oTree: Strategic interaction

The 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<<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

Treatments: framing

• We are going to frame the game eiter as a Voluntary Contribution game (VC) or as a Common Pool game (CP)

• Voluntary Contribution game
  • Participants explicitly decide how much of their endowment contribute to the public project
    • What is not contributed is kept in a private account

• Common Pool game
  • Participants explicitly decide how much to withdraw from the (already existing) public project
    • What is withdrawn is put in a private account

Parameters

• The interaction is repeated 10x in a partner fashion
  • Total earnings are given by the sum of earnings in each stage
• Groups of 4
  • Matched together for the entire expeirment (partner)
• The efficiency factor \(\alpha=.5\)
• The initial endowment is E=100
  • The individual payoff function is
    • VC
  • \(\Pi_i=E-c_i+\alpha \sum_j^N c_j\)
    • where, \(j\) are the members of \(i\)’s group (\(i\) include)
    • \(\sum_j^N c_j\) is the size of the public project
    • CP
      • \(\Pi_i=c_i+ \alpha (N*E-\sum_j^N c_j)\)
• Choices are in integer steps
  • \(c_i \in \{0, 100\}\)

Screens

Instructions

• VC

• CP

Choices

• VC

• CP

Results

• CP

• VC

oTree code

models.py

• Set here a few important constants
  • Players per group
  • Number of rounds
  • Individual endowment
  • Multiplier for the public project
    • \(\alpha=\frac{2=multiplier}{4=group~members}\)

class Constants(BaseConstants):
    name_in_url = 'PGG'
    players_per_group = 4
    num_rounds = 10

    endowment = c(100)
    multiplier = 2

models (ii)

• In class Subsession we defien the matching
  • No need to define roles in PGG

class Subsession(BaseSubsession):
    def creating_session(self):
#***************************************************************
# Partner matching
#***************************************************************
        if self.round_number == 1: # this way we get a fixed role across repetitions
            self.group_randomly()
        else:
            self.group_like_round(1)
#***************************************************************
# Copy treatment for each player, needed for data analysis
#! configurations are not saved in the data
#***************************************************************
        for p in self.get_players():# copy the treatment for each subject
            p.treatment=self.session.config['treatment']

models (iii)

• In class Group we define the payoffs
  • Typical of strategic interaction, while in individual decision making they are defined in Player

class Group(BaseGroup):
    total_choices = models.CurrencyField() # for VC is contributions , for CP is withdrawals
    individual_share = models.CurrencyField() #the share from public project
    total_earnings = models.CurrencyField() # share from public project + private account
#***************************************************************
# Define the method to compute payoff
#***************************************************************
    def set_payoffs(self):
    # conventional name for the payoff function
        players = self.get_players()
        # retrieve players in the subsession
        choices = [p.choice for p in players]
        # store their choices in a list. For CP they are withdrawals, For VC they are contributions
        self.total_choices = sum(choices)
        # sum the total choices (gives the size of the public project)
        if self.session.config['treatment'] == "VC":
        # if treatment is VC
            self.total_earnings = self.total_choices * Constants.multiplier
            # size of the public project
            self.individual_share = (
                self.total_earnings / Constants.players_per_group
            )
            # the individual share from the public project
            for p in players:
            # for all players in the group
                p.payoff = Constants.endowment - p.choice + self.individual_share
                # write the earnings in the payoff field (each player has automatically one)
                # then, we can use participant.payoff to get the sum across rounds
        else: # treatment CP
        # if treatment is CP
            self.total_earnings = ((Constants.endowment*Constants.players_per_group)-self.total_choices) * Constants.multiplier
            # size of the public project
            self.individual_share = (
                self.total_earnings / Constants.players_per_group
            )
            # the individual share from the public project
            for p in players:
            # for all players in the group
                p.payoff =  p.choice + self.individual_share
                # write the earnings in the payoff field (each player has automatically one)
                # then, we can use participant.payoff to get the sum across rounds

models (iv)

• Variables for players

class Player(BasePlayer):
    choice = models.CurrencyField(min=0,max=Constants.endowment)#
    # for VC is withdrawals, for CP is contributions
    treatment=models.CharField()
    # copy the treatment, mainly for data analysis

pages.py

• We have 5 pages
• page_sequence = [Instructions, Contribute, ResultsWaitPage, Results, FinalResults]
  • Instructions(Page)
    • Displayed only in round 1
  • Contribute(Page)
  • ResultsWaitPage(WaitPage)
    • WaitPage → oTree waits until all players in the group have arrived at that point in the sequence, and then all players are allowed to proceed
  • Results(Page)
  • FinalResults(Page)
    • Displayed only in last round

pages

• Instructions

class Instructions(Page):
    def is_displayed(self):
    # define this method to return True if the page should be show
        return self.round_number == 1
        # show the page only in round 1

    def vars_for_template(self):
    # to pass variables to the template
        return{
        'treatment': self.session.config['treatment'],# needed to create the right treatment in the intructions
        'common_proj': Constants.endowment*Constants.players_per_group
        }
        # dictionary with variables needed in the template

pages (ii)

