Research ArticleSOCIAL SCIENCES

Humans display a reduced set of consistent behavioral phenotypes in dyadic games

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Science Advances  05 Aug 2016:
Vol. 2, no. 8, e1600451
DOI: 10.1126/sciadv.1600451
  • Fig. 1 Summary of the games used in the experiment and their equilibria.

    Schema with labels to help identify each one of the games in the quadrants of the (T, S) plane (left), along with the symmetric Nash equilibria (center) and average empirical cooperation heatmaps from the 8366 game actions of the 541 subjects (right), in each cell of the (T, S) plane. The symmetric Nash equilibria (center) for each game are as follows: PD and HG have one equilibrium, given by the pure strategies D and C, respectively. SG has a stable mixed equilibrium containing both cooperators and defectors, in a proportion that depends on the specific payoffs considered. SH is a coordination game displaying two pure-strategy stable equilibria, whose bases of attraction are separated by an unstable one, again depending on the particular payoffs of the game (5, 6, 43). The fraction of cooperation is color-coded (red, full cooperation; blue, full defection).

  • Fig. 2 Results from the K-means clustering algorithm.

    For every cluster, a column represents a player belonging to his or her corresponding cluster, whereas the four rows indicate the four average cooperation values associated with his or her (from top to bottom: cooperation in HG, SG, SH, and PD games). We color-coded the average level of cooperation for each player in each game (blue, 0.0; red, 1.0), whereas the lack of value in a particular game for a particular player is coded in white. Cluster sizes: Envious, n = 161 (30%); Pessimist, n = 113 (21%); Undefined, n = 66 (12%); Optimist, n = 110 (20%); Trustful, n = 90 (17%).

  • Fig. 3 Summary results of the different phenotypes (Optimist, Pessimist, Envious, Trustful, and Undefined) determined by the K-means clustering algorithm, plus the aggregation of all phenotypes.

    For each phenotype (column), we show the word description of the behavioral rule and the corresponding inferred behavior in the whole (T, S) plane (labeled as Numerical). The fraction of cooperation is color-coded (red, full cooperation; blue, full defection). The last row (labeled as Experiment) shows the average cooperation, aggregating all the decisions taken by the subjects classified in each cluster. The fractions for each phenotype are as follows: 20% Optimist, 21% Pessimist, 30% Envious, 17% Trustful, and 12% Undefined. The very last column shows the aggregated heatmaps of cooperation for both the simulations and the experimental results. The simulation results assume that each individual plays using one and only one of the behavioral rules and respects the relative fractions of each phenotype in the population found by the algorithm. Note the agreement between aggregated experimental and aggregated numerical heatmaps (the discrepancy heatmap between them is shown in section S4.11). We report that the average difference across the entire (T, S) plane between the experiment and the phenotype aggregation is of 1.39 SD units, which represents a value inside the standard 95% confidence interval, whereas for any given phenotype, this difference averaged over the entire (T, S) plane is smaller than 2.14 SD units.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/8/e1600451/DC1

    Technical implementation of the experiment

    Running the experiment

    Translated transcript of the tutorial and feedback screen after each round

    Other experimental results

    fig. S1. System architecture.

    fig. S2. Age distribution of the participants in our experiment.

    fig. S3. Screenshots of the tutorial shown to participants before starting the experiment and feedback screen after a typical round of the game.

    fig. S4. Fraction of cooperative actions for young (≤15 years old) and adult players (>16 years old) and relative difference between the two heatmaps: (young − adults)/adults.

    fig. S5. Fraction of separate cooperative actions for males and females and relative difference between the two heatmaps: (males − females)/females.

    fig. S6. Fraction of cooperative actions separated by round number: for the first 1 to 3 rounds, 4 to 10 rounds, and last 11 to 18 rounds.

    fig. S7. Relative difference in the fraction of cooperation heatmaps between groups of rounds.

    fig. S8. Total number of actions in each point of the (T,S) plane for all 541 participants in the experiment (the total number of game actions in the experiment adds up to 8366).

    fig. S9. SEM fraction of cooperative actions in each point of the (T,S) plane for all the participants in the experiment.

    fig. S10. Average fraction of cooperative actions (and SEM) among the population as a function of the round number overall (left) and separating the actions by game (right).

