Inequality and visibility of wealth in experimental social networks

Abstract

Humans prefer relatively equal distributions of resources1,2,3,4,5, yet societies have varying degrees of economic inequality6. To investigate some of the possible determinants and consequences of inequality, here we perform experiments involving a networked public goods game in which subjects interact and gain or lose wealth. Subjects (n = 1,462) were randomly assigned to have higher or lower initial endowments, and were embedded within social networks with three levels of economic inequality (Gini coefficient = 0.0, 0.2, and 0.4). In addition, we manipulated the visibility of the wealth of network neighbours. We show that wealth visibility facilitates the downstream consequences of initial inequality—in initially more unequal situations, wealth visibility leads to greater inequality than when wealth is invisible. This result reflects a heterogeneous response to visibility in richer versus poorer subjects. We also find that making wealth visible has adverse welfare consequences, yielding lower levels of overall cooperation, inter-connectedness, and wealth. High initial levels of economic inequality alone, however, have relatively few deleterious welfare effects.

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Figure 1: The level of initial economic inequality and the visibility of connecting neighbours’ wealth information are experimentally manipulated in dynamic human social networks.
Figure 2: Wealth visibility increases economic inequality (relative to invisibility) in the presence of initial inequality, but not in the presence of initial equality.
Figure 3: Visibility of wealth undermines social welfare.
Figure 4: Wealth visibility leads to exploitation under initial inequality, but fairness under initial equality.

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Acknowledgements

We thank C. Apicella, D. G. Alvarez, A. A. Arechar, D. Bergemann, G. Iosifidis, J. Jordan, J. H. Fowler, O. Moav, and A. Zaslavsky for comments. M. McKnight provided expert programming assistance and P. Treut provided technical support. The data reported in this paper are archived at Yale Institute for Network Science and are available upon request. A.N. was supported by the Japan Society for the Promotion of Science (JSPS). Support for this research was provided by a grant from the Robert Wood Johnson Foundation.

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Contributions

A.N., H.S., D.G.R., and N.A.C. designed the project. A.N. and H.S. conducted the experiments. A.N., H.S., and D.G.R. performed the statistical analyses. A.N., H.S., D.G.R, and N.A.C. analysed the findings. A.N., D.G.R., and N.A.C. wrote the manuscript.

Corresponding author

Correspondence to Nicholas A. Christakis.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Lorenz curve description of the four wealth distributions.

We prepared four different wealth conditions (A–D). For example, the shaded area for condition B divided by the area of the largest isosceles right triangle represents the Gini coefficient for condition B (that is, 0.2). Any points on the same dotted line achieve the same level of economic inequality in terms of the Gini coefficient. Condition A is equivalent to any other condition on the line from (0,0) to (1,1). Conditions B and C are analysed together since they did not yield different analytical results (see Supplementary Information).

Extended Data Figure 2 Rules in our experiments and the implied dynamics of the Gini coefficient and mean difference.

The Gini coefficient is a relative measure of inequality, while the mean difference is an absolute measure of inequality. When we focus on a tie between two subjects (a richer ego and a poorer alter), there are four combinations in the choices of cooperation behaviours in a single round. For example, when a richer ego = C and a poorer alter = C (that is, when a richer ego cooperates and a poorer alter also cooperates), both of them pay 50 units, and obtain 100 units, in which case the payoff is +50 for both. As both of them get the same payoff, the mean difference between them does not increase or decrease (→). On the other hand, the difference in wealth between them becomes less important in a relative manner, which leads to the reduction in the Gini coefficient between them (↓). The behaviours of the mean difference and Gini coefficient vary for the four combinations. C represents cooperation, and D represents defection. GINI represents local Gini coefficient of the focal two individuals, and ‘Mean diff’ represents the mean difference in wealth of the two subjects. GINI or mean difference can show the following outcomes: does not change (→), increases (↑), increases to a greater degree (↑↑), decreases (↓), or decreases to a greater degree (↓↓).

Extended Data Figure 3 A majority of initially rich individuals stay wealthier than a majority of initially poor individuals over the ten rounds regardless of the initial conditions.

a, b, The mean and standard error of mean (bar) of the average wealth of a group of initially rich individuals and of a group of initially poor individuals are calculated at each round for the visible condition (a) and for the invisible condition (b). Error bars, mean ± s.e.m. cf, For each round at each session, we standardized wealth of each individual (that is, (individual wealth–mean)/s.d.), and calculated the minimum (min), 25th percentile (25th), median, 75th percentile (75th), and maximum (max) of the standardized wealth of a group of initially rich individuals and a group of initially poor individuals, separately. These figures show the trajectories of the mean of the five indicators (minimum, 25th, median, 75th, and maximum) among different sessions of the same initial condition (c for high-level initial inequality, visible; d for high-level initial inequality, invisible; e for low-level initial inequality, visible; and f for low-level initial inequality, invisible). Darker shades represent the mean of interquartile ranges (25th to 75th), lighter shades represent the mean of ranges (minimum to maximum), and the solid lines represent the mean of the median among the different sessions. Crossing of shades and medians between the two groups, if observed, implies the influence of the initial wealth difference on present wealth may be wiped out.