• Contribute
  • Different meaning in VC snd CP

class Contribute(Page):
    form_model = 'player'
    form_fields = ['choice']
#the player will fill out the field choice and it will be saved in player model (see models)

    def vars_for_template(self):
        return{
        'round_number':self.round_number,
        'treatment': self.session.config['treatment'],
        'endowment': Constants.endowment
        }
    # dictionary with variables needed in the template

pages (iii)

• This is a WaitPage

class ResultsWaitPage(WaitPage):
    #oTree waits until all players in the group have arrived at that point in the sequence, and then all players are allowed to proceed.
    after_all_players_arrive = 'set_payoffs'
    # see method 'set_payoffs' in class Group in models.py
    # payoffs are computed here

pages (iv)

• Results displayed at the end of each round

class Results(Page):
    def vars_for_template(self):
        return{
        'round_number':self.round_number,
        'treatment': self.session.config['treatment'],
        }

pages (v)

• Displayed only in the last period

class FinalResults(Page):
    def is_displayed(self):
        return self.round_number == Constants.num_rounds
        # displayed only in last round
    def vars_for_template(self):
        return{
        'final_payoff':self.player.participant.payoff
        }
        # Each player has a payoff field
        # self.participant.payoff automatically stores the sum of payoffs from all subsessions

templates: Instructions

{% extends "global/Page.html" %}
{% load staticfiles otree %}
<!--------------------------->

<!-- Title -->

{% block title %}
  <h1>  Instructions </h1>
{% endblock %}

<!--------------------------->

<!-- Main body -->

{% block content %}

<div class="container p-3 my-3 border" style="font-size:18pt">

<h2> The interaction</h2>

{% if treatment == "VC" %} <!-- VC -->
<p>In this study, you will be in a randomly formed group of {{ Constants.players_per_group }} participants. </p>
<p>Each participant in the group is given {{ Constants.endowment }}. </p>
<p>Each participant in the group decides how much she or he is going to contribute to a common project.</p>
<p>Contributions could be any integer between 0 to {{ Constants.endowment }}.</p>

<h2> Your payoff </h2>
<p> The earnings from the project are calculated as follows:
<ul>
  <li>
  The contributions of all {{ Constants.players_per_group }} participants are added up.</li>
  <li>
    The sum of contributions is multiplied by a factor of {{ Constants.multiplier }}: these are the <i>total returns from the project</i>.
  </li>
  <li>
    <i>Total returns from the project</i> are then evenly split among all {{ Constants.players_per_group }}  participants: : these are <i>your earnings from the project</i>.
  </li>
</ul>
<p><i>Your payoff</i> is given by your earnings from the project, plus the amount you did not contribute.</p>

{% else %} <!-- CP -->

<p>In this study, you will be in a randomly formed group of {{ Constants.players_per_group }} participants. </p>
<p> Your group is endowed with a common project of {{ common_proj }}. </p>
<p>Each participant in the group decides how much she or he is going to withdraw from the common project.</p>
<p>Withdrawals could be any integer between 0 to {{ Constants.endowment }}.</p>

<h2> Your payoff </h2>
<p> The earnings from the project are calculated as follows:
<ul>
  <li>
  The withdrawals of all {{ Constants.players_per_group }} participants are added up.</li>
  <li>
    The sum of withdrawals is subtracted from the common project and the resulting amount is multiplied by a factor of  {{ Constants.multiplier }}: these are the <i>total returns from the project</i>.
  </li>
  <li>
    <i>Total returns from the project</i> are then evenly split among all {{ Constants.players_per_group }}  participants: these are <i>your earnings from the project</i>.
  </li>
</ul>
<p><i>Your payoff</i> is given by your earnings from the project, plus the amount you withdrew from the project.</p>


{% endif %}

</div>

<!-- Continue Button -->

<div class="container" style="font-size:18pt">
  <div class="row">
    &nbsp;
  </div>
  <div class="row" style="padding-left:135px;">
    <div class="col-md-10">

    </div>
    <div class="col-md-2">
      <button name="btn_submit" value="True" class="btn btn-primary btn-large">
         <span style="font-size:18pt">Continue</span>
     </button>
    </div>
  </div>
</div>


{% endblock %}
<!--------------------------->

templates: Contribute

{% extends "global/Page.html" %}
{% load staticfiles otree %}


<!--------------------------->

{% block title %}

{% if  treatment == "VC" %} <!-- Treatment VC -->
    <h1> Contribute ( Round {{ round_number }} of {{Constants.num_rounds}})<h1> <!-- info about treatments -->
  {% else %} <!-- CP -->
  <h1> Withdrawal ( Round {{ round_number }} of {{Constants.num_rounds}})<h1> <!-- info about treatments -->
  {% endif %}

