Experimental Design Details
Sample. Participants are invited to an incentivized Qualtrics survey on economic decision making. We recruit participants into three groups that we refer to as Players 1, 2, and 3. For the main analysis using data from Player 2s, we sample US born and resident Black individuals on Prolific as participants. On top of the main analysis sample, we also recruit White US residents as Player 1s, and Black, Hispanic and White people born and resident in the US as Player 3s. Both Player 1 and Player 3 are real individuals, but in the analysis we exclusively focus on Player 2 behavior. We heavily oversample Players 2. All players play two experimental games and Player 3’s race is kept fixed within subject and their role is fully passive.
Demographics and priming. In the survey, participants fill out a demographic survey. A randomly selected part of the sample then fills out a module on their own experience of discriminatory behavior in general and in specific situations such as in school or at the workplace (7 questions). The aim is to increase the salience of the topic of discrimination. The remaining part of the sample fills out this module after the main experimental games are played. To make sure that the participants spend approximately the same amount of time answering questions before the main task, we also manipulate whether a corresponding number of demographic questions is asked at the beginning or at the end. This ensures that the cognitive effort exerted before the main task is equalized between the primed and not primed individuals.
Experimental games. We then introduce the two games. A Complicity Game and an accompanying Dictator Game.
Complicity Game (CG). In the Complicity Game, there are three players. Player 1, a majority (White) US resident has an option to affect own payoff and that of Player 3, a minority (Black or Hispanic) or a majority (White) US resident. We randomize Player 3’s race. Player 1 can either choose that the payoffs in USD are (5, 5) or (4.5, 3.5) for Players 1 and 3, respectively. Player 3 is always passive. Unlike in a dictator game, there is also another player, Player 2. This person is always a Black US resident. Player 2 can further affect the payoff of Player 3, while can no longer affect Player 1's payoff. Player 2 decides using a strategy method, conditional on Player 1 choices. We first ask Player 2 to make a decision in a situation in which (4.5, 3.5) was chosen by Player 1. We set the payoffs such that they allow for the entire spectrum of reactions: helping the victim at own cost, remaining indifferent by maintaining status quo, or even acting in a hostile way, in both costless and costly ways. The options for Player 2 are:
(4, 4.5) - very costly help
(4.5, 4) - costly help
(5, 3.5) - status quo
(5, 3) - costless harm
(4.5, 2) - costly harm
(4, 0.5) - very costly harm
In all cases, the payoff of Player 1 cannot be further affected and remains at $4.5.
Second, we ask Player 2 to make a decision in a situation in which (5, 5) was proposed by Player 1. In this situation we allow Player 2 to either maintain the equal allocation (5, 5), or to harm Player 3 at a cost (4.5, 3.5). Regardless of the choice, payoff of Player 1 remains unaffected at $5.
Dictator game (DG). A Dictator Game closely follows the design of the Complicity Game. The key difference is that Player 1 is absent. All other components of the game remain identical, including the choice sets for Player 2, the dictator. Player 2 thus decides within a set of available allocations.
Order of games. We are exclusively interested in reactions to a harmful action of Player 1 against Player 3. We randomize on an individual level the order in which Player 2 makes decisions in the Complicity Game and the Dictator Game. Player 2 first responds (in a random order) to a situation in which Player 1 harmed Player 3 (i.e., $4.5 for Player 1 and $3.5 for Player 3), and to a DG with an equivalent choice set for Player 2. Then, after both decisions are made, Player 2 responds to a situation in which Player 1’s choice resulted in an equal split of (5, 5) or its DG equivalent.
Matching and payoff relevance. Player 2’s are informed that only one of their choices is going to be payoff relevant. Namely, it is either a randomly selected DG or a CG conditional on the true behavior of a matched Player 1. A randomly selected decision is then payoff relevant for a matched Player.
