1. Introduction
Antisocial behavior is ubiquitous in the real world and often results in large efficiency costs (Gangadharan et al., Reference Gangadharan, Grossman, Vecci and Zimmermann2020). Over the last two decades, while more heterogenous and smaller than the experimental research on prosocial behavior, there has been a proliferation of experimental studies attempting to help us better understand the incidence and causes of antisocial behavior.Footnote 1 In this article, we present two meta-analyses on antisocial behavior in economic experiments, where antisocial behavior is defined as the act of reducing or destroying other players’ income without any prospects of pecuniary gains.Footnote 2
Our general meta-analysis includes 95 studies (24,086 participants) and 359 observations (treatments) in total using laboratory, online, and field experiments across 38 countries. It considers experiments where antisocial behavior can be identified in the Joy-of-Destruction (JoD) and money-burning (MB) games, vendetta games, contests, allocation and coordination games, and social dilemmas with counter-punishment. As we find significant heterogeneity across the studies, including within game classes, we also conduct a second meta-analysis in which we focus only on JoD/MB experiments, for which we have the largest number of observations, 51 studies and around 16,784 participants and 222 observations in total.Footnote 3
To understand what general lessons we can glean from experiments on antisocial behavior, we examine both the extensive and the intensive margins of antisocial behavior – that is, both the frequency of destruction and average destruction rates. In determining what drives individuals to act antisocially, we evaluate whether antisocial behavior is motivated by income inequality, group identity, social observability, pressure by authority and whether interactions are one-shot or repeated. We also assess the impact of researchers’ design choices by including methodological variables that capture the impact of using the strategy method, whether the study was conducted in a laboratory, online or in the field, or whether subjects have worked for their earnings (i.e., house money effects).
Overall, we find that subjects engage in payoff destruction in about 30% of cases and destroy on average 20% of the maximum amount that can be destroyed. In both meta-analyses, procedural fairness and being observed by others reduce the frequency of antisocial behavior. Surprisingly, field experiments consistently display more antisocial behavior than in laboratory experiments, while this is at least as high or higher in online experiments than in laboratory experiments. We also find that the strategy method biases antisocial behavior upward. However, we robustly do not find evidence for a positive publication bias correlated with higher destructive behavior, either in the general meta-analysis or in relation to JoD/MB experiments. The level of antisocial behavior differs significantly across games, with the highest destruction rates observed in vendetta games (60% of all decisions) and the lowest in social dilemmas with counter-punishment (14% of all decisions). In the general meta-analysis specifically, we find evidence that destruction rates are lower among exogenously advantaged subjects. In the JoD/MB meta-analysis specifically, we find evidence of negative discrimination against outsiders, of within-subject designs underestimating destructive behavior, and of more antisocial behavior in one-shot interactions; we also find that, if destruction is costly, its frequency is lower.
The rest of this paper is structured as follows. Section 2 provides an overview of the experimental games included in the meta-analysis. Section 3 describes the methodology we followed in generating and analyzing our dataset. Section 4 reports our results, and section 5 concludes with a discussion of our findings.
2. Experimental games included in the meta-analysis
We focus on experimental studies in which subjects decide to reduce the earnings of others without the prospect of financial gains, as opposed to, for example, games in which destroying money is entirely or partially profit-maximizing. By this definition, the papers included in the meta-analysis can be classified into six classes of economic games: JoD/MB games, vendettas, allocation games, coordination games, contests, and social dilemmas with counter-punishment.Footnote 4
Joy-of-Destruction/ money-burning games. In both JoD and MB games, subjects can choose to reduce the other players’ income with or without a cost to themselves (Abbink & Herrmann, Reference Abbink and Herrmann2011; Abbink & Sadrieh, Reference Abbink and Sadrieh2009; Zizzo, Reference Zizzo2003; Zizzo & Oswald, Reference Zizzo and Oswald2001). The two sets of games are identical in structure, and other than JoD games, they have equal endowments. This is to remove inequity aversion as an explanation of destructive behavior. In either class of games, there are no financial gains to this act; a payoff-maximizing, rational agent would choose not to engage in “money burning.” Thus, any income reduction corresponds to antisocial behavior, for example, due to spite or malice (or inequity aversion, for MB games).Footnote 5 Replications of the JoD/MB games and their variants have consistently supported the finding that individuals are willing to reduce other players’ income, even at a cost to themselves (e.g., Abbink et al., Reference Abbink, Masclet and Mirza2018; Abbink et al., Reference Abbink, Masclet and van Veelen2011; Dickinson & Masclet, Reference Dickinson and Masclet2019; Dickinson et al., Reference Dickinson, Masclet and Peterle2018; Gangadharan et al., Reference Gangadharan, Grossman, Molle and Vecci2019; Gangadharan et al., Reference Gangadharan, Grossman and Vecci2021; Gangadharan et al., Reference Gangadharan, Islam, Ouch and Wang2022; Grosch & Rau, Reference Grosch and Rau2020; Grossman & Komai, Reference Grossman and Komai2013; Sadrieh & Schröder, Reference Sadrieh and Schröder2016, Reference Sadrieh and Schröder2017; Zizzo & Fleming, Reference Zizzo and Fleming2011).
Vendettas. The vendetta game was developed by Bolle et al. (Reference Bolle, Tan and Zizzo2014) and further examined by Umashev (Reference Umashev2019), Sugden and Wang (Reference Sugden and Wang2020), and Cavatorta et al. (Reference Cavatorta, Zizzo and Daoud2023). It studies how an initial act of aggression can lead to socially inefficient feuds. The game involves two players moving alternatingly across a finite number of periods. Each player receives an amount of money or an exogenous percentage of winning a lottery, and at each player’s turn, they can choose to steal their co-player’s money or win probability in blocks of percentage, but at a cost. The game ends if no player steals from each other in two consecutive periods or when both cannot steal any longer. Under self-interest, altruism, reciprocity, or inequality aversion, counter-stealing should not occur in the subgame perfect equilibrium under equal initial endowment (Bolle et al., Reference Bolle, Tan and Zizzo2014).
Allocation games. By allocation games, we refer to variants of the dictator game in which the player chosen as the dictator can decrease the opponent’s earnings without any pecuniary consequences for themselves (Bracht & Zylbersztejn, Reference Bracht and Zylbersztejn2018; García-Gallego et al., Reference García-Gallego, Georgantzis and Ruiz-Martos2019; Sadrieh & Schröder, Reference Sadrieh and Schröder2016). We also include choice experiments, in which subjects can choose between different income allocations among themselves and their opponents (Beckman et al., Reference Beckman, Formby, Smith and Zheng2002; Fehr et al., Reference Fehr, Glätzle-Rützler and Sutter2013). In these games, the decision is considered costless burning if the subject chooses an option in which their partner receives a lower payoff, while they receive a payoff equal to the optimal amount, and costly burning if they receive a payoff less than the optimal amount.
