# Inequalities between Others Do Matter: Evidence from Multiplayer Dictator Games

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Envy

#### 2.2. Inequality and Conflict

#### 2.3. Strategic Considerations in a Non-Strategic Setting: A Theoretical Paradox

## 3. Model

**x**) assigned to self (i) and other players (j, k, etc.). A rational Dictator evaluates the options according to a personal function that converts material payoffs to effective utilities, and then chooses the option that maximizes utility [7]. We define utility as a linear combination of the option’s selfish and social consequences (

**X**), weighed by the decision-maker’s motives (${\beta}_{\mathrm{i}}$):

## 4. Method

#### 4.1. Participants

#### 4.2. Dictator Games

#### 4.3. Computer Program

#### 4.4. Procedure

#### 4.5. Statistical Model

#### 4.6. Bayesian Estimation

## 5. Results

#### 5.1. Model Selection

_{0}represents a selfish model, in which decision-makers are only motived by selfish concerns, although they may make occasional evaluation errors; M

_{1}expands the baseline model with a term to capture motives for social efficiency; M

_{2}then adds a term for self-centered inequality motives, and is similar to the Fehr and Schmidt [39] model. Our main model of interest is M

_{3}; this model expands M

_{2}with a term for non-self-centered inequality. Note that by restricting the appropriate parameters in M

_{3}to zero, the models M

_{0}, M

_{1}, and M

_{2}can be acquired. Table 6 summarizes the fit of the aforementioned models against our experimental data.

_{3}showed a better fit than the restricted models. However, in comparison to M

_{2}the improvement was only marginal: the incremental improvement in the DIC was small, ΔDIC(M

_{2}, M

_{3}) = 12, and only a 0.8% increase in predictive accuracy was achieved. This can be explained by the fact that the experiment contained 10 two-player DGs: for these games, the multiplayer model M

_{3}by definition cannot improve predictions. If we consider only the four-player DGs, M

_{3}did show a more pronounced improvement: for these games, the predictive accuracy increased by 2.3% compared to M

_{2}. For the second experiment, results were more straightforward. Again, M

_{3}fitted better than the restricted models, and the improvement over M

_{2}was larger: ΔDIC(M

_{2}, M

_{3}) = 555; the increase in predictive accuracy of M

_{2}over M

_{3}was 4.2%.

#### 5.2. Parameter Interpretation

_{3}are summarized in Table 7; estimates for M

_{2}are reported for reference. We note that for our particular scaled probit regression models it is valid to compare raw coefficients across models: the constrained weight of selfish outcomes ensures that the models’ coefficients have the same scale. Both experiments showed that the terms shared by M

_{2}and M

_{3}are of similar magnitude; adding non-self-centered inequality motives only marginally affected estimates for social efficiency and self-centered inequality motives, we can therefore conclude that non-self-centered inequality has a separate contribution to utility.

_{3}. First, we interpret the motives’ means. These estimates quantify the average weight of the associated outcome on a decision-maker’s utility function. In the first experiment, the posterior estimate for mean(${\beta}_{\mathrm{i}}^{\mathrm{Se}})$ did not differ credibly from zero, since the 95% credible interval (95%-CI) was [−0.118; 0.078]. This indicates that decision-makers were, on average, indifferent to social efficiency. In the second experiment, mean(${\beta}_{\mathrm{i}}^{\mathrm{Se}})$ was credibly positive, 95%-CI [0.073; 0.150]. This indicates an average motive to improve social efficiency. In both experiments, mean(${\beta}_{\mathrm{i}}^{\mathrm{Is}}$) was credibly smaller than zero (i.e., the 95%-CIs are [−0.340; −0.260] and [−0.116; −0.068] respectively). This indicates an average distaste for self-centered inequality. In the first experiment, mean(${\beta}_{\mathrm{i}}^{\mathrm{Ins}}$) did not differ credibly from zero, 95%-CI [−0.020; 0.113]; this indicates indifference to non-self-centered inequality. The second experiment showed that mean(${\beta}_{\mathrm{i}}^{\mathrm{Ins}}$) was credibly smaller than zero, 95%-CI [−0.135; −0.086], which indicates a distaste for non-self-centered inequality. We note that the average motives differed markedly across experiments; possible explanations for this are presented in the discussion.

