Introduction to z-Tree: Day 2
Andrew W. Bausch
NYU Department of Politics
[email protected]
January 10, 2012
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Overview: Interactive Games
Individual decision making experiments
Subject’s payoffs only depend on subject’s own decisions
Programs in the treatment only process information of a single subject
Interactive experiments
Payoffs of a subject also depend on the behavior of other subjects
Programs have to access information from records of other subjects
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Overview: Interactive Games
Matching
Scope Operator & the “same” function
Programming an experiment with interaction
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Matching
Random Partner Matching
In interactive experiments subjects are assigned into groups and the
game is played repeatedly over several rounds
Who interacts with whom in a given round?
z-Tree has built-in functions, but just as easy to do it yourself and you
retain more control
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Matching
Random Partner Matching
In the first stage, create a one-line Program in the Subjects Table
randGroup = random();
This generates a random number that we will use to create the groups
End this program so the subjects can access each other’s randGroup
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Matching
Random Partner Matching continued
Create a second Program in the Subjects Table right below the first
Define GroupSize in Background
ranking = count(randGroup >= : randGroup);
ranking = ranking - 1;
GroupNum = rounddown(ranking / GroupSize,1);
We rank each subjects random number and make groups based on
the ranking
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Matching
Keeping the Same Groups
Start with the same two programs as above
wrap if (Period == 1) around those programs
in the second program, put an else statement
else{
GroupNum= OLDsubjects.find(same(Subject), GroupNum);
}
z-Tree normally only allows access the value of variables from the
Subject’s current period
Use the OLDsubjects.find function to get each subject’s previous
value of GroupNum and passing it forward to the current round
If we do this every round, the subjects keep the same GroupNum
throughout the experiment
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Scope Operator
Main Use
Getting information from other subjects
The scope operator is a colon :
But, easier to read if you use the “same” function
I primarily use the colon when applying a function
ranking = count(randGroup >=: randGroup);
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same Function
Passing Information between players
Groupaverage = average(same(Group), Contribution);
Gets all contributions from a subjects group and uses the average
function to calculate the group average
Passing Information specific information from a player
Choice3 = find(same(GroupNum)&PlayerNum == 3, Choice);
Finds Player 3 in this subject’s group and assigns Player 3’s Choice to
a variable called Choice3 for all subjects
You can create player numbers similar to the way we assigned groups
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Programming an interactive experiment
The guessing game (beauty contest)
Nagel, R. (1995). Unraveling in guessing games: An experimental study.
American Economic Review, 85(5), 1313-1326.
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Programming an interactive experiment
The guessing game
6 subjects (2 groups of 3 subjects)
Keep the same group throughout
Subjects enter a number between 0 and 100
Subject closest to 2/3 of the group’s average entry wins a prize of 60
points
In case of a tie, the prize is shared equally among the winning group
members
Continue for 10 rounds
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Programming an interactive experiment
Background variables
Declare the variables we don’t plan on changing by creating a new
program under Background
I keep them all in the subjects table
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Programming an interactive experiment
Setting up Groups
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Programming an interactive experiment
Getting a Random Number
if(Period ==1) {
randGroup = random();
}
Assigning the Groups
if(Period == 1) {
ranking = count(randGroup >= : randGroup);
ranking = ranking - 1;
GroupNum = rounddown(ranking / GroupSize,1);
}
else {
GroupNum = OLDsubjects.find(same(Subject), GroupNum);
}
Note: These must be in two separate programs
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Programming an interactive experiment
Set the Active Screen for Stage 1
Can copy and paste from yesterday
Minimum input is 0
Maximum input is 100
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Programming an interactive experiment
Get the Group Average
Note that we are going to need to use three separate short programs
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Programming an interactive experiment
Get the Group Average
// Get the group average
Groupaverage=average(same(GroupNum), guess);
// find 2/3s of it
twoThirdsGroupAve = Groupaverage*2/3;
// Calculate the difference
Diff = abs(guess - twoThirdsGroupAve);
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Programming an interactive experiment
Calculate the lowest difference
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Programming an interactive experiment
Calculate the lowest difference
// Calculate the lowest difference for the group
Best = minimum( same(GroupNum), Diff);
// See if this subject is the winner
Winner = if(Diff == Best, 1, 0);
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Programming an interactive experiment
Find the Payoffs
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Programming an interactive experiment
Find the Payoffs
// Determine how many winners
NumWinners = sum(same(GroupNum), Winner);
// Set the round payoff using the number of winners and
//the Winner variable
RoundPayoff = Prize*Winner / NumWinners;
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Programming an interactive experiment
Conditional Displays
We want to tell each subject is she won
Add New Plot Text
Set Display Condition Winner == 1
<> You won! You were one of < NumWinners|1 > winners
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Programming an interactive experiment
Conditional Displays
Or lost
Add New Plot Text
Set Display Condition Winner == 1
You Lost!
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Programming an interactive experiment
Displaying the Payoff
Add New Plot Text
<> Your Payoff this round is < RoundPayoff |.1 >
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Programming an interactive experiment
Stage 1
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Programming an interactive experiment
Stage 2: Winners
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Programming an interactive experiment
Stage 2: Losers
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