Coordination games. Even though the coordination game class consists of a range of games, we only consider the first-strike game and the mobbing game. In the first-strike game, two or more players accumulate earnings over many rounds, and they can deactivate the opponent in any round. The deactivated player would lose all current earnings and face reduced future payoffs, without any monetary gains to the decision-makers, which makes deactivating a hostile act (Abbink & de Haan, Reference Abbink and de Haan2014; Abbink et al., Reference Abbink, Dong and Huang2021; Simunovic et al., Reference Simunovic, Mifune and Yamagishi2013). In the mobbing game, subjects are divided into groups and can nominate a group member to be “mobbed” (Abbink & Doğan, Reference Abbink and Doğan2019). If the same person is nominated by all other players, that person loses all their earnings. Following the inclusion criteria, we only include treatments in which mobbing players do not gain financially even if mobbing was successful. Because of the nature of the game, destruction decisions in the mobbing game are in terms of group decisions instead of individual decisions.
Contests. We consider two distinct types of contest games for our analysis. The first type involves a standard tournament in which subjects compete for a prize via a real-effort task under piece rate or tournament compensation schemes and then have a chance to underreport other players’ scores (Carpenter et al., Reference Carpenter, Matthews and Schirm2010; Charness, Masclet & Villeval Reference Charness, Masclet and Villeval2014). The second type resembles a gift exchange game in which an employer (principal) offers a wage and a prize to multiple employees (agents) (Falk et al., Reference Falk, Fehr and Huffman2008; Harbring & Irlenbusch, Reference Harbring and Irlenbusch2005; Reference Harbring and Irlenbusch2008; Reference Harbring and Irlenbusch2011). The agents then compete for the chosen prize by paying a cost to exert productive effort and sabotage the effort of others. Each unit of effort increases an agent’s output by one unit, while each unit of sabotage reduces the output of other agents by one unit. In this case, sabotage can be partially explained by self-interest, as agents earn a higher payoff by winning the game (Harbring & Irlenbusch, Reference Harbring and Irlenbusch2005).Footnote 6
Social dilemmas with counter-punishment. This set of games includes experiments where subjects play a social dilemma game in the first stage, followed by a subsequent stage of one round or multiple rounds of punishment and counter-punishment.Footnote 7 The social dilemma stage typically involves the public goods games, prisoner’s dilemmas, trust games, and power-to-take games. In the punishment and counter-punishment stage, in each and every round, subjects can either a) punish whoever they want whether or not they were punished in the previous round (Engel et al., Reference Engel, Kube and Kurschilgen2021; Fehr & Schurtenberger, Reference Fehr and Schurtenberger2018; Nikiforakis & Engelmann, Reference Nikiforakis and Engelmann2011; Nikiforakis et al., Reference Nikiforakis, Noussair and Wilkening2012), or b) only are allowed to punish those who punished them in the previous round (Berná, Reference Berná2013; Campos-Vazquez & Mejia, Reference Campos-Vazquez and Mejia2016; Cinyabuguma et al., Reference Cinyabuguma, Page and Putterman2006; Denant-Boemont et al., Reference Denant-Boemont, Masclet and Noussair2007; Engel et al., Reference Engel, Beckenkamp, Glöckner, Irlenbusch, Hennig-Schmidt, Kube, Kurschilgen, Morell, Nicklish, Normann and Towfigh2014; Kern, Reference Kern2014). The cycles of retaliatory punishment and counter-punishment in these experiments bear a close resemblance to vendettas, especially in the later stages where punishment appears fueled by anger, revenge or nastiness, and often result in very negative outcomes for both subjects (Hopfensitz & Reuben, Reference Hopfensitz and Reuben2009; Nikiforakis & Engelmann, Reference Nikiforakis and Engelmann2011).
3. Methodology
This section outlines our methodology, including study selection criteria, dataset description, analytical procedures, and hypotheses. We start by discussing the inclusion and exclusion criteria used for our literature search (3.1). We then proceed with describing our datasets (3.2) and the analytical methods employed (3.3). Next, we provide a descriptive overview of antisocial behavior for our complete and unweighted dataset (3.4). Finally, we define our variables and present our hypotheses (3.5).
3.1. Inclusion and exclusion criteria
We use economics papers that (a) present novel experimental data and follow the standard experimental economics methodology (i.e., financial incentives, no deception), (b) demonstrate antisocial behavior that involves subjects destroying other players’ income and which is not a profit-maximizing or dominant strategy from the perspective of a purely self-interested agent who cares only about their own payoff from the game, (c) are published journal articles or working papers that were last updated after January 2000, (d) do not (only) have ultimatum game data, which is excluded (see section 2), and (e) are written in the English language.
Based on the first criterion, we excluded experiments studying hypothetical and unincentivized decisions. Papers using the strategy method, such as Dickinson and Masclet (Reference Dickinson and Masclet2019), are included if all decisions are incentivized or at least one randomly chosen decision among them is payoff relevant. We also excluded papers on social dilemmas with only punishment and no counter-punishment because it is difficult to disentangle antisocial preferences with prosocial motives associated with punishment decisions in these contexts.