#### 5.3. Predictions Given Model M_{3}

_{3}. First, we estimated the percentage of purely pro-social decision-makers; these are individuals with a combination of social efficiency-preferences (${\beta}_{i}^{\mathrm{Se}}>0)$, aversion to self-centered inequality aversion (${\beta}_{i}^{\mathrm{Is}}<0$), and aversion to non-self-centered inequality $({\beta}_{i}^{\mathrm{Ins}}<0)$. In the first experiment, 16.10% qualified as purely pro-social; in the second experiment, this percentage was considerably higher, namely 43.07%. Secondly, we estimated the percentage of purely competitive decision-makers; these are individuals with (${\beta}_{i}^{\mathrm{Se}}<0)$, (${\beta}_{i}^{\mathrm{Is}}>0$), and (${\beta}_{i}^{\mathrm{Is}}>0$). In the first experiment, approximately zero players were pure competitors; in the second experiment this percentage was 8.67%. Finally, we estimated the percentage of individuals with aversion to inequality between others (${\beta}_{i}^{\mathrm{Ins}}<0$). For the first experiment, 43.28% were averse to non-self-centered inequality. In the second experiment, this percentage was again considerably higher, namely 74.00%.

## 6. Exploratory Analyses

#### 6.1. Non-Linearities in the Evaluation of Self-Centered Inequality

_{2}* and M

_{3}* were estimated. These resemble M

_{2}and M

_{3}, but have exponentiated terms to capture inequalities. The first experiment contained too few multiplayer observations, therefore these analyses were only done for the data from the second experiment. The posterior densities of M

_{2}* and M

_{3}* are summarized in Table 8.

_{2}* and M

_{3}* outperform their respective linear counterparts; this indicates that our original models omitted relevant nonlinearities. The exponent $\delta $ was (credibly) smaller than 1 in both specifications, which shows that inequalities yield decreasing returns. The non-linear model with a term for non-self-centered inequality (M

_{3}*) fitted the data better than the model without such a term (M

_{2}*). This shows that although there are non-linearities in the evaluation of inequality, non-self-centered inequality motives remain relevant to explain DG choices.

#### 6.2. Alternative Comparison Mechanisms: Pairwise Comparisons and Social Reference Points

_{2}, but includes a reference-point term for self-centered inequality, rather than a pairwise term. Results showed that this model fitted the data substantially better than the ERC model (DIC = 4897, pD = 400.8), but the model performed worse than our main model M

_{3}. Third, a hybrid ERC variant was estimated; this model is similar to M

_{3}, the only difference is that a references-point comparison process is modeled for the evaluation of inequalities between self and others. Not surprisingly, this model fitted the data almost as well as M

_{3}(DIC = 4147, pD = 651.2). Although our data does not discriminate between these models, parsimony favors M

_{3}, since it assumes a common comparison process for both types of inequality. Further research is needed to study the precise social comparison process used to evaluate inequality; we recommend the use of specialized DGs designed to disentangle these models.

#### 6.3. Social Motives as a Function of Economic Status

_{3}to both subsamples, and then compare the estimated coefficients between high-status and low-status choices. But we were unable to do so: the dichotomization based on status induced a severe, but understandable, dependency between self-centered inequality and the other manipulated selfish and social consequences. The resulting collinearity issues could only be resolved by restricting the weight of self-centered inequality motives to zero. We fitted this restricted version of M

_{3}to both subsamples via Stata’s gsem procedure; for reference, we also estimated this model on the total sample. Since Stata scaled coefficients relative to the decision errors; we therefore transformed the parameters back to the desired scale via Stata’s nlcom post-estimation procedure (see Appendix 4 for a more detailed comparison of Bayesian and frequentist estimates). Table 9 summarizes the transformed coefficients. Results show clear differences between motives in low-status and high-status games. High-status choices revealed stronger average preferences for social efficiency, and more aversion to non-self-centered inequality. This suggests that decision-makers show social motives to the extent that they can afford it.

