Not all Group Members are created Equal: Heterogeneous Abilities in Inter-group Contests

Competition between groups is ubiquitous in social and economic life, and groups are typically not created equal. Here we experimentally investigate the implications of this general observation on the unfolding of symmetric and asymmetric competition between groups that are either homogeneous or heterogeneous in the ability of their members to contribute to the success of the group. Our main finding is that, in contrast with a number of theoretical predictions, efforts in contests involving heterogeneous groups are higher than in contests involving only homogeneous groups, leading to reduced earnings (to contest participants) and increased inequality. This effect is particularly pronounced in asymmetric contests, where both homogeneous and heterogeneous groups increase their efforts. We find that asymmetry between groups changes the way group members condition their efforts on those of their peers. Implications for contest designers are discussed.


Introduction
Many situations in social and economic life are characterized by rivalry and conflict between two or more competing parties. Warfare, socio-political conflicts, political elections, lobbying, R&D competitions, and promotion tournaments, are all examples of inter-group conflicts in which groups spend scarce and costly resources in order to gain an advantage over other groups. Within each competing group, group members may differ with respect to a variety of characteristics such as preferences, resources, wealth, productivity, or motivation, which, in turn, can affect their ability and willingness to compete. Acknowledging that such within-group heterogeneity is the rule rather than the exception, a straightforward implication is that competing groups are rarely identical, and contests are typically not symmetric.
Examples abound. For instance, countries competing for access to natural resources or geopolitical influence will typically (if not always) differ with regard to the degree of diversity in society, such as the distribution of income, education, or other sociodemographic characteristics. In the domain of organizations, firms often rely on interfirm alliances to compete with other firms or alliances (for example in the context of developing new products). Such alliances can be cross-function when partners contribute diverse and complementary resources, or same-function when firms have similar competencies (Amaldoss and Staelin, 2010). The resulting competition can then be either symmetric (between two cross-function alliances or two same-function alliances) or asymmetric (between a cross-function and a same-function alliance). Within firms, asymmetric contests between heterogeneous teams can occur in the context of performance-contingent payment schemes, such as paying bonuses to the best performing team(s) in order to increase productivity (Nalbantian and Schotter, 1997;Bandiera et al., 2013). Within-team heterogeneity in such settings is only natural, as team members can have different skills or abilities. It follows that the competing teams themselves are also not necessarily similar, resulting in an asymmetric competition. 2 Despite these rather natural applications, the behavioral literature on group competition has largely focused on situations in which symmetrical agents or teams compete against each other (see Dechenaux et al., 2015 andSheremeta, 2017, for overviews). Whether the insights from this 2 The effect of heterogeneity on effort when individuals rather than groups compete for a reward has been analyzed by Chen et al. (2011) and Orrison et al. (2004), and the behavioural consequences of heterogeneity in team production by Hamilton et al. (2003) and Brandts et al. (2007Brandts et al. ( , 2016 3 literature translate into more complex situations, however, is far from obvious as heterogeneity can affect conflict behavior in non-trivial ways. For example, while it has long been argued that belonging to a group can cause individuals to develop a feeling of group identity (Sherif et al., 1961;Tajfel and Turner, 1979), the salience of this group identity might be mitigated if group members are unequal. Furthermore, while team diversity is often thought of as creating positive synergy effects (Cox and Blake, 1991;Horwitz and Horwitz, 2007), heterogeneity within groups might also backfire as it can lead to a plurality of potentially conflicting behavioral rules and norms, which, in turn, may dampen coordination and collaboration (Reuben and Riedl, 2009). 3 In sum, "… the direction and magnitude of effects of team diversity on team outcomes have been an important question that is still not fully understood" (Horwitz and Horwitz, 2007, p. 988).
In the current paper, we systematically analyze and test how heterogeneity, both within and between groups, affects competition between groups. For ease of exposition, we will use the terms homogeneous and heterogeneous to describe within-group structures (i.e., whether group members are similar or not), and symmetric and asymmetric to capture the relationship between the groups (i.e., whether competing groups are similar or not). In particular, we are interested in how heterogeneity with regard to players' abilities to contribute to the group effort affects competition between groups. In our setting, a high-ability person is more efficient in converting her effort to a contribution to the group than a low-ability person, i.e., for each unit of invested effort, the former contributes more to the group than the latter. Heterogeneity in this respect is only natural, as some group members may be stronger, smarter, or wealthier than others. As an illustration, think of a team of salespersons, with one member that is more talented, experienced, or is endowed with a more densely populated sales territory, than the others. The high ability individual has a higher marginal productivity in the sense that even if all team members exert the same effort (in terms of, e.g., hours worked or energy expenditure), she will contribute more to the team's success than her less able peers.
We investigate the role of ability heterogeneity within and between groups with the help of a laboratory experiment. The major advantage of using a laboratory experiment is that it allows us to tightly distinguish between a player's ability and her effort choice, something that is almost impossible to achieve in the field, where one can typically only observe performance, which is a function of both effort and ability (and noise). It further allows us to exogenously manipulate the composition of players within groups, which circumvents complicating factors such as selfselection that emerge in most real-world situations where groups form endogenously. As a workhorse for studying group contests, we use an experimental version of Tullock's contest game (Tullock, 1980) in which two groups compete for a prize that is divided equally among all members of the winning group (see Konrad, 2009). Each group member decides how much of a given endowment to invest into the group's joint production and how much to keep for herself. The contribution of each individual to the group is deterministic (determined by the effort and the ability), and contributions by each group member are perfect substitutes. The group's probability of winning the contest is equal to the proportion of its total contributions out of the total contributions by both groups.