We also did not include second-price auctions (SPAs), in which an agent who knows he cannot win might feel tempted to raise his bid above his own evaluation to minimize the winner’s profit because we could not establish a clear-cut rule to disentangle spiteful bidding from overbidding. The literature on overbidding in SPAs presents various explanations for overbidding behavior but lacks consensus on their dominance. While some studies investigate nonstandard preferences such as the “joy of winning” or “spite” (Georganas et al., Reference Georganas, Kagel and Levin2017; Sheremeta, Reference Sheremeta2010; Tan, Reference Tan2020) in SPAs, bounded rationality – specifically, the illusion that overbidding enhances winning probabilities with minimal cost – emerges as a compelling explanation of overbidding behavior (Cooper & Fang, Reference Cooper and Fang2008; Kagel, Reference Kagel, Kagel and Roth1995). Cognitive abilities, computation, or strategic mistakes have been found to play a key role in shaping overbidding behavior (Georganas et al., Reference Georganas, Kagel and Levin2017; Kagel, Reference Kagel, Kagel and Roth1995; Kagel et al., Reference Kagel, Harstad and Levin1987; Kagel & Levin, Reference Kagel and Levin1993; Lee et al., Reference Lee, Lee and Rhee2020; Li, Reference Li2017; Schneider & Porter, Reference Schneider and Porter2020). As have experience and learning (Gwin et al., Reference Gwin, List and Price2005; Garratt, Walker & Wooders, Reference Garratt, Walker and Wooders2012), level-k and cursed equilibrium (Brocas et al., Reference Brocas, Carrillo and Kodaverdian2017; Crawford & Iriberri, Reference Crawford and Iriberri2007), risk aversion (Andreoni, Che, Kim, Reference Andreoni, Che and Kim2007), feedback mechanisms (Harstad, Reference Harstad2000), and information provision (Zhang et al., Reference Zhang, Shang and Tang2019). Given the diverse explanations for overbidding and the challenges in isolating antisocial preferences from other plausibly more dominant motives, we opted to exclude SPAs from our analysis.
3.2. Literature search and dataset
Figure 1 summarizes our selection process and the number of studies excluded at each step. Details of each study are presented in Online Appendix B. Four main sources were utilized to identify relevant studies on antisocial behavior in noncooperative games: EconLit, Scopus, Web of Science, and Google Scholar. All databases were searched using combinations of keywords on types of game (JoD, MB, vendetta, contests/tournaments/competition, lotteries, riots), types of antisocial behavior or behavioral reason behind these actions (sabotage, spite, malice, envy), as well as other descriptive aspects of the studies (economic, experiment, game, game theory). The search phrase used was experiment* AND economic AND antisocial* AND game AND (destroy* OR burn* OR nast* OR sabotage* OR contest OR competition OR tournament OR lottery OR riots OR spite* OR malice*). The search was limited to economic journal articles and working papers written in English published from 2000 to 2020, which yielded 2,000–5,000 hits on EconLit, Scopus, and Web of Science. An independent search on Google Scholar using the same combination of keywords resulted in 7,470 hits, of which Google Scholar displayed the first thousand. To identify papers on social dilemma games with counter-punishment produced from the year 2000 onward, we also conducted a search using the search phrase counter punishment AND antisocial AND experiment on the same databases, which returned 488–692 results.
Fig. 1 Flow diagram of the literature search
To supplement the electronic search, we conducted a manual search through the reference sections of all papers included in the first stage. Relevant papers based on title and abstract were then extracted for full-text screening. We searched studies using Google Scholar’s “cited by” function to find further research that did not contain the above keywords or did not explicitly refer to spiteful preferences as antisocial behavior and thus was not included in the initial search, identifying a further 23 studies. We also posted a topic in the ESA Experimental Methods Discussion group calling for more published and unpublished papers, and we received suggestions of 27 studies, among which 5 were added to our list as they met the inclusion criteria. All searches and screening were conducted between August and November 2020, with one exception. Specifically, on July 11, 2023, we checked whether any unpublished paper had been published by then: This was done to minimize any bias arising from extended publication lags in Economics. For instance, working papers posted online between 2018 and 2020 might not have had sufficient time for acceptance for publication and published online by the end of 2020. If they did get published, the analysis presented in the main text of this paper includes the data as presented in the published version.Footnote 8
For all articles, we first attempted to infer the necessary information from the test statistics and/or figures provided. If this was not possible, we contacted the authors to obtain the primary data between July and October 2021. After receiving data from 60 of the 76 sets of contacted authors, we ended up with sufficient measures for 95 studies. Table 1 summarizes the distribution of the included studies categorized by types of games and geographic region. Overall, our dataset includes 95 studies (24,086 participants) and 359 observations (treatments) in total using laboratory, online, and field experiments across 38 countries. Specifically, 54 studies (17,654 subjects) examined destruction in JoD/MB and vendetta games, 20 (2,923 subjects) examined social dilemma with counter-punishment opportunities, and the rest (21 studies, 3,509 subjects) looked at contest, allocation, and coordination games. The majority of experiments are conducted in Europe (57 studies, 15,575 subjects), followed by Asia-Pacific (18 studies, 4,544 subjects), America (16 studies, 2,867 subjects), and Africa (4 studies, 1,100 subjects). Lastly, of the 95 studies, 18 were unpublished at the time of the July 2023 check.
Table 1 Summary of included articles by classes of games
Notes: The coordination game class consists of the first-strike and mobbing games. The allocation game class includes dictator, double-dictator, heaven-dictator, allocation, and voting games. N refers to the number of observations.
Our data is aggregated to the player type within a treatment, and an “observation” is defined as each of these treatments by type. For example, if, within a treatment, subjects are randomly assigned into Low- and High-income categories and the study reports sufficient data, we coded the treatment into four observations – High versus High, High versus Low, Low versus High, and Low versus Low. If, in the same treatment, subjects make decisions against other players from the same group and from a different group, we separated the treatment into two observations – Ingroup and Outgroup. If there is no type, we have one observation per treatment. We use n to refer to the number of these observations and k to refer to the number of studies.
3.3. Analytical methods
Following Gerlach et al. (Reference Gerlach, Teodorescu and Hertwig2019), we use two standardized measures to compare the frequency and magnitude of antisocial behavior across diverse game settings.
Mean destruction decision rate (
${M_{dd}}$) measures the average percentage of times subjects engaged in destruction. Specifically, we calculate the mean destruction decision rate by dividing the number of decisions in which subjects decide to destroy other players’ income by the total number of decision opportunities. Thus, it captures the extensive margin of antisocial behavior.
\begin{equation*}{M_{dd}} = \frac{{Number\,of\,destruction\,decisions}}{{Total\,number\,of\,opportunities\,to\,destroy}}\end{equation*} Mean destruction rate (
${M_{dr}}$) measures the average percentage of income subjects destroyed relative to the maximum amount that they could destroy. Specifically, it is calculated by subtracting the mean amount of income subjects destroyed by the equilibrium level of destruction determined by the game and dividing the result by the maximum amount of income subjects were allowed to destroy. Thus, it measures how much subjects are willing to destroy or the intensive margin of destruction.
\begin{equation*}{M_{dr}} = \frac{{Amount\,destroyed - Equilibrium\,destruction}}{{Maximum\,amount\,allowed\,to\,destroy}}\end{equation*}To analyze the two continuous dependent variables, we treat them as individual “effect sizes.” We first use random-effects meta-analysis procedures to determine the average level of antisocial behavior for our full sample and for the subsamples based on game classes, separately for Mdd and Mdr. This type of meta-analysis allows the true effects to vary between studies by assuming that they have a normal distribution around a mean effect (DerSimonian & Laird, Reference DerSimonian and Laird1986; Hedges, Reference Hedges1983; Hedges & Vevea, Reference Hedges and Vevea1998). These are simply aggregated estimates for the overall level of antisocial behavior in the relevant samples; they do not control for independent variables. The procedure weighs each observation by the inverse of its standard error, thus assigning more importance to results from studies with larger samples and smaller deviation from the mean (Whitehead & Whitehead, Reference Whitehead and Whitehead1991).