## 7. Discussion

## Author Contributions

## Conflicts of Interest

## Appendix 1. Instructions Experiment 1

## 1. Instructions for the First Part of the Questionnaire

## 2. Overview

## 3. Earnings

**35 Points = 1 Euro**

#### First Phase (10 Rounds)

**one**other participant, who we call Player A. This player is randomly selected each round. You will be presented two options on how to distribute points between the two of you. Your task is to choose the option that you prefer. See the example below:

## Appendix 2. Instructions Experiment 2

## 1. Instructions for Second Part of the Experiment

## 2. Overview

## 3. Earnings

**150 Points = 1 Euro**

#### 3.1. First Phase (20 Rounds)

**three**other participants, we will call Player A, B and C. These players are randomly chosen each round. You will see two options on how to distribute points between yourself and the other players. See the example below:

**percentage**of participants choosing

**option 1**(0–100).

#### 3.2. Second Phase (One Round)

**one**other participant. You will see two options on how to distribute points between yourself and the other players. See the example below:

## Appendix 3. Sensitivity to Priors

Different Degrees of Prior Uncertainty for the Means of Social Motives | Different Parametrizations for the Wishart Prior for the (Inverse) Covariance Matrix | |||||
---|---|---|---|---|---|---|

SD = 1 | SD = 2.5 | SD = 10 | Scale = 1 | Scale = 2.5 | Scale = 10 | |

Post. M (SD) | Post. M (SD) | Post. M (SD) | Post. M (SD) | Post. M (SD) | Post. M (SD) | |

mean(${\beta}_{i}^{\mathrm{Se}}$) | 0.111 (0.020) | 0.111 (0.020) | 0.111 (0.020) | 0.109 (0.018) | 0.111 (0.020) | 0.123 (0.025) |

mean(${\beta}_{i}^{\mathrm{Is}}$) | −0.093 (0.012) | −0.092 (0.012) | −0.092 (0.012) | −0.095 (0.011) | −0.092 (0.012) | −0.082 (0.017) |

mean(${\beta}_{i}^{\mathrm{Ins}}$) | −0.110 (0.012) | −0.110 (0.012) | −0.111 (0.012) | −0.116 (0.011) | −0.110 (0.012) | −0.095 (0.018) |

sd(${\beta}_{i}^{\mathrm{Se}}$) | 0.321 (0.016) | 0.321 (0.016) | 0.320 (0.016) | 0.302 (0.016) | 0.321 (0.016) | 0.413 (0.020) |

sd(${\beta}_{i}^{\mathrm{Is}}$) | 0.177 (0.010) | 0.177 (0.010) | 0.177 (0.010) | 0.157 (0.010) | 0.177 (0.010) | 0.274 (0.013) |

sd(${\beta}_{i}^{\mathrm{Ins}}$) | 0.171 (0.010) | 0.171 (0.010) | 0.171 (0.010) | 0.144 (0.010) | 0.171 (0.010) | 0.277 (0.013) |

cor(${\beta}_{i}^{\mathrm{Se}}$,${\beta}_{i}^{\mathrm{Is}}$) | −0.468 (0.065) | −0.468 (0.067) | −0.469 (0.066) | −0.588 (0.063) | −0.468 (0.066) | −0.220 (0.067) |

cor(${\beta}_{i}^{\mathrm{Se}}$,${\beta}_{i}^{\mathrm{Ins}}$) | −0.281 (0.074) | −0.282 (0.075) | −0.281 (0.073) | −0.315 (0.079) | −0.279 (0.074) | −0.187 (0.065) |

cor(${\beta}_{i}^{\mathrm{Is}}$, ${\beta}_{i}^{\mathrm{Ins}}$) | 0.471 (0.061) | 0.473 (0.063) | 0.473 (0.061) | 0.674 (0.056) | 0.470 (0.063) | 0.194 (0.062) |

sd(ε_{A} − ε_{B}) | 0.443 (0.015) | 0.443 (0.015) | 0.443 (0.015) | 0.433 (0.014) | 0.444 (0.014) | 0.485 (0.017) |

