in the choice (some of players choose A and some of them choose B)
then players who have chosen A will get zero while players who chosen B will get 3
points.
The assignment schedule is as follows:
1. Rank all subjects according their grid score.
2. Assign first highest four participants with high-grid score into first team, then
assign the second best ranked four subjects into second team, etc.
The assurance game can be set up so that with sufficiently high grid, a person will
continue to follow the most cooperative (Pareto superior) strategy unconditionally, even
if others fail to do so. High group, on the other hand, would clearly tend to lead to this
strategy only conditional on others following it.
DESIGN 4:
(4-1) Collective compensation-partial visibility-without sorting (NPPR)
Game Setup: Shuffle VCM with no punishment, 10 periods, teams of 4. 1 random
individual's contributions are visible to everyone in perids 1-5, rest not visible, specific
individuals are not announced. 2 random individual's contributions are visible to
everyone in perids 6-10, rest not visible, specific individuals are not announced. Total
payoff cannot be seen until end.
Assignment Rule: random
(4-2) Collective compensation - partial vision (
Game Setup: Shuffle VCM with punishment, 10 periods, teams of 4. 2 individuals can see
contributions of all others and may punish, rest cannot see anything. Total payoff cannot
be seen until end.
Assignment Rule: random
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(4-3) Coordinative Compensation - 4 person (4AGR)
(4-3a)
Game Setup: N-person Assurance Game, 1 period, teams of four.
Choice A (norm): 5 if everyone chooses A, or 0 otherwise
Choice B (non-norm): 3 regardless of what other players choose
Assignment Rule: random
(4-3b)
Game Setup: N-person Assurance Game, 1 period, teams of four.
Choice A (norm): 5 if everyone chooses A, or 0 otherwise
Choice B (non-norm): (3-number of people chosen (A)) regardless of what other players
choose
Assignment Rule: random
(4-4) Coordinative Compensation - 2 person (2AGR)
(4-4a)
Game Setup: N-person Assurance Game, 1 period, teams of two
Choice A (norm): 5 if both choose A, or 0 otherwise
Choice B (non-norm): 4 regardless of what other player chooses
Assignment Rule: random assignment
(4-4b)
Game Setup: N-person Assurance Game, 1 period, teams of two
Choice A (norm): 5 if both choose A, or 0 otherwise
Choice B (non-norm): 4 if both players choose (B) and 2 if other player chooses (A)
Assignment Rule: random assignment.
To insure the understanding of payoffs involved in the experiment subjects complete a
quiz and two practice periods are conducted before treatment starts to ensure that they are
familiar with the software. After the experiment, a questionnaire is given to ascertain the
participants’ strategies and opinions about the experience.
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Table 3. Experimental Design of stage 2
Design 1
Treatments
NPA, PA, Trust, Convex UG
Periods
Groups Session
10, 10, 2, 2 10
1, 6
Design 2
NPR, PR, Trust, Convex UG
10, 10, 2, 2 9
3, 7
Design 3
NPPA, PPA, 4AGA, 2AGA
10,10, 2, 2
10
2, 5
Design 4
NPPR, PPR, 4AGR, 2AGR
10,10, 2, 2
10
4, 8
NP-stands for VCM with no punishment; P stands for VCM with punishment; NPP
stands VCM with no punishment-partial visibility; PP –VCM with punishment-partial
vision; AG indicates N-person assurance game; all last letters such as A indicate
assignment algorithm and R means random.
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