Random-effects meta-regressions allow us to include independent variables in the analysis and thus explain the between-study heterogeneity as a function of moderators (Berlin & Antman, Reference Berlin and Antman1994; Berkey et al. Reference Berkey, Hoaglin, Mosteller and Colditz1995; Thompson & Higgins, Reference Thompson and Higgins2002). These models account for potential additional variability unexplained by the included moderators by assuming that the true effects follow a normal distribution around the linear predictor (Harbord & Higgins, Reference Harbord and Higgins2008; Thompson & Sharp, Reference Thompson and Sharp1999). They can be considered either an extension to fixed-effects meta-regression that allows for residual heterogeneity or an extension to random-effects meta-analysis that includes study-level covariates and other controls.
3.4. Overview of the complete dataset
Our dataset contains a total of 359 observations (95 studies), including 346 observations (90 studies) for the destruction decisions and 326 observations (82 studies) for the destruction rate. Table 2 reports the descriptive statistics for our complete set of variables based on the number of observations for the destruction decision rate (346 observations). On average, subjects reduced their co-players’ income in 30% of all destruction opportunities and destroyed approximately 20% of the maximum amount that could be destroyed. In total, 61% of our observations examine antisocial behavior in JoD/MB games, and 85% are from published studies. Figure 2 depicts the distributions of our outcome variables, showing a considerable variation across studies.
Fig. 2 Distribution of antisocial behavior
Table 2 Descriptive statistics
Notes: Data is unweighted. N refers to the number of observations. Destruction rates are available for fewer observations than destruction decision rates.
Table 3 highlights how antisocial behavior differs across classes of games. The highest destruction is observed in the vendetta game, where subjects engaged in payoff destruction in 60% of all decisions and destroyed 51% of the maximum amount. In contrast, antisocial behavior is lowest in social dilemmas, with only 14% of destruction decisions and 6% of the upper cap destroyed via punishment and counter-punishment. This indicates that the difference in game contexts might have induced subjects toward feuding in vendettas and cooperating in social dilemmas, thus lowering destruction in the latter case (e.g., Abbink et al., Reference Abbink, Masclet and van Veelen2011; Bolle et al., Reference Bolle, Tan and Zizzo2014; Ferraro & Vossler, Reference Ferraro and Vossler2010). It is also worthwhile noting that reported destruction rates are unconditional, implying considerably higher destruction rates by those who choose to destroy. The dependence of antisocial behavior on its context, and the interpretation of the summary statistics, are further discussed in section 5.
Table 3 Antisocial behavior by classes of games
Notes: Data is unweighted.
Figures 3 and 4 provide a breakdown of the data by region and type of experiments conducted. Figure 3 shows that antisocial behavior seems to be highest among field experiments, while Fig. 4 seems to suggest more antisocial behavior in Africa.
Fig. 3 Antisocial behavior by experiment type
Fig. 4 Antisocial behavior by geographic region
3.5. Independent variables and hypotheses
This subsection presents our hypotheses for the effects of potential moderators and experimental settings, namely inequality, group identity, observability, cost, and house money effect, on antisocial behavior, based on economics theories and experimental evidence. We then present the methodological and other variables to be included in the main regression analysis. Table 4 presents the complete set of independent variables used in our analysis.
Table 4 List of independent variables
Inequality and procedural fairness. In line with the theoretical and experimental literature on inequality aversion (e.g., Abbink et al., Reference Abbink, Masclet and Mirza2018, Reference Abbink, Masclet and van Veelen2011; Charness & Rabin, Reference Charness and Rabin2002; Fehr & Schmidt, Reference Fehr and Schmidt1999; Gangadharan et al., Reference Gangadharan, Grossman and Vecci2021; Grosch & Rau, Reference Grosch and Rau2020; Zizzo, Reference Zizzo2003; Zizzo & Oswald, Reference Zizzo and Oswald2001) we predict that subjects would behave more antisocially when they are exogenously disadvantaged in terms of income relative to when they are not.Footnote 9 This literature also shows that agents care about the procedure by which earnings are obtained – that is, they care about procedural fairness, and thus would behave more antisocially if the income-generating process is unfair.Footnote 10
Hypothesis 1 (H1): Subjects make antisocial decisions less often and destroy less income when (a) they play against a more disadvantaged player rather than an advantaged player or when there is no inequality, and (b) when there is procedural fairness.
Group identity. The theory of social identity predicts that when placed in groups, regardless of whether they are natural or artificially induced, people tend to favor the ingroup at the expense of the outgroup (e.g., Akerlof & Kranton, Reference Akerlof and Kranton2000; Bauer et al., Reference Bauer, Chytilová and Miguel2020; Chen & Li, Reference Chen and Li2009; Hargreaves Heap & Zizzo, Reference Hargreaves Heap and Zizzo2009; Tajfel, Reference Tajfel and Tajfel1978; Tajfel et al., Reference Tajfel, Turner, Austin, Worchel, Hatch and Schultz1979). Following this literature, we hypothesize that antisocial behavior would be lower against outgroup members relative to groups with no group identity manipulation. As the existing literature on ingroup versus outgroup effects primarily focuses on ingroup favoritism (alias prosocial behaviors) and antisocial hostilities directed at outgroup members, we do not make predictions on antisocial behavior directed toward ingroup members.
Hypothesis 2: The frequency and extent of antisocial behavior is higher against outgroup subjects than under no-group identity manipulation (negative discrimination).