Beliefs. We elicit incentivized beliefs about the number of Player 1’s playing the harming (4.5, 3.5) option. We ask Player 2’s how many Player 1’s out of 10 randomly selected they believe selected this option. Player 2 gets rewarded based on how close their response is to the actual data. We use this data to ensure that the participants assign a positive probability for occurrence of both options being played by at least one Player 1. Otherwise, the incentives in the CG may not apply, which may affect Player 2 behavior. We report our results for both the full sample and the sample of individuals reporting positive probability of both options being selected by at least one Player 1.
Attention check. We want to make sure our sample pays attention to the instructions. We use a simple attention check in a set of demographic questions that asks respondents to fill out a specific response on a likert scale.
Comprehension check. After reading the instructions of each of the first two games (i.e., the reaction to the harmful action of Player 1 and an equivalent DG), before playing them, respondents get prompted with a comprehension check, asking about the number and/or role of the players in the game in question. Those who fail have to read the instructions again and get prompted the same comprehension check. If they fail again they’re excluded from the study and the analysis.
Manipulation check. To further check their attentiveness to the instructions, we ask our participants at the end of the survey about the race of Player 3 and Player 1. We will present our results for the full sample but also study whether the results differ for those who answer the checks correctly. This question is not incentivized.
Outcomes.
Primary:
Comparison of the payoffs offered to Player 3 in the two games (CG_{p3} and DG_{p3}). We exclusively compare games in which P2 gets prompted with a situation where discrimination happened (Player 1 played (4.5, 3.5)) and dictator games which have the same payoff structure. The outcome is measured separately by the identity of Player 3 (Black ingroup vs. Hispanic outgroup vs. White outgroup). Unless we detect significant order effects between CG and DG behavior, we focus on within-subject comparison. In case of significant order effects, we use the first decision made by an individual in a between-subject fashion.
Secondary:
We construct two dummy variables: prosocial and harmful behavior. We also study another measure of differences between the games by subtracting these two binary variables. Since norms may be looser for CG, we also look at differences in payoffs distribution between CG and DG (KS test).
Primary hypotheses:
Group Identity and Behavioral Differences:
First, we test for differences in Player 2's behavior across the Complicity Game and the Dictator Game separately for each Player 3 group (ingroup, minority outgroup, or majority outgroup).
Null hypothesis: There are no differences in behavior across the two games.
Alternative hypothesis: Behavior differs, either toward more restorative or more harmful actions.
In cases where we detect a null result for a given Player 3 group at the mean level, we additionally compare the equality of distributions across the two games using a KS test.
Minority vs. White Player 3:
Second, we test whether the differences in Player 2's behavior across the Complicity Game and the Dictator Game when the mistreated Player 3 belongs to a minority group (Black or Hispanic) differ from the differences in behavior across the two games when the mistreated Player 3 is White.
Null hypothesis: There are no differences in behavior across the two games between situations where Player 3 is from a minority group and situations where Player 3 is White.
Alternative hypothesis: The behavior differs, either toward more restorative or more harmful actions, depending on the group identity of Player 3.
Multiple hypothesis testing:
To address multiple hypothesis testing for the race treatment, we correct p-values using the method developed by Barsbai et al. (2020), which extends the procedure of List et al. (2019) by allowing for corrections in multivariate regression models. We apply these corrections separately to the first set of three hypotheses and the second set of two hypotheses.
Secondary hypotheses:
Effect of Priming:
We test whether priming Player 2 with their own experiences of discrimination affects the differences in behavior across the Complicity Game and the Dictator Game.
Heterogeneity by Socio-Demographic Characteristics:
We test whether the effects of priming and the differences in behavior across the two games vary based on socio-demographic characteristics such as gender, education, age, and income. For continuous variables (e.g., age, income), the sample is split at the median to facilitate subgroup analysis.
Additional Secondary Hypotheses:
We examine changes in binarized helping and harming behaviors as secondary outcomes.
Controls and Robustness Checks:
In all regressions, we control for demographic characteristics and the order of treatments. Robustness checks include sensitivity analyses for including or excluding covariates. We also implement a two-step LASSO procedure to select control variables.
Standard Errors:
For within-subject data, standard errors are clustered at the individual level (see detailed primary outcome description). For between-subject variation, we report Huber-White robust standard errors.
Full survey: see attached pdf.