We study this basic decision situation in three different treatments. In the first treatment, we study the commonly explored symmetric contest between two homogeneous groups, in which all group members in both groups are equally able to compete. To study the pure effect of within-group heterogeneity, in the second treatment both competing groups are (equally) heterogeneous. In particular, each group consists of one low-ability, one medium-ability, and one high-ability player, while holding the average ability of group members constant compared to homogeneous groups (consisting of three medium-ability players). In the third treatment, we focus on the most interesting and natural situation in which the two competing groups differ from each other. To provide a clean comparison to the first two treatments, we examine an asymmetric contest between a homogeneous group and a heterogeneous group.
We establish three distinct theoretical benchmarks (see Section 2), assuming that individuals strive to maximize either their individual payoff (standard equilibrium), their team's joint earning (Joint payoff maximization, as in Leibbrandt and Sääksvuori, 2012), or the difference between their team and the other (parochial altruism, as in Abbink et al., 2012). Our results reveal that effort levels in contests involving heterogeneous groups are higher than in contests involving only homogeneous groups, and that this effect is particularly pronounced in asymmetric contests, where both homogeneous and heterogeneous groups increase their effort relative to the symmetric cases. 4 5 While overall effort levels are well captured by the joint payoff maximization predictions (efforts are significantly higher than the standard selfish prediction and significantly lower than the levels predicted by parochial altruism), none of the models capture the comparative statics we observe across treatments. Furthermore, in heterogeneous groups we find that-in contrast to all theoretical predictions, which agree in stating that only high-ability players should contribute, while low-and medium-ability players should free-ride, but in line with a notion of fairness-players of all ability levels contribute almost equally to the success of the group.
Intra-and inter-group dynamics-the way individuals condition their behavior on the past behavior of others-help explain these results. We find that individual choices are driven by a hierarchy of conditional behavior: individuals react to their own previous effort, their own group's effort, and the effort exerted by the other group, in that order. Interestingly, asymmetric competition exacerbates the sensitivity of homogeneous group members to the previous contributions of their group members, but there is no such effect for heterogeneous groups. Within heterogeneous teams, players of different abilities condition their effort on that of their 'relevant' peer, as in Croson et al. (2005Croson et al. ( , 2015 or Kölle (2015). Low-and medium-ability players-in both symmetric and asymmetric contests-mostly react to each other's past behavior, but not to that of high ability players. High players are sensitive to the behavior or their medium-ability group member, but only in symmetric contests; when the contest is asymmetric they become unconditional cooperators, as their contribution is not driven by the effort levels of their group members.
Finally, we show that asymmetric contests are not only more intense, but also more volatile, suggesting that facing a group that is different from your own can lead to an increase in strategic uncertainty. From a managerial perspective, the main policy lesson from our data is that asymmetric contests outperform symmetric ones, as group outcome is significantly higher. If managers are free to assign individuals to teams, and match groups with each other, our results suggest that asymmetric competition generates more overall output. Our design also allows us to quantify the risks of asymmetric contests. In particular, we find that from the perspective of the individuals who take part in the contest, asymmetric contests have two detrimental effects: they decrease individual earnings and they increase inequality within groups. To the extent that individuals who take part in the contest care about these aspects, there could be detrimental effects Electronic copy available at: https://ssrn.com/abstract=3266558 6 on the organization as a whole due to increased dissatisfaction (and, in turn, increased adverse behavior or higher turnover rates). Taken together, our results show that heterogeneity in abilities significantly affects contest behavior, and that these effects are strongest in the most natural setting where heterogeneity exists both within and between groups.
We contribute to the literature on inter-group contests by focusing on how heterogeneity in abilities affects the unfolding of competition. Previous studies primarily investigated symmetric contests between homogeneous groups, but a respectable (and growing) number of studies have looked into the effects of asymmetries in group size (Abbink et al., 2010;Ahn et al., 2011), endowments (Rapoport et al., 1989;Hargreaves Heap et al., 2015), costs (Ryvkin, 2013;Bhattacharya, 2016), prize evaluation (Sheremeta, 2011b;Chowdhury et al., 2013), communication (Cason et al., 2017), punishment 2011), and profit sharing rules (Kurschilgen et al., 2017), on the unraveling of competition between groups. However, none of these studies have investigated the role of heterogeneous abilities, and, in contrast to the current paper, most only investigated asymmetries either within or between groups, but not in conjunction.
A number of papers are of particular relevance to ours. Our general experimental design is reminiscent to that of Sheremeta (2011b), who analyzes symmetric and asymmetric contests under different contest rules between groups whose members differ in their evaluation of the prize. In line with our results, heterogeneous groups share labor much more equally than predicted by theory. In contrast to our findings, increasing heterogeneity does not lead to an intensification of conflict. Note, however, that Sheremeta (2011b) studies heterogeneity with respect to prize valuations, not in abilities, as we do in the current work. As shown by Kölle (2015) in a slightly different setting without competition between groups, heterogeneity in valuations can lead to very different behavioral reactions than heterogeneity in abilities as payoff consequences are very different between these two. Chen and Lim (2017) compare the effectiveness of homogeneous and heterogeneous sales teams under different contest rules. They find that while heterogeneity in abilities has no effect when the winner is determined by the average team effort, it does have detrimental effects when the winner is determined by the minimum or maximum effort level within each team. Note, however, that in Chen and Lim (2017) effort and ability are substitutes, while in our case a player's ability determines her marginal productivity of exerting effort, i.e., effort and ability are complements. Our paper is further related to the studies by Ryvkin (2011)