Fit: DIC | 4172 | 4174 | 4172 | 4141 | 4175 | 4311 |

pD | 709.2 | 709.6 | 708.8 | 630.7 | 710.2 | 835.3 |

^{T}-decompositions) allow for element-wise priors (and thus more flexible control for the researcher), these methods need not yield uninformative priors. Even if the elements of a decomposed matrix have uninformative priors, the resulting covariance matrix is construed via a non-linear transformation; thus, the priors for (partial) correlations can become informative, even if the bivariate correlations have an uninformative prior. Another solution proposed by Gelman [49] is to use redundant parametrizations. We found that both decomposition methods and redundant parametrizations lead to severe convergence problems in our particular models, and have therefore not investigated these models any further.

## Appendix 4. A comparison of Bayesian and Frequentist Estimates

Experiment 1 (N = 148) | Experiment 2 (N = 305) | |||
---|---|---|---|---|

Bayesian | Frequentist | Bayesian | Frequentist | |

Post. M. (SD) | Point Estimate (SE) | Post. M. (SD) | Point Estimate (SE) | |

mean(${\beta}_{i}^{\mathrm{Se}}$) | −0.017 (0.050) | 0.005 (0.047) | 0.111 (0.020) | 0.110 (0.018) |

mean(${\beta}_{i}^{\mathrm{Is}}$) | −0.319 (0.030) | −0.280 (0.029) | −0.092 (0.012) | −0.095 (0.011) |

mean(${\beta}_{i}^{\mathrm{Ins}}$) | 0.045 (0.034) | 0.119 (0.043) | −0.110 (0.012) | −0.115 (0.011) |

sd(${\beta}_{i}^{\mathrm{Se}}$) | 0.492 (0.042) | 0.448 (0.041) | 0.321 (0.017) | 0.298 (0.015) |

sd(${\beta}_{i}^{\mathrm{Is}}$) | 0.239 (0.021) | 0.199 (0.023) | 0.177 (0.010) | 0.153 (0.010) |

sd(${\beta}_{i}^{\mathrm{Ins}}$) | 0.266 (0.029) | 0.285 (0.050) | 0.171 (0.010) | 0.139 (0.010) |

cor(${\beta}_{i}^{\mathrm{Se}}$,${\beta}_{i}^{\mathrm{Is}}$) | −0.055 (0.138) | 0.004 (0.165) | −0.468 (0.067) | −0.612 (0.062) |

cor(${\beta}_{i}^{\mathrm{Se}}$,${\beta}_{i}^{\mathrm{Ins}}$) | −0.399 (0.122) | −0.223 (0.145) | −0.282 (0.075) | −0.316 (0.082) |

cor(${\beta}_{i}^{\mathrm{Is}}$,${\beta}_{i}^{\mathrm{Ins}}$) | 0.241 (0.136) | 0.406 (0.190) | 0.472 (0.063) | 0.753 (0.063) |

sd(ε_{A} − ε_{B}) | 0.315 (0.014) | 0.318 (0.015) | 0.443 (0.015) | 0.435 (0.013) |

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^{1}We currently investigate the effect of group size on social motives in a separate study.^{2}We suspect that a desire to make models applicable to strategic games has guided this decision. For such games, parsimony is highly relevant: to calculate equilibria requires knowledge about the incentive structure and the players’ motives, as well as knowledge of the players’ expectations regarding the rationality and motives of others. Evidently, an additional motive complicates calculations considerably. Recent studies have showed that expectations are in part contingent on an individual’s motives [16,17,18]; hence it may be possible to retain an acceptable level of parsimony even without stringent assumptions on the absence of motives.^{3}Note that an alternate strategy to avoid conflict is to increase inequality to such levels that the disadvantaged lack the means to engage in conflict.^{4}We assume linear evaluations throughout. Convex or concave evaluations of efficiency and inequality plausible, but also considerably more complex to investigate. To estimate the parameters that describe non-linear evaluations requires specialized DGs and substantially more data. We thus maintain a linear specification throughout the main analyses. We conducted a number of exploratory robustness tests to show that our findings hold in models that differ slightly in the specification of how inequality is evaluated.