    fig. S11. Distribution of fraction of rational actions among the 541 subjects of our experiment, when considering only their actions in HG or PD, or both.

    fig. S12. Fraction of rational actions as a function of the round number for the 541 subjects, defined by their actions in the PD game and HG together (top) and independently (bottom).

    fig. S13. Values of risk aversion averaged over the subjects in each phenotype.

    fig. S14. Average response times (and SEM) as a function of the round number for all the participants in the experiment and separating the actions into cooperation or defection.

    fig. S15. Distributions of response times for all the participants in the experiment and separating the actions into cooperation (top) and defection (bottom).

    fig. S16. Testing the robustness of the results from the K-means algorithm.

    fig. S17. Davies-Bouldin index as a function of the number of clusters in the partition of our data (dashed black) compared to the equivalent results for different leave-p-out analyses.

    fig. S18. Average value for the normalized mutual information score, when doing pairwise comparisons of the clustering schemes from 2000 independent runs of the K-means algorithm both on the actual data and on the randomized version of the data.

    fig. S19. Age distribution for the different phenotypes compared to the distribution of the whole population (black).

    fig. S20. Difference between the experimental (second row) and numerical (or inferred; first row) behavioral heatmaps for each one of the phenotypes found by the K-means clustering algorithm, in units of SD.

    fig. S21. Average level of cooperation over all game actions and for different values of T (in different colors).

    fig. S22. Average level of cooperation as a function of (T,S) for both hypothesis and experiment.

  • Supplementary Materials

    This PDF file includes:

    • Technical implementation of the experiment
    • Running the experiment
    • Translated transcript of the tutorial and feedback screen after each round
    • Other experimental results
    • fig. S1. System architecture.
    • fig. S2. Age distribution of the participants in our experiment.
    • fig. S3. Screenshots of the tutorial shown to participants before starting the experiment and feedback screen after a typical round of the game.
    • fig. S4. Fraction of cooperative actions for young (≤15 years old) and adult players (>16 years old) and relative difference between the two heatmaps: (young − adults)/adults.
    • fig. S5. Fraction of separate cooperative actions for males and females and relative difference between the two heatmaps: (males − females)/females.
    • fig. S6. Fraction of cooperative actions separated by round number: for the first 1 to 3 rounds, 4 to 10 rounds, and last 11 to 18 rounds.
    • fig. S7. Relative difference in the fraction of cooperation heatmaps between groups of rounds.
    • fig. S8. Total number of actions in each point of the (T,S) plane for all 541 participants in the experiment (the total number of game actions in the experiment adds up to 8366).
    • fig. S9. SEM fraction of cooperative actions in each point of the (T,S) plane for all the participants in the experiment.
    • fig. S10. Average fraction of cooperative actions (and SEM) among the population as a function of the round number overall (left) and separating the actions by game (right).
    • fig. S11. Distribution of fraction of rational actions among the 541 subjects of our experiment, when considering only their actions in HG or PD, or both.
    • fig. S12. Fraction of rational actions as a function of the round number for the 541 subjects, defined by their actions in the PD game and HG together (top) and independently (bottom).
    • fig. S13. Values of risk aversion averaged over the subjects in each phenotype.
    • fig. S14. Average response times (and SEM) as a function of the round number for all the participants in the experiment and separating the actions into cooperation or defection.
    • fig. S15. Distributions of response times for all the participants in the experiment and separating the actions into cooperation (top) and defection (bottom).
    • fig. S16. Testing the robustness of the results from the K-means algorithm.
    • fig. S17. Davies-Bouldin index as a function of the number of clusters in the partition of our data (dashed black) compared to the equivalent results for different leave-p-out analyses.
    • fig. S18. Average value for the normalized mutual information score, when doing pairwise comparisons of the clustering schemes from 2000 independent runs of the K-means algorithm both on the actual data and on the randomized version of the data.
    • fig. S19. Age distribution for the different phenotypes compared to the distribution of the whole population (black).
    • fig. S20. Difference between the experimental (second row) and numerical (or inferred; first row) behavioral heatmaps for each one of the phenotypes found by the K-means clustering algorithm, in units of SD.
    • fig. S21. Average level of cooperation over all game actions and for different values of T (in different colors).
    • fig. S22. Average level of cooperation as a function of (T,S) for both hypothesis and experiment.

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