and Brookins
Electronic copy available at: https://ssrn.com/abstract=3266558 7 et al. (2015) who analyze the effects of heterogeneity in players' cost of effort (which could be seen as another way to operationalize heterogeneity in abilities) on sorting into teams. In line with the theoretical predictions of Ryvkin (2011), Brookins et al. (2015 find that efforts are higher in balanced contests, where the average ability is held equal between the two groups, than in unbalanced contests, where the average ability in one group is higher than in the other. In contrast to our setup, they do not study the natural benchmark, featured in the bulk of the literature, of contests involving completely homogeneous groups.
The rest of the paper is organized as follows. Section 2 presents the general setup of our group contests as well as theoretical predictions. In Section 3 we describe our experimental design and procedures in more detail. Section 4 summarizes our results. Section 5 concludes.

Model and Predictions
Consider the following inter-group contests for public goods by Katz et al. (1990). Let there be n = 2 groups of ≥ 1 risk-neutral players each, competing to win a prize . All group members are endowed with the same amount of resources (e.g., time) w, which they can either use to help the own group win the contest, or they can use it for themselves (e.g., for an alternative private activity). Let , ≥ 0 represent the effort (resources) spent by player i in group j. Importantly, players may differ in their ability to contribute to their group activity; a high-ability player is better able than a low-ability player in converting her effort to an actual contribution to the group. That is, her contribution to the group output is given by , = , • , , where , is the ability of player i in group j determining her marginal productivity of effort. We assume that individual group members' efforts are perfect substitutes, i.e., total effort of group j is given by = ∑ , =1 and the total contribution of group j is given by = ∑ , , =1 . Following Tullock (1980), the probability of group j winning the contest and securing the prize is given by the following contest success function: Electronic copy available at: https://ssrn.com/abstract=3266558 8 When a group wins, each member of the winning group receives an equal share of the prize, . 5 The expected payoff of player i in group j is then given by In our experiment (see Section 3), we consider two different type of groups, which can be either homogeneous or heterogeneous in the composition of the ability of their members. If follows that three types of inter-group contests can arise: two symmetric contests where both groups share the same internal composition in ability of their members (either homogeneous or heterogeneous), and one asymmetric contest with a homogeneous group competing with a heterogeneous one. The different contests may lead to different predicted outcomes. We describe below the resulting equilibria predicted under three distinct assumptions: players maximize either their own earnings; the joint-profit of the group; or the difference in earnings between their own and the competing group.
Under the standard assumption of purely self-interested individuals, following Konrad (2009), if all players in all groups are equally able to contribute to the group output, i.e., , is the same for all players (symmetric homogeneous contest), there is a unique equilibrium prediction for the total group effort that is the same as in a two-player contest and equal to 1 = 2 = 4 . Theory, however, remains silent about the behavior of individual group members: any combination of efforts that add up to 4 constitutes an equilibrium. When both groups are heterogeneous but identical (symmetric heterogeneous contest), the prediction about the group effort level does not change, but there is a clear-cut prediction for the individual efforts. As contributions to the group are perfect substitutes and costs of effort are linear, in equilibrium only the member with the highest ability in each group should exert effort, while the other group members should free ride (see Baik, 2008, for a similar result when group members differ with regard to the evaluation of the prize).
When groups differ with respect to the most able group member (asymmetric contests), the group contest reduces to an asymmetric contest between the most able group members in each group. In the following, we denote the ability of the most able member within each group by � . The solution is then given by simultaneously solving the two reaction functions of the optimal efforts of the two players, yielding 1 = (� 1 � 2 2 ) 1 2−� 2 2 � 1 and 2 = (� 1 � 2 1 ) 1 2−� 1 1 � 2 . By denoting = � 1 � 2 ⁄ as the relative ability between the most able player of both groups, the resulting unique symmetric Nash Equilibrium is given by 1 = 2 = (1+ ) 2 , which for ≠ 1 is strictly smaller than 4 . As a result, effort is predicted to be lower in asymmetric than in symmetric contests (see also Fonseca, 2009, for a similar result investigating heterogeneity between players in individual contests).
Experimental evidence from group contests typically shows a departure from standard predictions, with a general tendency of over-dissipation (see Sheremeta, 2017, for an overview). Possible explanations that have been put forward to explain such over-investments by groups are joint profit maximization (i.e., striving to maximize the sum of payoffs within the own group; Leibbrandt and Sääksvuori, 2012) or parochial altruism (i.e., the display of altruism towards in-group members along with hostility towards out-group members; Bernhard et al., 2006, Choi andBowles, 2007;Abbink et al., 2012). When applying these concepts to our setting, compared to the standard predictions from above, the following qualitative predictions across treatments can be derived.
When players try to maximize joint payoffs, the objective function is given by + 1 + 2 − . In this case, in symmetric contests the predicted effort is equal to 1 = 2 = 4 , while in asymmetric contests aggregate effort is predicted to be 1 = 2 = (1+ ) 2 . Hence, while compared to the standard prediction of purely selfish players effort levels are predicted to be higher, it still holds that effort should be lower in asymmetric than in symmetric contests, and that in heterogeneous groups only high ability players should exert any effort.
If, instead, group members are motivated by parochial altruism, they strive to maximize the difference between their own and the other groups' payoff, ( 1 In this case, the total effort exerted by each group in symmetric contests will be 1 = 2 = 2 , which is higher than predicted efforts in asymmetric contests, given by 1 = 2 = 2 (1+ ) 2 . Both of these effort levels are higher than the ones predicted under the assumption of pure self-interest and joint payoff maximization. Yet, as before it holds that in heterogeneous groups only high ability players should be active, while in homogeneous groups any combination of efforts leading to the predicted aggregated effort is an equilibrium.
To summarize, while the three different assumptions about subjects' objective function lead to differences in absolute predicted total effort levels, they all share some common qualitative characteristics. First, irrespective of the type of contest (symmetric or asymmetric) homogeneous and heterogeneous groups are predicted to exert the same level of aggregate effort. Second, within heterogeneous groups only the member with the highest ability should exert any positive effort (the others should free ride), while in homogeneous groups there is a continuum of optimal effort combinations. Third, total effort is predicted to be lower in symmetric compared to asymmetric contests.
In our experiment (see below) we empirically test each of these predictions. With regard to the predicted effort levels within heterogeneous groups, we expect behavior to deviate from theory as it predicts an extreme distribution of labor, which, in turn, creates substantial inequality within groups. There is now ample evidence from a variety of contexts that many people care about the relative distribution of outcomes (see e.g., Fehr and Schmidt, 1999;Bolton and Ockenfels, 2000;Sobel, 2005;Fehr and Schmidt, 2006). Applied to our context, if players dislike inequality within groups they have an incentive to match their group members' efforts, as payoff equality can only be obtained if all group members exert the same level of effort, irrespective of their ability. For heterogeneous groups, this is in stark contrast to the theoretical predictions above which state that only the high ability player should contribute. Hence, if players are also motivated by fairness considerations within groups, we should expect a more equal distribution of labor in heterogeneous groups. 6