Abbreviation | Term | Weights | |
---|---|---|---|

Selfish outcomes | ${\mathrm{X}}^{\mathrm{S}}$ | ${\mathrm{x}}_{\mathrm{i}}^{\text{}}$ | ${\beta}_{i}^{\mathrm{s}}=1$ |

Social efficiency | ${\mathrm{X}}^{\mathrm{Se}}$ | ${\overline{\mathrm{x}}}_{-\mathrm{i}}^{\text{}}$ | ${\beta}_{i}^{\mathrm{Se}}$ |

Self-centered inequality | ${\mathrm{X}}^{\mathrm{Is}}$ | $\frac{1}{\left(n-1\right)}{\displaystyle \sum}_{\mathrm{i}\ne \mathrm{j}}\left|{\mathrm{x}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{j}}\right|$ | ${\beta}_{i}^{\mathrm{Is}}$ |

Non-self-centered inequality | ${\mathrm{X}}^{\mathrm{Ins}}$ | $\frac{2}{\left(n-1\right)\left(\mathrm{n}-2\right)}{\displaystyle \sum}_{\mathrm{i}\ne \mathrm{j},\mathrm{i}\ne \mathrm{k},\mathrm{j}\ne \mathrm{k}}\left|{\mathrm{x}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{k}}\right|$ | ${\beta}_{i}^{\mathrm{Ins}}$ |

Experiment 1 | Experiment 2 | |
---|---|---|

Participants | 148 | 305 |

Sessions | 6 | 16 |

Dictator Games per participant | 10 × N = 2 | 20 × N = 4 |

10 × N = 4 | 1 × N = 2 | |

Average age (years) | 23.4 (SD = 5.0) | 23.5 (SD = 4.3) |

Gender (% male) | 55.0% | 51.2% |

Average earnings (€) | 1.06 (SD = 0.41) | 3.53 (SD = 1.54) |

**Table 3.**Descriptive statistics and material payoffs for the two- and four-player DGs in Experiment 1.

Game No. | Prop. That Chose 1. | Subjects That Played the DG | Material Payoffs Option 1 | Material Payoffs Option 2 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Self | Other 1 | Other 2 | Other 3 | Self | Other 1 | Other 2 | Other 3 | |||