Social observability and pressure. Both theory and experimental evidence on social observability and the effect of eye cues suggest that people tend to behave less antisocially when their action can be observed by others (e.g., Bohnet & Frey, Reference Bohnet and Frey1999; Dea et al., Reference Dear, Dutton and Fox2019; Ekström, Reference Ekström2012; Ernest-Jones et al., Reference Ernest-Jones, Nettle and Bateson2011; Haley & Fessler, Reference Haley and Fessler2005; Kraft-Todd et al., Reference Kraft-Todd, Yoeli, Bhanot and Rand2015). Consistently with the literature, we would expect to observe less antisocial behavior when such behavior is observable to victims and to other subjects compared to when it is hidden from them. An exception to this observation occurs when individuals are peer pressured to take an antisocial action along the lines of the literature on obedience to authority (Karakostas & Zizzo, Reference Karakostas and Zizzo2016).
Hypothesis 3 (H3): The frequency and extent of antisocial behavior is lower (a) when their actions can be observed by other subjects and (b) when there is social pressure from an authority.
Economic cost. Standard economic theory posits that the consumption of goods increases when the cost of obtaining them increases. Under the assumption that the act and outcome of destruction is an ordinary good and not a Giffen good, we expect less antisocial behavior when such behavior is costly compared to when it is costless.Footnote 11
Hypothesis 4 (H4): The frequency and extent of antisocial behavior is lower if acting antisocially comes at a monetary cost.
Repetition vs. one-shot. Repeated play with the same players yields the possibility of retaliation. Therefore, we expect one-shot interaction to lead to greater antisocial behavior than in the case of repeated interaction with other players.
Hypothesis 5 (H5): The frequency and extent of antisocial behavior is higher with one-shot than with repeated interaction.
Methodological variables. One methodological concern is that laboratory MB exaggerates the relevance of antisocial behavior. The Experiment type variable checks the effect of having an online or a field experiment relative to a laboratory experiment. Another methodological concern is that research on antisocial behavior may suffer from publication bias. Published work may differ from unpublished work for its average scientific quality rather than just due to publication bias. Nonetheless, our Published variable provides one test for the extent of publication bias. A third methodological concern is that in at least some experiments money is given and not earned; as a result, potentially, there may be a house money effect that increases the incidence of antisocial behavior. The house money effect variable allows us to test for this. Within-subject designs may be more subject to experimenter demand effects (Zizzo, Reference Zizzo2010) and, while generally benign (Brandts & Charness, Reference Brandts and Charness2011) and used infrequently, the use of the strategy method might also lead to bias: This leads to additional methodological variables. Taken together, these methodological variables speak to different dimensions that may reduce the external validity of experimental evidence on antisocial behavior.
Additional controls. We expect there to be considerable heterogeneity across games and therefore our main meta-analysis below includes controls for games. Additional controls are for the geographic region in which the study was conducted, the number of players, and whether the experiment was one-shot or repeated.
4. Results
Our results are grouped into three subsections. Section 4.1 presents a meta-analysis summary of studies by game class and economic variables. Section 4.2 examines the impact of our economic, methodological and other variables on antisocial behavior using meta-regressions on the complete dataset. Finally, section 4.3 restricts the meta-regression analysis to the largest game class subset – namely, to the JoD/MB games, to identify the robustness of our results within a more homogenous set of studies.
4.1. Meta-analysis: distributional analysis
4.1.1. Variation across game classes
First, we conduct a univariate random-effects meta-analysis on the whole dataset. The overall levels of antisocial behavior are 29% for the destruction decisionsFootnote 12 (CI = [27%, 32%]) and 20% for the destruction rate (CI = [18%, 22%]). Figure 5 summarizes our findings, split by game class and publication status. Details on each observation can be found in Online Appendix B.
Fig. 5 Plots by game class and publication status
As shown in Fig. 5, destruction decisions and destruction rates varied significantly across games and within games. Heterogeneity (in terms of I2 and τ2) was above 70% in all game classes, which is expected due to large variations across game and experimental designs. Other meta-analyses studying behavior across different experimental paradigms (e.g., Gerlach et al., Reference Gerlach, Teodorescu and Hertwig2019; Li et al., Reference Li, Maniadis and Sedikides2021) also reported substantial heterogeneity of above 80% among their studies. Allowing for this variability, destruction decisions frequency and destruction rates are highest for vendetta games and lowest for social dilemmas with counter-punishment, as per Table 4 above.
To test for publication bias, we ran specialized meta-analysis regressions with game dummies, a Published dummy and game x dummies interaction terms (see Table A5 in the online appendix). The Published dummy is not significant, and no game-specific coefficients are significant at the p = .05 level.Footnote 13 Further tests of publication bias are presented in subsections 4.2 and 4.3.
4.1.2. Variation across subgroups by economic variables
Tables 5 and 6 provide descriptive statistics by economic variables for which we have hypotheses (descriptive statistics for other variables can be found in Tables A1 and A2 in the online appendix).
Table 5 Summary of extensive margin by economic variables
Notes: Cost refers to whether the destruction was free or costly. Inequality is endogenous when it is due to effort, exogenous when it is due to luck, exogenous advantageous when a subject has an advantage over their opponent, and exogenous disadvantageous when their opponent has an advantage. Procedural fairness = 1 if income is exogenously and equally endowed or endogenously earned with equal returns on effort for all subjects, and = 0 otherwise. To induce group identity, a subject is matched against either members of their own group (ingroup) or players from other groups (outgroup). Antisocial behavior can be observed by other players, observed by the victim, or no one (not observed). Pressure = 1 when subjects are under pressure to comply by an authority and = 0 otherwise. Finally, the game can be played only once (one-shot) or repeatedly (repeated).
Table 6 Summary of intensive margin by economic variables
Notes: Cost refers to whether the destruction was free or costly. Inequality is endogenous when it is due to effort, exogenous when it is due to luck, exogenous advantageous when a subject has an advantage over their opponent, and exogenous disadvantageous when their opponent has an advantage. Procedural fairness = 1 if income is exogenously and equally endowed or endogenously earned with equal returns on effort for all subjects, and = 0 otherwise. To induce group identity, a subject is matched against either members of their own group (ingroup) or players from other groups (outgroup). Antisocial behavior can be observed by other players, observed by the victim, or no one (not observed). Pressure = 1 when subjects are under pressure to comply by an authority and = 0 otherwise. Finally, the game can be played only once (one-shot) or repeatedly (repeated).
Because the number of studies looking at different factors varies across games, the results of statistical tests should be taken with caution and be verified via the meta-analysis regressions in the next subsections. The fact that there is the most destruction under inequality is a case in point: This is very likely to reflect the specific features of the large number of studies that have no inequality. More plausibly, cost appears to reduce destruction rates. Group identity does not appear to affect destruction decisions, but, when subjects are split by groups, destruction rates are higher. Being observed by others seems to lead to less destruction, while pressured by an authority seems to increase it. Other results are in a more plausible direction.