The Experiment
Our experimental game is based on the model described above. Subjects were randomly divided into three-person groups (m = 3). Each group was then matched with another, randomly selected, group (n = 2), to repeatedly compete for a prize for 45 consecutive periods using a partnermatching protocol. The prize was worth 300 points, to be shared equally among the members of the winning group (i.e., for each member V = 100). In each period, each group member received an endowment of 100 tokens (w = 100), which they could either use for their own private consumption or use to exert effort ∈ [0, 100] to increase the probability of the group winning the contest. There were three types of players, low-ability, medium-ability, and high-ability, which differed in the effectiveness of their effort. Homogeneous groups consisted of three medium-ability players, while heterogeneous groups consisted of one low-ability player, one medium-ability player, and one high-ability player. 7 Each token spent by a low-ability player yielded a contribution of one for the group ( , = 1); each token spent by a medium-ability player yielded a contribution of two for the group ( , = 2); and each token spent by a high-ability player yielded a contribution of three for the group ( ℎ ℎ, = 3). Player types were assigned randomly and remained constant throughout the whole experiment. Importantly, both homogeneous and heterogeneous groups have the same total endowment (300 tokens) and the same strategy space (contributions between 0-600). Cross matching these two group types yields two symmetric contests and one asymmetric contest, for a total of three experimental treatments: Symmetrichomogeneous, Symmetric-heterogeneous, and Asymmetric.
The Experiment was conducted at LabSi (University of Siena) using z-Tree (Fischbacher, 2007).
A total of 258 subjects were recruited for 15 sessions (13 with 18 subjects and 2 with 12 subjects each) resulting in 15 independent observations in symmetric homogeneous contests, 14 in symmetric heterogeneous contests, and 14 in asymmetric contests. At the beginning of each session, written instructions were handed out to participants and read aloud by the experimenter.
After that, and before the start of the experiment, subjects had to correctly answer a set of control questions to ensure correct understanding of the incentives and structure of the game. At the end of the experiment, participants were paid their earnings in cash. Sessions lasted between 50 and 60 minutes, and subjects earned on average around €8.50. Table 1 summarizes our experimental design as well as the theoretical predictions for each of the three conditions. Note, that the predictions for parochial altruism (players try to maximize the payoff difference between both groups) slightly differ from those derived in Section 2, because effort levels of players were capped at a maximum equal to individuals' endowment (w = 100), while in Section 2 there was no such constraint. While this cap does not change the prediction that in heterogeneous groups only the high-ability player should exert any effort, predicted group efforts in asymmetric contests are no longer the same for homogeneous and heterogeneous groups.