1 | 0.39 | 148 | 0 | 24 | 28 | 2 | ||||

2 | 0.69 | 148 | 8 | 6 | 4 | 30 | ||||

3 | 0.61 | 148 | 26 | 30 | 30 | 0 | ||||

4 | 0.64 | 148 | 26 | 26 | 30 | 0 | ||||

5 | 0.24 | 148 | 0 | 28 | 14 | 14 | ||||

6 | 0.39 | 148 | 28 | 0 | 0 | 28 | ||||

7 | 0.70 | 148 | 30 | 0 | 0 | 0 | ||||

8 | 0.78 | 148 | 30 | 0 | 18 | 20 | ||||

9 | 0.48 | 148 | 0 | 30 | 10 | 10 | ||||

10 | 0.69 | 148 | 8 | 6 | 0 | 30 | ||||

11 | 0.70 | 148 | 20 | 24 | 30 | 30 | 2 | 30 | 30 | 30 |

12 | 0.55 | 148 | 12 | 26 | 10 | 6 | 30 | 0 | 0 | 0 |

13 | 0.84 | 148 | 4 | 16 | 2 | 30 | 0 | 28 | 26 | 26 |

14 | 0.84 | 148 | 28 | 8 | 30 | 2 | 18 | 16 | 18 | 16 |

15 | 0.92 | 148 | 10 | 16 | 12 | 14 | 0 | 16 | 28 | 0 |

16 | 0.44 | 148 | 28 | 4 | 28 | 30 | 28 | 6 | 6 | 6 |

17 | 0.74 | 148 | 28 | 4 | 0 | 30 | 26 | 26 | 22 | 24 |

18 | 0.75 | 148 | 22 | 22 | 26 | 22 | 2 | 0 | 30 | 22 |

19 | 0.50 | 148 | 8 | 8 | 10 | 12 | 28 | 16 | 4 | 2 |

20 | 0.58 | 148 | 10 | 30 | 18 | 8 | 0 | 30 | 30 | 28 |

Game No. | Prop. That Chose 1. | Subjects That Played the DG | Material Payoffs Option 1 | Material Payoffs Option 2 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Self | Other 1 | Other 2 | Other 3 | Self | Other 1 | Self | Other 1 | |||

1 | 0.30 | 305 | 10 | 210 | 10 | 20 | 10 | 320 | 320 | 320 |

2 | 0.65 | 305 | 10 | 320 | 320 | 320 | 10 | 100 | 10 | 10 |

3 | 0.27 | 305 | 40 | 290 | 290 | 300 | 80 | 10 | 20 | 290 |

4 | 0.71 | 305 | 50 | 20 | 320 | 20 | 10 | 280 | 280 | 290 |

5 | 0.74 | 281 | 60 | 20 | 230 | 60 | 10 | 310 | 320 | 310 |

6 | 0.12 | 305 | 60 | 60 | 60 | 60 | 160 | 10 | 320 | 320 |

7 | 0.06 | 305 | 60 | 60 | 90 | 80 | 180 | 160 | 20 | 320 |

8 ¹ | 0.82 | 45 | 100 | 0 | 0 | 0 | 50 | 50 | 0 | 0 |

9 | 0.17 | 305 | 110 | 100 | 90 | 100 | 170 | 290 | 10 | 320 |

10 | 0.20 | 284 | 120 | 120 | 130 | 150 | 170 | 320 | 260 | 20 |

11 | 0.89 | 305 | 140 | 30 | 320 | 300 | 40 | 40 | 40 | 50 |

12 | 0.16 | 305 | 160 | 160 | 180 | 250 | 320 | 10 | 20 | 20 |

13 | 0.14 | 305 | 160 | 210 | 200 | 200 | 300 | 10 | 320 | 30 |

14 | 0.95 | 305 | 170 | 290 | 10 | 310 | 10 | 10 | 10 | 10 |

15 | 0.24 | 305 | 200 | 310 | 280 | 260 | 320 | 30 | 20 | 10 |

16 | 0.84 | 305 | 220 | 210 | 220 | 210 | 220 | 310 | 120 | 10 |

17 | 0.07 | 305 | 220 | 310 | 10 | 20 | 240 | 260 | 250 | 260 |

18 | 0.33 | 305 | 250 | 220 | 10 | 320 | 280 | 40 | 20 | 30 |

19 | 0.41 | 305 | 280 | 280 | 320 | 250 | 310 | 20 | 10 | 20 |

20 | 0.92 | 305 | 310 | 310 | 300 | 300 | 200 | 20 | 10 | 40 |

21 | 0.73 | 305 | 320 | 10 | 10 | 10 | 230 | 240 | 100 | 320 |

Parameter | Prior Distribution | Description |
---|---|---|

$\mathrm{mean}\left({\beta}_{i}^{\mathrm{Se}}\right)$ | $N\left(0,5\right)$ | The mean of social motives received normal priors centered around zero, with a variance of five. The relatively small variance eases estimation, and reflect a conservative attitude with respect to the magnitude of motives. |

$\mathrm{mean}\left({\beta}_{i}^{\mathrm{Is}}\right)$ | $N\left(0,5\right)$ | |

$\mathrm{mean}\left({\beta}_{i}^{\mathrm{Ins}}\right)$ | $N\left(0,5\right)$ | |

$\text{}{\Sigma}^{-1}$ | $\text{}Wishart\left(4,\text{}I\left(4\right)\right)$ | The inverse covariance-matrix received a Wishart prior, evaluated at four degrees of freedom. This balances the lack of informative-ness regarding the level of heterogeneity, and regarding the strength of associations |