4.2. Meta-regressions on the complete dataset
We begin this section by examining the impact of our economic variables on the levels of destruction. We then explore how the games, methodological variables, and geographic location influence antisocial behavior. Table 7 presents our meta-regressions on the complete dataset.Footnote 14
Table 7 Meta-regressions on complete dataset
Notes: All models were specified using random-effects meta-regressions, which weigh each observation by the inverse of its standard error, assigning more weight to results from studies with larger samples and smaller deviation from the mean (Harbord & Higgins, Reference Harbord and Higgins2008; Thompson & Sharp, Reference Thompson and Sharp1999).
Standard errors in parentheses,
* p < .10, ** p < .05, *** p < .01.
Games variables. Different game classes generally display robust differences. Relative to the largest class of games (JoD/MB games), vendetta games exhibit a considerably larger frequency of destruction decisions and larger destruction rates by about 1/3 when including all covariates. Coordination games also exhibit more destruction decisions and higher decision rates. Contest games also exhibit more destruction decisions, while the negative coefficient on the destruction rate is insignificant once we control for all covariates. Social dilemmas with counter-punishment have less destruction, though the negative coefficient on the destruction rates is again insignificant once we control for all covariates. Overall, the picture is broadly consistent with the one emerging from Table 4 and Fig. 5 above.
Economic variables. The coefficients on exogenous advantageous inequality are negative and significant at the 1% level in Models 2 and 3 and at the 10% level in Model 5 but become insignificant when controls are added in Model 6. This indicates that, when subjects play against disadvantaged opponents, they engage in destruction significantly less often but destroy just as much income as when there is no inequality. The coefficient on exogenous disadvantageous inequality is negative and significant at the 1% level in Model 2, which is counterintuitive; however, this effect attenuates and is only marginally significant when accounting for other factors in Model 3.Footnote 15 It may be an effect of (expected) reciprocity given that lower destruction frequency is observed from the exogenously advantaged subjects they are playing with. Additionally, we found a negative effect of endogenous inequality on the destruction rate, indicating that subjects destroy less from their opponent when the endowment is earned rather than exogenously given. Nonetheless, this effect vanishes with the addition of controls. The coefficient on procedural fairness is significant at the 1% level in Model 3, indicating that subjects make fewer destruction decisions when the income-generating process is fair.
Result 1 (H1): Subjects engage in destruction less often when (a) there is exogenous advantageous inequality and (b) when there is procedural fairness.
The coefficient on “Outgroup” is marginally significant at the 10% level in Model 5, but the effect disappears when controlling for covariates. No other coefficients on “Ingroup” and “Outgroup” are statistically significant.
Result 2 (H2): We did not find evidence for negative discrimination toward outgroup subjects.
The coefficient on “Observed by others” is negative and marginally significant (once again controlling for covariates) at the 10% level in Model 3. Subjects appear to engage in less antisocial behavior when their actions can be observed relative to when they are hidden. The effect size is relatively large: On average, subjects make 15% fewer destruction decisions when their action is observable to others, but the 10% level significance points to large variability across observations. “Pressure” increases the destruction rate and possibly the frequency of destruction, though this effect is only marginally significant at the 10% level for the latter.Footnote 16
Result 3 (H3): (a) In the complete sample, subjects appear to make antisocial decisions less often when their actions can be observed by other participants and the experimenters but not when they are observed by the victims. (b) Pressure by an authority to destroy leads them to destroy more.
The coefficients on “Costly” are not significant in any of the models.
Result 4 (H4): We did not find an effect of cost on either destruction decisions or destruction rates.
One-shot interaction significantly increases destruction rates by around 8% in Model 5, though the effect is halved and at the 10% significance level once we control for covariates.Footnote 17
Result 5 (H5): Destruction rates tend to be higher in one-shot interactions.
Methodological variables. The coefficient on “Published” is negative and significant at the 1% level in Model 6, indicating a negative publication bias – on average, subjects destroyed about 7% less in published studies. This complements previous results in section 4.1 where, when not controlling for covariates, we broadly found no evidence of a positive publication bias. We will discuss these findings in section 5.
The use of the strategy method appears problematic in that it appears to increase both the frequency and the rate of destruction. There is a house money effect on the frequency but, fortunately, not on the rate of destruction. The results of other methodological variables are reassuring for laboratory experiments. Specifically, it does not matter whether the experiment is between-subject or within-subject. Online studies have a higher destruction rate (by around 13%, p < .01) and field studies have a higher frequency of destruction decisions and a higher destruction rate (in both cases by around 15%) relative to laboratory experiments.
Result 6: The use of the strategy method biases destruction frequency and rates upward, whereas house money effects only affect destruction frequency.
Result 7: Controlling for covariates, there is evidence for a negative publication bias for destruction rates.
Result 8: Online studies have higher destruction rates than laboratory experiments. Field studies have more antisocial behavior than laboratory experiments, for both destruction decisions and destruction rates.
Geographical variables. Both levels of destruction are significantly lower in experiments conducted in America and Asia-Pacific compared to those conducted in Europe (see Models 3 and 6), which is consistent with the descriptive statistics. There is no difference in the levels of destruction detected among studies conducted in Africa and Europe.
4.3. Meta-regressions on JoD and MB experiments
We conjecture that a key explanation of why we may be getting such weak results in relation to our key economic variables, and possibly in relation to some methodological variables, is the sheer heterogeneity that we observe between and within game classes. We can control at least for the former by running a meta-analysis that focuses on what are often considered as antisocial games, the JoD and MB games. In the meta-regression that follows, we consider both the JoD and MB games as a single category due to the limited number of observations, and thus power, for each of these games separately. The class of JoD/MB games is the one game class that has around 62% of our observations and that therefore has enough statistical power to enable a meaningful meta-analysis to be conducted. We can then verify the extent to which within-game class heterogeneity can be explained by our economic (and other) variables.
The JoD/MB dataset includes 51 studies (222 observations and 16,784 subjects) in total, with 47 studies (211 observations and 16,466 subjects) for the destruction decisions and 44 studies (206 observations and 15,573 subjects) for the destruction rates. Table 8 presents our meta-regressions on the JoD/MB dataset.
Table 8 Meta-regressions on JoD/MB dataset
Notes: All models were specified using random-effects meta-regressions which weight each observation by the inverse of its standard error, assigning more weights to results from studies with larger samples and smaller deviation from the mean (Harbord & Higgins, Reference Harbord and Higgins2008; Thompson & Sharp, Reference Thompson and Sharp1999).