Results
We divide the presentation of our results into four subsections. In Section 4.1 we provide an overview of the main treatment differences. In Sections 4.2 and 4.3 we focus in more detail on individual, type-and group-specific behavior. Finally, in Section 4.4 we discuss the implications of the observed behavior on efficiency and inequality.

The effects of contest type on the degree of competition
- Note: Homogenous groups consist of three players who all have a medium ability of , = 2. Heterogeneous groups consist of three players with abilities , = 1, , = 2, and ℎ ℎ, = 3. * These predictions are altered by the fact that in our experiment players' endowment was capped at w = 100.
14 To test the significance of these results, we run multilevel linear mixed-effects regressions that take into account the inter-dependency of observations (repeated observations of individuals that are nested within a contest of two competing groups). The results are shown in Table 2. Model (1) reveals that while the differences between Symmetric homogeneous and Symmetric heterogeneous and between Symmetric heterogeneous and Asymmetric are not significant (p = 0.283 and p = 0.267, respectively), the equality of group efforts between Symmetric homogeneous and Asymmetric can be rejected at the 5% level (p = 0.028). 8  Table 1.
As is apparent from the left panel of Figure 1, these differences are robust over time and already present in the early stages of the repeated interaction (compare also model (2) in Table 2).
Additionally, in line with previous results (e.g., Abbink et al., 2010, Sheremeta, 2010, 2011a12 Using non-parametric tests yields very similar results. 15 Fallucchi et al., 2013;Brookins & Ryvkin, 2014), we observe that efforts significantly decrease over time in all treatments. This decay is thereby somewhat more pronounced in the asymmetric contest as indicated by the significant negative coefficient of the Asymmetric × Period interaction term in model (2) in Table 2 (see also Table A1 in Appendix A), suggesting that treatment differences slightly reduce over time. We summarize these findings in our first result: Result 1: Compared to two homogeneous groups competing in a fully symmetric contest, heterogeneity in abilities within and in particular between groups leads to an intensification of competition. To what extent can these findings be explained by our theoretical predictions in Section 2? The left panel of Figure 1 shows the predictions of the different models as references lines. In line with In addition to the effect on the overall level of competition intensity, the type of contestsymmetric or asymmetric-also has an effect on the volatility of competition, both between and within groups. To measure between-group volatility, we calculate the absolute distance in group efforts between the two competing groups in a given period. We find that in asymmetric contests the average absolute difference in group efforts is substantially and significantly higher than in symmetric contests ( suggest a substantially increased degree of volatility when contests are asymmetric. A possible reason for this result is that when facing a group different from your own, it becomes harder to put oneself into the shoes of others and, hence, predict the opponent's behavior. As a consequence, strategic uncertainty increases, and behavior is less stable. We summarize these findings in our second result: Result 2: When the contest is asymmetric, there is a substantial increase in the volatility of competition, both within and between groups.

Group-and type-specific behavior
To understand what drives our treatment differences, we now zoom into group-and type-specific behavior. Panel A of Figure 2 depicts the average group efforts of homogeneous and heterogeneous groups, conditional on the type of contest (symmetric or asymmetric). It shows that both homogeneous and heterogeneous groups compete more aggressively in asymmetric contests, i.e., when faced with a group different from their own. This effect is particularly pronounced for homogeneous groups, who significantly increase their efforts from 67.2 to 97.5 tokens (+45%, linear mixed effects model, p = 0.023; see model (1) in Table A2 in Appendix A). For heterogeneous groups, effort also increases but this effect is much less pronounced (+11%, from 79.8 to 88.7 tokens) and not statistically significant (linear mixed effects model, p = 0.452; see model (2) in Table A2).
When comparing the behavior of the two different group types, we find that in contrast to our findings from the symmetric contests where heterogeneous groups exert more effort than homogeneous groups (compare Figure 1), in asymmetric contests we observe the opposite pattern.
In this case, homogeneous groups exert more effort than heterogeneous groups (97.5 vs. 88.7).
Strikingly, they even outperform heterogeneous groups in terms of actual contributions (effort × ability; 195.0 vs. 183.3), although neither of these effects is significant (linear mixed effects models, p = 0.313 and p = 0.531, respectively). As a result, heterogeneous groups do not utilize their comparative advantage over homogeneous groups as the latter win the contest in 49.8% of the cases, significantly more often than the 40% predicted by standard theory (Wilcoxon Signrank test, p = 0.022).
Next, we take a closer look at the type-specific behavior. Recall that heterogeneous groups consist of players of different abilities-one low-, one medium-, and one high-ability player-and that all theories considered in Section 2 predict that only the high-ability player exerts effort, while the other players are predicted to completely free ride. Our empirical results are in stark contrast to these predictions. In symmetric contests, the efforts of low-, medium-, and high-ability players are practically identical, accounting for 33%, 34%, and 33%, respectively, of the group's overall effort. This suggests that other motivations such as inequality concerns within the group matter for individual behavior, too. In asymmetric contests, the picture slightly changes. The efforts of low-, medium-, and high-ability players now account for 30%, 33%, and 37%, respectively, of the group's overall effort. This indicates that in asymmetric contests high-ability players take over a leading role by exerting more effort, an observation we will come back to in the next section.