${\tau}_{c}$ | Uniform [0,5] | The variance of the combined evaluation error has a positive, uniform prior truncated at five to reflect uncertainty on the degree of model misfit. The truncation reflects a “common-sense” plausible maximum for the amount of error. |

Experiment 1 (N = 148) | Experiment 2 (N = 305) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model Fit | CCR | Model Fit | CCR | ||||||

All Games | Only N = 2 | Only N = 4 | All Games | ||||||

Models and Constraints | DIC | pD | Post. M (SD) | Post. M (SD) | Post. M (SD) | DIC | pD | Post. M (SD) | |

M_{0}: | ${\beta}_{i}^{Se}={\beta}_{i}^{Is}={\beta}_{i}^{Ins}=0$ | 2429 | 0.9 | 0.737 (0.008) | 0.747 (0.010) | 0.727 (0.010) | 6335 | 1.0 | 0.656 (0.006) |

M_{1}: | ${\beta}_{i}^{Is}={\beta}_{i}^{Ins}=0$ | 2084 | 119.1 | 0.792 (0.007) | 0.810 (0.009) | 0.777 (0.010) | 4973 | 272.4 | 0.755 (0.005) |

M_{2}: | ${\beta}_{i}^{Ins}=0$ | 1637 | 214.2 | 0.852 (0.007) | 0.878 (0.007) | 0.815 (0.009) | 4699 | 476.9 | 0.780 (0.005) |

M_{3}: | 1623 | 278.1 | 0.860 (0.006) | 0.881 (0.008) | 0.838 (0.010) | 4173 | 708.4 | 0.822 (0.005) |

Experiment 1 (N = 148) | Experiment 2 (N = 305) | ||||
---|---|---|---|---|---|

M_{2} | M_{3} | M_{2} | M_{3} | ||

Post. M (SD) | Post. M (SD) | Post. M (SD) | Post. M (SD) | ||

Motives: | mean(${\beta}_{i}^{\mathrm{Se}}$) | −0.014 (0.049) | −0.017 (0.050) | 0.120 (0.022) | 0.111 (0.020) |

mean(${\beta}_{i}^{\mathrm{Is}}$) | −0.310 (0.029) | −0.319 (0.030) | −0.068 (0.013) | −0.092 (0.012) | |

mean(${\beta}_{i}^{\mathrm{Ins}}$) | 0.045 (0.034) | −0.110 (0.012) | |||

sd(${\beta}_{i}^{\mathrm{Se}}$) | 0.483 (0.041) | 0.492 (0.042) | 0.358 (0.019) | 0.321 (0.017) | |

sd(${\beta}_{i}^{\mathrm{Is}}$) | 0.233 (0.021) | 0.239 (0.021) | 0.177 (0.011) | 0.177 (0.010) | |

sd(${\beta}_{i}^{\mathrm{Ins}}$) | 0.266 (0.029) | 0.171 (0.010) | |||

cor(${\beta}_{i}^{\mathrm{Se}}$,${\beta}_{i}^{\mathrm{Is}}$) | −0.072 (0.134) | −0.055 (0.138) | −0.260 (0.084) | −0.468 (0.067) | |

cor(${\beta}_{i}^{\mathrm{Se}}$,${\beta}_{i}^{\mathrm{Ins}}$) | −0.399 (0.122) | −0.282 (0.075) | |||

cor(${\beta}_{i}^{\mathrm{Is}}$,${\beta}_{i}^{\mathrm{Ins}}$) | 0.241 (0.136) | 0.472 (0.063) | |||

Errors: | sd(ε_{B}- ε_{A}) | 0.329 (0.014) | 0.315 (0.014) | 0.637 (0.017) | 0.443 (0.015) |