A negative effect of exogenous inequality on destruction frequency and rate disappears conditioning on the covariates. Controlling for covariates, endogenous inequality increases the frequency of destruction. but not the destruction rate. Procedural fairness consistently reduces the frequency of destruction: The effect is large (around 9%).
Result 9 (H1): In the JoD/MB games, (a) controlling for covariates, there is no evidence to support greater antisocial behavior by exogenously advantaged subjects; (b) procedural fairness decreases the destruction frequency.
There is now some evidence of negative discrimination against outsiders: Destruction rates are higher with respect to subjects who are not part of one’s own group (at p < .01 and p < .10 in Models 3 and 4, respectively).
Result 10 (H2): In the JoD/MB games, there is some evidence of negative discrimination in the form of higher destruction rates against outgroup subjects.
In relation to the social information variables, the picture is the same for the JoD/MB sample as for the complete sample.
Result 11 (H3): In the JoD/MB games, (a) subjects appear to make antisocial decisions less often when their actions can be observed by other participants and the experimenters but not when they are observed by the victims; (b) pressure by an authority to destroy leads them to destroy more.
We now find an effect of cost on the extensive margin of antisocial behavior: Costly destruction leads to lower destruction decisions relative to when it is costless (p < .05). The coefficient on one-shot is now significant in all models (p < .01).
Result 12 (H4): In the JoD/MB games, costly destruction appears to decrease the frequency of destruction decisions but not affect destruction rates.
Result 13 (H5): In the JoD/MB games, one shot interaction increases the frequency of destruction decisions as well as destruction rates.
There is evidence of a negative publication bias: The coefficient on “Published” is significant at the 5% level for destruction decisions and at the 1% level for destruction rates. The strategy method still increases the destruction rate, and both field studies and online studies have more antisocial behavior than laboratory experiments for both destruction decisions and destruction rates. A between-subjects design now increases destruction frequency and possibly also the destruction rate.
The picture with geographical variables is less pronounced than in the complete sample. In part this may be a matter of statistical power, but point coefficients also tend to be smaller. Destruction rates, however, remain statistically significantly lower in America than in Europe.
5. Discussion and conclusion
Our meta-analyses investigated the potential determinants of antisocial behavior and how such behavior varies across different aspects of the experimental design. A key choice was in how to define the boundaries of antisocial behavior. We only considered behavior that entails subjects reducing another player’s income without any pecuniary gains and is not a dominant strategy of a payoff-maximizing, rational agent. This excludes behavior that may be partially explained by self-interest or is difficult to disentangle from other motives. Examples of the latter, the exclusion of which we respectively justified in sections 2 and 3.1, include punishment in the public goods game when not followed by counter-punishmentFootnote 18 or overbidding in the SPAs.Footnote 19
Overall, based on the general meta-analysis, we find that subjects engaged in socially inefficient payoff destruction in 29% of the times and destroyed about 20% of the maximum destruction allowed. Given the across-games and across-settings heterogeneity, the game level values are more worth focusing on. The highest level of destruction is observed in the vendetta game, while destruction is lowest in social dilemmas with counter-punishment. One explanation is that the moral cost of destruction is lower in the JoD/MB and vendetta games, which are contexts where antisocial behavior is salient by nature (Abbink & Herrmann, Reference Abbink and Herrmann2011; Zizzo, Reference Zizzo2003; Zizzo & Oswald, Reference Zizzo and Oswald2001). This result also suggests that the economic setting matters for nastiness: The social dilemma context where cooperation is socially desirable may have prompted subjects toward cooperating in these games (e.g., Ferraro & Vossler, Reference Ferraro and Vossler2010; Zizzo, Reference Zizzo2010), as opposed to rivalry and nasty feuding in vendettas (e.g., Abbink et al., Reference Abbink, Masclet and van Veelen2011; Bolle et al., Reference Bolle, Tan and Zizzo2014).
There is significant heterogeneity not just across but also within different classes of games. This heterogeneity makes inference regarding economic variables difficult, particularly given the limited number of studies looking at antisocial behavior – let alone all the key economic variables – in most classes of games. The limited evidence on the effect of costly destruction may be explained by the bluntness of the variable, which simply states whether MB is costly or free – not the price; however, given the heterogeneity of pricing schemes, it was not possible to have a more precise price measure.
Nevertheless, some results emerge. There is evidence that the frequency of destruction is reduced with social information, specifically being observed by others (but not the victim) and pressure by an authority. Procedural fairness leads to significantly fewer destruction decisions in both meta-analyses. Within JoD/MB games, destruction rates are higher toward outgroup members. While much of the literature focuses on the prosocial benefit of group identity (such as Akerlof & Kranton, Reference Akerlof and Kranton2000; Tajfel et al., Reference Tajfel, Billig, Bundy and Flament1971; Tajfel, Reference Tajfel and Tajfel1978; Tajfel et al., Reference Tajfel, Turner, Austin, Worchel, Hatch and Schultz1979), this result shows that group identity may be damaging toward outsiders (as emphasized in Eswaran & Neary, Reference Eswaran and Neary2022; Hargreaves Heap & Zizzo, Reference Hargreaves Heap and Zizzo2009; Zizzo, Reference Zizzo2011). We also find that one-shot interaction plausibly increases antisocial behavior, at least in the JoD/MB subsample, but the effect is robust to the general meta-analysis for destruction rates.
An unexpected finding was the broad lack of support for H1 on the effect of payoff inequality on destruction. If anything, both exogenous advantage and disadvantage lead to a lower destruction frequency according to the general meta-analysis (Table 7). The picture is less clear in the JoD/MB meta-analysis (Table 8): The coefficients on exogenous advantage or disadvantage are significant in Model 1 – with the point estimate for exogenous advantage larger – but their significance disappears in Model 2 while endogenous inequality becomes significant. In both meta-analyses, in terms of destruction rates, no inequality variables are significant controlling for covariates. Not controlling for them, the coefficient on exogenous advantage has the predicted negative sign, and that on endogenous inequality is also significantly negative.