Figure 2: Group efforts depending group and contest type (Panel A). Change in individual efforts in asymmetric contests compared to symmetric contest by player's type (Panel B).
To better illustrate how the different player types react to a change in the opponent's group type, Panel B of Figure 2 depicts the difference in individual efforts between asymmetric and symmetric contests, separately for low-, medium-, and high-ability players. As can be seen, while all types increase their effort levels in asymmetric contests, the magnitude of this effect varies across types.
In particular, in heterogeneous groups the difference is much more pronounced for high-ability players, who increase their effort by 6.1 tokens on average, accounting for 69% of the total group increase. Low-and medium-ability players, in contrast, increase their efforts by only 0.9 and 1.8 tokens, respectively. Yet, despite these asymmetric reactions, the distribution of efforts is still very Electronic copy available at: https://ssrn.com/abstract=3266558 19 far from the theoretical predictions that only high ability players should exert any effort. We summarize these findings in our third result:

Result 3:
(i) Both homogeneous and heterogeneous groups increase their efforts in asymmetric compared to symmetric contests, but only in the former case this effect is significant.
(ii) In heterogeneous groups, the different player types tend to share the burden of exerting effort much more equally than predicted by theory. In asymmetric contests, high-ability players start exerting higher efforts than their lower ability group members.

Conditional cooperation and the inter-dependency of effort within and between groups
To better understand these effects, in the following section we provide a more detailed account of individual behavior by investigating the group dynamics of effort provision. In particular, we explore to what extent individual behavior is contingent on the lagged efforts of the other playersboth within their own and the opponent group-as well as on the type of contest.
To answer these questions, we run a set of multilevel mixed-effects regressions that explicitly take into account the inter-dependency of individual observations within a given (6-person) contest. As the dependent variable, we use an individual's effort choice in period t. The main explanatory variables are the lagged average efforts of the two other members of the own group (Ingroup effort t-1), and the lagged average efforts of the opponent group (Outgroup effort t-1). To see whether behavior differs depending on the type of contest, we include interaction terms with an Asymmetric dummy which takes the value 1 if the contest is asymmetric, and 0 otherwise. For clarity and ease of interpretation, we use separate models for homogeneous (Model 1) and heterogeneous groups (Models 2). Because in heterogeneous groups different ability types might display different behavioral patterns, we run three additional regression models in which we distinguish between low-, medium-, and high-ability players (Models 3-5). To investigate whether effort contingencies also depend on the other player's type, instead of using the lagged average efforts of all own group members, we include player specific lagged efforts (Low-ability effort t-1, Medium-ability effort t-1, High-ability effort t-1). In all regressions we include a Period variable to capture Electronic copy available at: https://ssrn.com/abstract=3266558 20 learning/general time trends, as well as lagged individual efforts (Own effort t-1) to capture individual path dependency. Notes: Multilevel linear mixed-effects models using random intercepts for matching groups (a contest between two groups), groups, and individuals. Numbers in parentheses indicate standard errors. Significance levels * p < 0.1, ** p < 0.05, *** p < 0.01.