Linear Models (Original) | Non-Linear Models | ||||
---|---|---|---|---|---|

M_{2} | M_{3} | M_{2}* | M_{3}* | ||

Post. M (SD) | Post. M (SD) | Post. M (SD) | Post. M (SD) | ||

Motives: | mean(${\beta}_{i}^{\mathrm{Se}})$ | 0.120 (0.022) | 0.111 (0.020) | 0.140 (0.021) | 0.119 (0.020) |

mean(${\beta}_{i}^{\mathrm{Is}})$ | −0.068 (0.013) | −0.092 (0.012) | −0.124 (0.018) | −0.116 (0.014) | |

mean(${\beta}_{i}^{\mathrm{Ins}})$ | −0.110 (0.012) | −0.107 (0.010) | |||

sd(${\beta}_{i}^{\mathrm{Se}})$ | 0.358 (0.019) | 0.321 (0.017) | 0.346 (0.018) | 0.318 (0.016) | |

sd(${\beta}_{i}^{\mathrm{Is}})$ | 0.177 (0.011) | 0.177 (0.010) | 0.248 (0.017) | 0.187 (0.013) | |

sd(${\beta}_{i}^{\mathrm{Ins}})$ | 0.171 (0.010) | 0.127 (0.009) | |||

cor(${\beta}_{i}^{\mathrm{Se}}$,${\beta}_{i}^{\mathrm{Is}})$ | −0.260 (0.084) | −0.468 (0.067) | −0.542 (0.061) | −0.638 (0.056) | |

cor(${\beta}_{i}^{\mathrm{W}}$,${\beta}_{i}^{\mathrm{Ins}})$ | −0.282 (0.075) | −0.279 (0.088) | |||

cor(${\beta}_{i}^{\mathrm{Is}}$, ${\beta}_{i}^{\mathrm{Ins}})$ | 0.472 (0.063) | 0.526 (0.077) | |||

Exponent: | $\delta $ | 1 | 1 | 0.184 (0.023) | 0.513 (0.078) |

Errors: | sd(ε_{B}- ε_{A}) | 0.637 (0.017) | 0.443 (0.015) | 0.186 (0.005) | 0.143 (0.005) |

Model fit: | DIC | 4698 | 4143 | 4472 | 4126 |

pD | 454.7 | 647.8 | 481.2 | 648.9 |

**Table 9.**Frequentist Estimates of the Population Distribution of Social Motives in Low-status and High Status DGs.

Full Sample | Low Status DGs | High Status DGs | ||
---|---|---|---|---|

Coef. (SE) | Coef. (SE) | Coef. (SE) | ||

Motives: | mean(${\beta}_{i}^{\mathrm{Se}}$) | 0.128 (0.023) | 0.113 (0.027) | 0.233 (0.026) |

mean(${\beta}_{i}^{\mathrm{Ins}}$) | −0.079 (0.013) | 0.054 (0.038) | −0.193 (0.013) | |

sd(${\beta}_{i}^{\mathrm{Se}}$) | 0.365 (0.020) | 0.306 (0.028) | 0.401 (0.022) | |

sd(${\beta}_{i}^{\mathrm{Ins}}$) | 0.167 (0.014) | 0.332 (0.030) | 0.111 (0.020) | |

cor(${\beta}_{i}^{\mathrm{Se}},{\beta}_{i}^{\mathrm{Ins}}$) | −0.356 (0.087) | 0.503 (0.077) | −0.891 (0.113) | |

Errors: | sd(ε_{A} − ε_{B}) | 0.651 (0.017) | 0.333 (0.026) | 0.570 (0.021) |

Number of choices | 6100 | 2766 | 3334 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Macro, D.; Weesie, J.
Inequalities between Others Do Matter: Evidence from Multiplayer Dictator Games. *Games* **2016**, *7*, 11.
https://doi.org/10.3390/g7020011

**AMA Style**

Macro D, Weesie J.
Inequalities between Others Do Matter: Evidence from Multiplayer Dictator Games. *Games*. 2016; 7(2):11.
https://doi.org/10.3390/g7020011

**Chicago/Turabian Style**

Macro, David, and Jeroen Weesie.
2016. "Inequalities between Others Do Matter: Evidence from Multiplayer Dictator Games" *Games* 7, no. 2: 11.
https://doi.org/10.3390/g7020011