4: A z-Tree Course: Matteo Ploner

A z-Tree Course

5: A Public Goods Game

Matteo Ploner
Università degli Studi di Trento

A Public Goods Game

A Public Goods Game

Participants can decide how much contribute to a "public" project out of their endowment
Participants are in a group of N subjects (usually 4)

What is contributed is multiplied by an efficiency factor $1/N<\alpha<1 $
What is not contributed is kept in a private account

Private incentives are to contribute nothing to the public account
But, contributions are efficient

$\Rightarrow$ social dilemma

The interaction is repeated T times in a partner fashion

Preliminaries

Define first the random period that is going to be selected for payment
This program is executed in the globals table (globals.do)

random_period=roundup(random()*NumPeriods,1);

The, define some general parameters

Contribution Stage

Remember participants of the Period they are in
Collect contribution as an integer between 0 and 10

Stage Paytoffs

First sum up all contributions by those in the group (subject.do)
The compute own payoff as defined by the payoff function

$\Pi_i=E_i-c_i+\alpha \sum_j c_j$


			TOT_contribution=subjects.sum(same(Group),contribution);

			//here we compute the payoffs
			Payoff=endowment-contribution+TOT_contribution*gain;

Stage Payoffs (ii)

We also provide participants with additional information

The exact contribution of those in the group

//find the best among others
top_other_group=subjects.maximum(same(Group) & not(same(Subject)),contribution);

//find the worst among others
low_other_group=subjects.minimum(same(Group)  & not(same(Subject)),contribution);

//find the median among others (smart way)
median_other_group=TOT_contribution-contribution-low_other_group-top_other_group;

We exploit the fact that we have groups of 4

Stage Payoffs (iii)

We provide detailed information to participants about the choices

The exact contribution of those in the group
We also convert the earnings in EURO, according to the conversion rate we chose

History

We provide participants with information about the choices in each Period
We use an History Box

A very convenient box to retrieve history data
Just specify the variable of interest as an output variable

However, we also "store" data away for later in the summary table

//write the relevant data in a table

summary.new{
Period=:Period;
Subject=:Subject;
Payoff=:Payoff;
}

Final Payoff

This stage is displayed only if the last period is reached
```
Participate=if(Period==NumPeriods,1,0);
```
Then we also retrieve the payment in the randomly defined period (in globals)
The payment is in summary table

//selected period
selected_period=globals.find(random_period);
Final_payment=summary.find(same(Subject) & Period==selected_period,Payoff);

Assignment

Take the PGG

Replicate it as it is, but with groups of 5 participants
Create a new experiment that has the same structural features of the PGG but differs in the way data are collected

2 Participants
One chooses (Pl.1) an integer between 0 and 10
The other (Pl.2) chooses an integer between 0 and 10, for each potential integer chosen by the other
Choice of the other
0 1 2 3 4 5 6 7 8 9 10
Your choice
The choices of the two in the group are then matched and payoffs computed

As an example, if Pl.1 chooses 3, and Pl.2 had chosen 2 in correspondence to 3, the total contribution is 5