{% endblock %}

<!--------------------------->

{% block content %}

<div class="container p-3 my-3 border" style="font-size:18pt">

{% if  treatment == "VC" %}<!-- Treatment VC -->
    {% formfield player.choice label="How much do you contribute to the common project?" %}
{% else %}<!-- CP -->
    {% formfield player.choice label="How much do you withdraw from the common project?" %}
{% endif %}

<small>An integer number between 0 and {{endowment}}</small>

</div>

<!-- Continue Button -->

<div class="container" style="font-size:18pt">
  <div class="row">
    &nbsp;
  </div>
  <div class="row" style="padding-left:135px;">
    <div class="col-md-10">

    </div>
    <div class="col-md-2">
      <button name="btn_submit" value="True" class="btn btn-primary btn-large">
         <span style="font-size:18pt">Continue</span>
     </button>
    </div>
  </div>
</div>

{% endblock %}
<!--------------------------->

templates: Results

{% extends "global/Page.html" %}
{% load staticfiles otree %}
<!--------------------------->

{% block title %}
    Results ( Round {{ round_number }} of {{Constants.num_rounds}})
{% endblock %}
<!--------------------------->

{% block content %}

<div class="container p-3 my-3 border" style="font-size:18pt">
{% if treatment == "VC" %}
    <table class="table-condensed" style="width:500px; margin-top:20px;">
        <tr><td>You contributed:</td><td>{{ player.choice }}</td></tr>
        <tr><td>Other participants contributed:</td><td></td></tr>
        {% for p in player.get_others_in_group %} <!-- get the list of all players-->
            <tr><td></td><td>{{ p.choice }}</td></tr>
        {% endfor %}
        <tr><td>Total contribution:</td><td>{{ group.total_choices }}</td></tr>
        <tr><td colspan="2"><hr/></td></tr>
        <tr><td>Total earnings from the project:</td><td>{{ group.total_earnings }}</td></tr>
        <tr><td>Your earnings from the project:</td><td>{{ group.individual_share }}</td></tr>
        <tr><td colspan="2"><hr/></td></tr>
        <tr><td>Thus in total you earned:</td><td>{{ player.payoff }}</td></tr>
    </table>
{% else %}
    <table class="table-condensed" style="width:500px; margin-top:20px;">
        <tr><td>You withdrew:</td><td>{{ player.choice }}</td></tr>
        <tr><td>Other participants withdrew:</td><td></td></tr>
        {% for p in player.get_others_in_group %} <!-- get the list of all players-->
            <tr><td></td><td>{{ p.choice }}</td></tr>
        {% endfor %}
        <tr><td>Total withdrawals:</td><td>{{ group.total_choices }}</td></tr>
        <tr><td colspan="2"><hr/></td></tr>
        <tr><td>Total earnings from the project:</td><td>{{ group.total_earnings }}</td></tr>
        <tr><td>Your earnings from the project:</td><td>{{ group.individual_share }}</td></tr>
        <tr><td colspan="2"><hr/></td></tr>
        <tr><td>Thus in total you earned:</td><td>{{ player.payoff }}</td></tr>
    </table>
    {% endif %}
</div>
<!--------------------------->
<!-- Continue Button -->

<div class="container" style="font-size:18pt">
  <div class="row">
    &nbsp;
  </div>
  <div class="row" style="padding-left:135px;">
    <div class="col-md-10">

    </div>
    <div class="col-md-2">
      <button name="btn_submit" value="True" class="btn btn-primary btn-large">
         <span style="font-size:18pt">Continue</span>
     </button>
    </div>
  </div>
</div>
{% endblock %}
<!--------------------------->

FinalResults

• Displayed only in last round

{% extends "global/Page.html" %}
{% load staticfiles otree %}

<!--------------------------->
{% block title %}
    <h1> Final Results </h1>
{% endblock %}
<!--------------------------->

{% block content %}
<div class="container p-3 my-3 border" style="font-size:18pt">

Your total earnings in the game are {{final_payoff}}
<div class="container" style="font-size:18pt">
  <div class="row">
    &nbsp;
  </div>
  <div class="row" style="padding-left:135px;">
    <div class="col-md-10">

    </div>
    <div class="col-md-2">
      <button name="btn_submit" value="True" class="btn btn-primary btn-large">
         <span style="font-size:18pt">Continue</span>
     </button>
    </div>
  </div>
</div>
{% endblock %}
<!--------------------------->

Thank you

🦄

To contact me just write me an email

matteo.ploner@unitn.it

or write me on the forum of the course

Appendix

Assignment

1. Easy

• Change endowment from 100 to 10000

2. Less easy

• Final payment is not the sum of all periods, but a randomly chosen period
  • Hint: use the built-in method in_round()

OTree code

• The oTree app of this lecture:

Download PGG.zip

References