It is difficult to interpret these findings. We cannot exclude that they possibly simply reflect unobserved and uncaptured across-studies heterogeneities. One conjecture is that, in sufficient studies with endogenous inequality, the inequality is seen as justified and therefore attenuating antisocial behavior, though it is not clear why this is not fully captured by the procedural fairness variable. The limited or no evidence of asymmetry between exogenous advantage and disadvantage may be easier to explain: The structure of many studies entails that, if I believe or observe that the exogenously advantaged will be less likely to destroy, then from a reciprocity viewpoint, I may be in turn less likely to destroy even if I am exogenously disadvantaged. It is of course also possible that inequality aversion does not operate in the antisocial behavior domain as it does in the prosocial behavior domain. Clearly, further research is needed.
The use of the strategy method biases destruction rates upward in both the complete dataset and in the JoD/MB subsample; this is consistent with Oosterbeek et al. (Reference Oosterbeek, Sloof and Van De Kuilen2004), who found a higher rejection rate in their meta-analysis of ultimatum games. The results on house money effects and between-subject manipulations are less clear. House money effects increase only the frequency of destruction decisions in the complete sample but not in the JoD/MB sample. Somewhat counterintuitively, between-subject manipulations raise destruction decisions and possibly destruction rates in the JoD/MB sample. A possible explanation could be that in within-subject designs, subjects draw inferences about the nature of the decision problem that leads them to be more compliant to social norms not to destroy. This would be an instance of a class of experimenter demand effects discussed by Zizzo (Reference Zizzo2010) and would suggest that within-subject designs tend to underestimate destructive behavior.
Another issue that applies particularly to the simplest and acontextual (Abbink & Herrmann, Reference Abbink and Herrmann2011) type of JoD design is whether, when there is only one choice to make in the experiment, a choice to destroy may be motivated by a desire of “doing something.” While this cannot be ruled out in baseline cases, a lot of the interest in these studies is in the between-treatment variation, which cannot be explained by this conjecture. Furthermore, in a very simple setting Sadrieh and Schröder (Reference Sadrieh and Schröder2016) try to control for this bias and still find antisocial behavior. What it does point to, however, is that, depending on the specifics of the experimental designs, the fact that behavior in JoD games may be driven by more than “joy of destruction,” often deliberately so (as for example in Karakostas & Zizzo, Reference Karakostas and Zizzo2016).Footnote 20
Two methodological findings speak to the value of experimental findings on antisocial behavior and particularly conventional laboratory experiments. First, and relevantly for any type of experiment, we do not find evidence that there is a publication bias toward finding antisocial behavior. This is true in aggregate and in the sample of JoD/MB experiments. As discussed in section 4.1.1, Table A5 in the online appendix shows the lack of a positive publication bias. If anything, in Table 7 (for destruction rates) and 8 (for both destruction frequency and destruction rates), and controlling for covariates, the evidence is one of a negative publication bias. Table A7 in the online appendix shows that, if we do not consider the July 2023 check of which working papers have been published up to then, the negative publication bias remains significant only at the 10% level, and is smaller, though there is still no positive publication bias. However, if we consider as Published the working papers that have been published up to our July 2023 check – allowing time for the most recent working papers to be published but making no other change to the dataset – Table A7 shows that this is enough to get the same negative publication bias results as in Tables 7 and 8. We conclude that a possible negative publication bias may have become more prominent in recent years. Based on Table A5, JoD games might be particularly affected. Second, we find a higher level of antisocial behavior in field and online experiments compared to laboratory experiments, both in the complete dataset and the JoD/MB dataset. Our results on laboratory versus field lends support to the external validity of laboratory experiments (Alm et al., Reference Alm, Bloomquist and McKee2015; Anderson & Bushman, Reference Anderson and Bushman1997; Armantier & Boly, Reference Armantier, Boly, Serra and Wantchekon2012; Stoop, Reference Stoop2014) and specifically to the importance of antisocial behavior as elicited in the laboratory literature.
Sanjaya (Reference Sanjaya2023) does a meta-analysis on destruction rates in JoD/MB games; however, due to a smaller sample size (44 studies, 88 observations), he can only consider a small set of independent variables. He uses a combination of covarying proxies to determine whether the data is from a field experiment, such as a students dummy. His results are consistent with ours regarding field experiments having more destruction. In his sample he finds a “Working paper” effect, but we do not replicate this in our larger sample. He has a “one-shot” variable that is positive and significant in one out of two of his more ambitious models. His “costly” variable is not significant once covariates are included, and ours is also not significant for destruction rates. His one regional variable, “Europe,” displays a significantly positive coefficient; what we find is that in the JoD/MB games sample, this effect is driven by less destruction than in America-based experiments. While Sanjaya (Reference Sanjaya2023) does not look at within-sample heterogeneity, we found this as a major concern.
Apart from the scale and scope, an advantage of our study over Sanjaya (Reference Sanjaya2023) lies in our meta-analysis technique. While he uses standard linear regressions with observations weighted by the number of observations, our meta-analysis procedure weighs each study by the inverse of the variance of the effect estimate (i.e., one over the square of its standard error). Thus, larger studies with smaller standard errors, contribute more to the weighted average estimate than smaller studies with larger standard errors, which improves the precision of the estimate (Whitehead & Whitehead, Reference Whitehead and Whitehead1991). Our meta-regressions also account for the between-study variance unexplained by the included moderators by assuming that the true effects follow a normal distribution around the linear predictor (Harbord & Higgins, Reference Harbord and Higgins2008; Thompson & Sharp, Reference Thompson and Sharp1999).
If we consider together our methodological results on the absence of any upward bias of antisocial behavior in laboratory experiments, on the broad absence of publication bias, and on the excessive heterogeneity obstructing firm conclusions on key economic variables, we conclude that there is value in more laboratory experiments that systematically build on paradigmatic experimental designs to enable comparability and the identification of key economic drivers of antisocial behavior.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/eec.2024.10.
Data availability statement
The usual disclaimer applies. The list of papers included in the meta-analyses, and the corresponding dataset, can be found in the online appendix. The replication material for the study is available at https://osf.io/rbupm/.
Acknowledgements
This paper is dedicated to the memory of the late Klaus Abbink. The paper was presented at conferences based in Nankai, Sydney and Tokyo, and we thank participants, as well as Gilles Grolleau and two reviewers, for valuable feedback. We also thank for their help all the authors who have made available to us data for the meta-analyses.
Statements and declarations
A previous version of this paper was posted as a working paper (Karakostas et al., Reference Karakostas, Tran and Zizzo2022). The authors have no competing interests to declare. They certify that they have no affiliations with or involvement in any organization or entity with any financial interest or nonfinancial interest in the subject matter or materials discussed in this manuscript. They have no financial or proprietary interests in any material discussed in this article.
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