Extended Data Figure 4 Cumulative degree distributions at the final (tenth) round.

The proportion of subjects who have at least k social ties (degree) is calculated for each k (1 to 20) at each initial condition. Each distribution of the three initial inequality conditions in the invisible setting is significantly different from that in the visible setting (Kolmogorov–Smirnov test, P < 0.01), and has fatter tails. The pairwise comparison in different initial inequality conditions at the same neighbours’ wealth information setting (that is, none versus low, none versus high and low versus high) show those distributions are not significantly different (Kolmogorov–Smirnov test, P > 0.12) except none versus high in the invisible condition (Kolmogorov–Smirnov test, P = 0.030). The means of these distributions, by round, are shown in Fig. 3c.

Extended Data Figure 5 Changes in mean difference in wealth and in excess transitivity in the experimental conditions.

a, The dynamics of mean difference in each of six settings is shown. Inset, the differences between mean difference at the first to tenth rounds in the visible compared to the invisible condition are shown separately for three different conditions of initial inequality (none, blue; low, grey; high, orange). Positive bars indicate that making neighbours’ wealth visible increases mean difference in wealth. b, The dynamics of excess transitivity (transitivity adjusted for network degree at each session) in each of the six settings is shown. (See Fig. 3d for the dynamics of transitivity unadjusted for degree.) As a larger degree naturally results in a larger transitivity, we calculate the expected value of transitivity given a certain network degree and a certain size in a random graph in simulations (10,000 iterations), and report the deviation of the observed transitivity from the expected transitivity (that is, observed transitivity minus expected transitivity). Inset, the differences between excess transitivity at the first to tenth rounds in the visible compared to the invisible condition are shown separately for three different conditions of initial inequality (none, blue; low, grey; high, orange). Negative bars indicate that making neighbours’ wealth visible decreases excess transitivity. Error bars, mean ± s.e.m. NS for P ≥ 0.05, *P < 0.05.

Extended Data Figure 6 Additional results regarding behavioural mechanisms.

a, b, Stratified results of Fig. 4 according to the prior move (cooperation or defection). Bars represent standard errors. cf, Cooperation rate in the different conditions with respect to the variable of social comparison (ego (a focal individual) is richer or alters (given as the average of an ego's connecting neighbours) are richer) for each setting. For example, e shows that richer subjects are more likely to cooperate (82.9%) when the initial economic inequality is set to none in the visible condition. Panel f shows that richer subjects are less likely to cooperate (17.3%) when the initial economic inequality is set to high in the visible condition. Error bars, mean ± s.e.m. NS for P ≥ 0.05, **P < 0.01, ***P < 0.001.

Extended Data Figure 7 Relationship between population-level cooperation rates at first round and outcomes at final rounds.

ad, Scatter plots of the first-round cooperation rate and the tenth-round Gini coefficient (a); average wealth (b); cooperation rate (c); and degree (d). Loess smoothed fitted curves are shown. The proportion of innately cooperative subjects in each session was not experimentally manipulated here (or in agent-based simulations).

Extended Data Figure 8 Agent-based simulations reproduced the results that were observed in the online experiments with human subjects.

ae, Results of agent-based simulations for Gini coefficient, mean difference, average wealth, proportion of cooperation, and degree (interconnectedness) are shown, respectively. The medians (solid and dashed lines) and 90% confidence regions (shaded area, 5th percentile to 95th percentile) are presented.

Extended Data Figure 9 Results of agent-based simulations with session up to 20 rounds show that the effect of visibility in Gini dynamics is robustly observed.

ae, The medians and 90% confidence regions (shaded area, 5th percentile to 95th percentile) are presented.

Extended Data Table 1 Parameters for experimental settings

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Tables 1–11 and Supplementary References; see contents page for details. (PDF 3446 kb)

Visibility of neighbours' wealth reduces cooperation, interconnectedness, and wealth (bottom two), and visibility leads to greater inequality especially in initially more highly unequal setting (bottom right).

The states from round 0 (before interactions start) to round 10 (after they end) in 4 out of 80 sessions are shown. The bold frame of a node indicates the “visible” condition and otherwise the “invisible” condition Node size (area) indicates wealth. The letter in the node denotes the initial wealth to which subjects were randomly assigned: N is a non-poor/non-rich subject, P is an initially poor subject, and R is an initially rich subject. Gini represents the Gini coefficient. Node colours represent the last move (blue: cooperate, red: defect, grey: no history). (MP4 3761 kb)

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Nishi, A., Shirado, H., Rand, D. et al. Inequality and visibility of wealth in experimental social networks. Nature 526, 426–429 (2015). https://doi.org/10.1038/nature15392

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