Dataset and computer code for "The dynamics of collective action in heterogeneous groups"

Description of dataset “ThresholdPGG_ExperimentalData.xlsx”

These data were generated to investigate how players with different endowments and productivities cooperate in asymmetric threshold public goods games.

Experimental setting:

Five treatments: (1) Full equality (N=110), (2) Endowment inequality (N=118), (3) Productivity inequality (N=112), (4) Aligned inequality (N=104), (5) Misaligned inequality (N=110).

Each participant is assigned to one treatment only. Each treatment includes two session: participants play Session 1 first and then Session 2. At the beginning of Session 1, participants are randomly matched in pairs, where in each pair one participant is assigned to Player 1 and the other is Player 2. They then play 20 rounds of the asymmetric threshold public goods game. Throughout a session, the pair of participants and their roles do not change. After Session 1, participants engage in Session 2. Again, they play 20 rounds of the asymmetric threshold public goods game but now with a different partner and in the opposite role. Finally, after completing both sessions, participants complete a questionnaire on their perception of the fair contribution pattern and the minimum contribution they expect from their co-player for successful coordination.

Each participant answers these questions twice: once from the perspective of Player 1 and once from the perspective of Player 2. However, in the full equality treatment, each participant answers only once because Player 1 and Player 2 are identical in this treatment. Nevertheless, in the dataset, their responses are recorded twice to maintain consistency with the data format used in other treatments (essentially duplicating the same response for both roles).

Structure of the Data:

Each treatment has two sheets: “TreatmentName_Type 1” and “TreatmentName_Type 2”.

In "TreatmentName_Type 1" sheet, focus players are Type 1 who act as Player 1 in Session 1 and Player 2 in Session 2. 

In "TreatmentName_Type 2" sheet, focus players are Type 2 who act as Player 2 in Session 1 and Player 1 in Session 2. 

The data format across treatments is consistent.

Each player's experimental data is represented by four rows:

- The first two rows correspond to Session 1.

- The last two rows correspond to Session 2.

Missing data codes: None

Abbreviations used: n/a; not applicable

Column Descriptions:

1        Column A: Participant ID.

2        Column B: Pairing information for each focal player in both games.

3        Columns C to V (Contributions): 

(1) Data is organized in blocks of four rows:

-  The first two rows in each block record contributions from both players in Session 1 (20 rounds).

-  The last two rows contributions from both players in Session 1 (20 rounds).

(2) Within each block:

-  The first and third rows (Columns C–V) record Player 1's contributions in Session 1 and Session 2, respectively.

-  The second and fourth rows (Columns C–V) record Player 2's contributions in Session 1 and Session 2, respectively.

4        Columns W to Z (Questionnaire Responses):

(1) Columns W and X record Player 1's answers. Columns Y and Z record Player 2's answers.

(2) In each block of four rows:

-  The first two rows record responses from both players in Session 1.

-  Column W: Player 1's perception of fair contributions.

Top cell: The contribution Player 1 believes they should make.

Bottom cell: The contribution Player 1 believes Player 2 should make.

-  Column Y: Player 2's perception of fair contributions.

Top cell: The contribution Player 2 believes Player 1 should make.

Bottom cell: The contribution Player 2 believes they should make.

-   Columns X and Z: Minimum contributions expected by Player 1 and Player 2, respectively, for successful coordination.

(3) The last two rows follow the same format as the first two rows but represent responses from Session 2.

Description of Dataset: “linearPGG_ExperimentalData.xlsx”

These data were generated to investigate how players with different endowments and productivities cooperate in asymmetric linear public goods games.

Experimental Setting:

Five treatments: (1) Full equality (N=114), (2) Endowment inequality (N=110), (3) Productivity inequality (N=110), (4) Aligned inequality (N=106), (5) Misaligned inequality (N=110).

The session setup is same as in the threshold public goods game described earlier, but the questionnaire was replaced with the following two questions:

1.     What is your preferred contribution pattern? (Specify contributions for both players).

2.     Given your co-player's contribution (from 0 to their endowment), how much would you contribute?

Similar to the threshold public goods experiment, except for the full equality treatment, each participant answered these questions twice, assuming the roles of Player 1 and Player 2, respectively. Although participants in the full equality treatment answered the questions only once, their responses were recorded twice in the dataset to maintain consistency with the data format used in other treatments (essentially duplicating the same response for both roles).

Structure of the Data:

The dataset contains 10 sheets, with two sheets for each treatment.

Each treatment consists of two sheets. The data format across treatments is consistent.

Each player's experimental data is represented by four rows:

-  The first two rows correspond to Session 1.

-  The last two rows correspond to Session 2.

Missing data codes: None

Abbreviations used: n/a; not applicable

Column Descriptions:

1       Column A: Participant ID.

2       Column B: Pairing information for each focal player in both sessions.

3       Columns C to X:

(1) Data is organized in blocks of four rows:

-  The first two rows in each block record contributions from both players in Session 1 (22 rounds).

-  The last two rows record contributions in Session 2 (21 rounds).

(2) Within each block:

-  The first and third rows (Columns C–X) record Player 1's contributions in Session 1 and Session 2, respectively.

-  The second and fourth rows (Columns C–X) record Player 2's contributions in Session 1 and Session 2, respectively.

4       Columns Y and Z (Preferred Contribution Patterns):

(1) Column Y: The Player 1's preferred contribution pattern (from Player 1’s perspective).

(2) Column Z: The Player 2's preferred contribution pattern (from Player 2’s perspective).

(3) Both Column Y and Column Z record Player 1's contribution on the top row and Player 2's contribution on the bottom row.

(4) In each block of four rows:

-  The first two rows record responses from both players of Session 1.

-  The last two rows record responses from both players of Session 2.

5       Columns AA and Beyond (Conditional Contributions):

(1) Column titles with "CC_k" indicate conditional contributions when the co-player contributes k.

(2) In each block of four rows:

-  The first two rows record responses from the two players of Session 1:

    The first row corresponds to the Player 1's answer (from Player 1’s perspective).

    The second row corresponds to the Player 2's answer (from Player 2’s perspective).

-  The last two rows record responses from the two players of Session 2:

   The third row corresponds to the Player 1's answer (from Player 1’s perspective).

   The fourth row corresponds to the Player 2's answer (from Player 2’s perspective).

Computer code used for evolutionary simulations

we used the Matlab scripts LinearPGG_CreateDataIntrospection.m and ThresholdPGG_CreateDataIntrospection.m, which we ran with Matlab R2020b. Its usage is documented inline.