21
The regression results are reported in Table 3. We start by discussing the results from our first two models investigating aggregate behavior in homogeneous and heterogeneous groups. In both cases, we find a positive and significant Own effort t-1 coefficient, indicating evidence for individual path dependency as found in many previous studies (e.g., Abbink et al., 2010;Brookins et al., 2015;Chowdhury et al., 2016). Furthermore, players in both types of groups condition their effort provision on that of their own group members (Ingroup effort t-1) as well as on the behavior of their opponent (Outgroup effort t-1). Both of these effects are highly significant. While in symmetric contests, the magnitude of these effects is very similar across homogeneous and heterogeneous groups, it seems that when the contest becomes asymmetric, the two group types adjust behavior differently. In particular, in homogeneous groups, facing a heterogeneous group as an opponent leads to strengthened collaboration within groups as indicated by the significant Ingroup effort t-1 × Asymmetric interaction term. Contrary to that, in heterogeneous groups we observe a diminished degree of interdependency of efforts as indicated by the negative coefficients of the Ingroup effort t-1 × Asymmetric and Outgroup effort t-1× Asymmetric interaction terms, although only the latter effect is significant.
To better understand these asymmetric reactions of homogeneous and heterogeneous groups, we now turn to the results of models 3-5 investigating type-specific behavior in heterogeneous groups.
The results reveal several interesting patterns. In particular, they show that while low-ability and medium-ability group members condition their effort on each other's past behavior (with the magnitude being comparable to the one observed in homogeneous groups), they both largely ignore the efforts of their high-ability group member. The high-ability player, in contrast, responds to the effort of the medium-ability player when the contest is symmetric (as indicated by the positive and significant Medium-ability effort t-1 coefficient), but does not do so when the contest is asymmetric (as indicated by the negative and significant Medium-ability effort t-1 × Asymmetric coefficient). In this case, he instead starts to increase his effort unconditionally as indicated by the significant Asymmetric dummy. In neither case he relates his decision to the one made by the lowability player.
Taken together, these results suggest that the different players react very differently to other's effort depending on the other player's type, and that these effects seem to be contest-specific. This highlights that, as in Reuben and Riedl (2013), heterogeneity within groups can lead to a Electronic copy available at: https://ssrn.com/abstract=3266558 22 multiplicity of (potentially conflicting) behavioral norms and rules that, as we show here, might additionally depend on situational factors such as the opponent's type in a contest. We summarize these findings in our fourth result:

Efficiency and inequality
It this section, we investigate the consequences of the observed behavior on overall welfare. We distinguish between the perspective of the contest participants and that of the contest designer.    Table A3 in Appendix A).
The type of contest, in contrast, has a strong impact on both efficiency and the distribution of wealth. In particular, compared to the case in which two identical groups compete against each other (symmetric contests), asymmetric contests not only have detrimental effects on individual earnings (due to the increased efforts as highlighted in Section 4.1), but also on inequality. While earnings significantly decrease on average by about 5% from 125.6 to 119.0 tokens (linear mixed effects model, p = 0.058, see Table A4 in Appendix A), inequality significantly increases by 23% from 16.2 to 20.0 (p = 0.036). As shown by Figure 3, while these effects occur in both types of groups, the effect of decreased earnings is particularly pronounced for homogeneous groups (-8% (p = 0.026) compared to -2% (p = 0.524) in heterogeneous groups), and the effect of increased inequality is particularly pronounced in heterogeneous groups (+30% (p = 0.049) compared to +17% (p = 0.226) in homogeneous groups; see also

Conclusion
Some people are stronger, smarter, or wealthier than others. An obvious consequence is that the ability to perform particular tasks is not identical for everyone. In this light, research on contests that presupposes identical abilities is rather idiosyncratic. To address this issue, the current work investigates the effects of within-group heterogeneity in abilities on behavior in inter-group contests. We compare the commonly explored symmetric contests between homogeneous groups-in which the ability is identical for all group members in both groups-to symmetric contests between two heterogeneous groups, and to asymmetric contests between a homogeneous and heterogeneous group.
Our main result is that, in contrast with a number of theoretical equilibrium predictions, efforts in contests involving heterogeneous teams are higher than in contests involving only homogeneous teams. The effect is particularly pronounced in asymmetric contests, where both homogeneous and heterogeneous teams increase their efforts. As a result, heterogeneous groups do not utilize their comparative advantage when competing against homogeneous groups, as both groups win the contest equally often. At the individual level, we find that players in heterogeneous groups divide the labor much more equally than predicted by theory, which states that only the highest ability group members should exert effort, while all others free ride. This effect is particularly pronounced in symmetric contests in which efforts of low-, medium-, and high-ability players are practically identical. In line with a notion of fairness or inequity concerns, it seems that high-ability players are not willing to accept the relatively lower payoffs that are inevitably associated with exerting more effort than the other group members, nor do the less able group members expect them to do so. 10 Such equal sharing of labor is attenuated, however, when heterogeneous groups compete against homogeneous groups in asymmetric contests. In this case, high-ability players invest more effort despite their less able peers not willing to match these increased contributions. It thus seems that in asymmetric contests high-ability players understand the comparative advantage they have and are willing to accept the responsibility that comes with being the most able member of the group. Interestingly, while in heterogeneous groups we observe a weaker interdependency of efforts between group members when the contest becomes asymmetric, the opposite pattern is observed in homogeneous teams where conditional cooperation is increased when the opponent team is different from the own. The latter effect might be due to an increased sense of identity that is triggered by facing a different group (Chowdhury et al., 2016), or due to an increased sense of threat triggered by the presence of a high-ability member in the opposing team.
Our findings have some important policy implications. For example, when knowing that workers are heterogeneous in their ability, managers in firms can construct groups that are either homogeneous or heterogeneous and organize contests that are either symmetric or asymmetric. A clear hierarchy of the amount of effort that these settings extract from the workers emerges from our data; efforts are highest in asymmetric contests and lowest in symmetric homogeneous contests. Hence, a manager who is only interested in maximizing group output should opt for the former. However, asymmetric contest may also have several drawbacks. For example, as highlighted by our experiment, the increased overall output comes at the cost of increased volatility in participants' behavior, which might be due to an increase in strategic uncertainty that arises when facing a group that is different from the own and whose behavior is more difficult to predict.
Such volatility might be undesirable for the manager as it makes the reliability and security of his planning more difficult. Furthermore, insofar as the manager also cares (at least to some extent) about the well-being of his employees, asymmetric contests might have negative side effects as they reduce the workers' overall welfare due to a decrease in earnings and an increase in inequality.
But even if the manager does not care about the well-being of the employees per se, it might be optimal to refrain from asymmetric contests because in the long-run they can lead to dissatisfaction in the workforce, which, in turn, may increase adverse behavior or turnover rates.

27
Future research should address these questions by studying how teams are formed endogenously in these type of contexts, both in situations in which managers can determine the group composition as well as in situations in which agents can self-select into different teams.
Furthermore, while our laboratory experiment provided only a minimal environment for analyzing the effects of heterogeneity in symmetric and asymmetric contest, we believe that more research is needed in order to test the robustness of our results in more complex and rich environments, like in natural field settings. A different interesting avenue for future research is to investigate whether common institutions such as communication, leadership, or punishment, which have been found to be effective in increasing cooperation in homogeneous teams (e.g., Abbink et al. 2010;Leibbrandt and Sääksvuori, 2012;Cason et al., 2012;Eisenkopf 2014), are similarly effective in heterogeneous teams.   Notes: Multilevel linear mixed-effects models using random intercepts for matching groups (a contest between two groups), groups, and individuals. Numbers in parentheses indicate standard errors. Model (1) uses only data from homogeneous groups and Model (2) uses only data from heterogeneous groups. Model (3) compares behaviour from homogeneous and heterogeneous groups in the asymmetric contest. Significance levels * p < 0.1, ** p < 0.05, *** p < 0.01.  tokens the other members of your group receive, and which type of tokens each member of the other group receives.
Tokens that are not used to buy contest tickets are worth 1 point per token, regardless of the colour. These points will be added to the respective person's point balance.
In each round each person must decide how many tokens to use to buy contest tickets. Each participant will enter his or her decision via the computer. An example screenshot is shown below.

Determining the Winning Team
After each round, as soon as everybody has made a decision, the computer will calculate the total number of contest tickets purchased by each team and determine which team wins the prize. The prize is worth 300 points, which are divided equally between the three members of the winning team, so each team member receives 100 points. The chance that your team wins the prize depends on the number of contest tickets bought by your team, and the number of contest tokens bought by the other team. In general, the more contest tickets your team purchases, the higher your chance of winning the contest; the less contest tickets your team purchases, the lower your chances of winning the contest. The same applies for the other team Electronic copy available at: https://ssrn.com/abstract=3266558 38 The exact chance of winning the contest is given by the number of contest tickets bought by your team, divided by the total number of contest tickets bought by both teams. If your team buys X contest tickets and the other team buys Y contest tickets, then your team's chance of winning the prize is + , and the other team's chance of winning is + .

Example:
1. If your team purchases 300 contest tickets and the other team purchases 300 contest tickets, then the total number of contest tickets is 600, and your team's chance of winning is Note that if one of the teams doesn't buy any contest tickets, the other team wins the prize with certainty. If both teams do not buy any contest tickets, no lottery takes place and the prize is lost.

Determining Payoffs
If your team wins the contest: you will earn points from the tokens you kept for yourself, and your share from the team prize.
= 100 − ℎ + ℎ ℎ If your team does not win the contest: you will only earn points from the tokens you kept for yourself. You will earn 80 points from the 80 RED tokens you kept for yourself, and 100 points from your share of the team prize, for a total of 180 points in the round. The second member in your group will earn 80 points from the 80 BLUE tokens he/she kept for him/herself, and 100 points from his/her share of the team prize, for a total of 180 points in the round.
= 100 − 20 + 100 = 180 The third member in your group will earn 90 points from the 90 GREEN tokens he/she kept for him/herself, and 100 points form his/her share of the team prize, for a total of 190 points in the round. ℎ = 100 − 10 + 100 = 190 Electronic copy available at: https://ssrn.com/abstract=3266558 40 If your team does not win the contest: You will earn 80 points from the 80 RED tokens you kept for yourself, and nothing from the prize.
= 100 − 20 = 80 The second member in your group will earn 80 points from the 80 BLUE tokens he/she kept for him/herself, and nothing from the prize = 100 − 20 = 80 The second member in your group will earn 90 points from the 90 GREEN tokens he/she kept for him/herself, and nothing from the prize = 100 − 10 = 90

End of each period
After all participants have made a decision, a feedback screen will appear showing the results from the current round. Each participant will receive the following summary of the period: • Number of contest tickets purchased by his/her team • Number of contest tickets purchases by other team • Which team won the competition As well as the following information about him/herself and each of his/her two group members: • Initial number of tokens • Type (color) of tokens • Number of tokens kept • Number of tokens used to purchase contest tickets • Number of contest tickets purchased • Earnings from the contest • Total earnings in the period The information is sorted by the number of contest tickets purchased in descending order (with the