# Competition, Income Distribution, and the Middle Class: An Experimental Study

Authors: Bernhard Kittel; Fabian Paetzel; Stefan Traub
Journal: Journal of Applied Mathematics
 (2015)

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## Abstract

We study the effect of competition on income distribution by means of a two-stage experiment. Heterogeneous endowments are earned in a contest, followed by a surplus-sharing task. The experimental test confirms our initial hypothesis that the existence of a middle class is as effective as institutional hurdles in limiting the power of the less able in order to protect the more able players from being expropriated. Furthermore, majoritarian voting with a middle class involves fewer bargaining impasses than granting veto rights to the more able players and, therefore, is more efficient.


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## Body

## 1. Introduction

In recent years, public awareness of an increasingly lopsided distribution of income and wealth in Western countries has strongly increased [1]. Most OECD countries have witnessed growing inequality over the past 20 years [2]. In particular, the gap between the bottom and the top deciles of the household income distribution has risen dramatically. The decile ratio currently amounts to about 1 : 15 in the US and 1 : 9 in the OECD-34, and even in a Nordic welfare state like Sweden it is close to 1 : 6. Given the fact that the typical OECD income distribution is right-skewed [3], it does not come as a surprise that income tax progression is much higher in the US than in Sweden [4].Observers diagnose the formation, as well as deliberate establishment, of a winner-take-all society in which the middle class is gradually eroded [5–7]. A few superstars, which may (or may not) be the most able practitioners in a particular area, receive all the profit while the others’ efforts are in vain (e.g., [8–10]). Some commentators expect this development to result in increasing societal division, distributive struggle, and violent conflict [11].On the other hand, the fall of communist regimes in 1989 has demonstrated the crippling effects of excessive egalitarianism on economic efficiency and growth [12, 13]. Societies, or groups, thus need to strike a balance between both excessive inequality and excessive equality. In principle, either an institutional or a structural condition is sufficient to protect a society against excesses from both sides. On the one hand, institutional rules of collective decision-making giving veto power to all stakeholders [14, 15] enforce a consensual decision and thereby make the distributional struggle an issue of explicit negotiation. On the other hand, the existence of a neutral but opportunistic middle class serves as a buffer between the upper and the lower classes because they fear expropriation from both sides and will thus side with the weaker group in case of conflict [16–18]. Moreover, not being the main target of redistribution, members of the middle class will let their decisions be guided more by moral values such as justice norms than the other two socioeconomic groups [19–21].The two conditions, however, differ with respect to their decision efficiency. Although the unanimity rule minimizes external costs due to the inclusion of all members of the society, it also allows every member to hold up the decision until the outcome satisfactorily represents its particular interests. For this reason, this arrangement is almost inexistent at the level of nation states and is notorious for its detrimental effects in the security council of the United Nations. Because of its crippling implications, the unanimity rule has been replaced by qualified majority for many policy areas in the European Council by the Lisbon Treaty in 2007. In contrast, the position-based interests of the middle class limit the costs burdened upon the minority because its members will shift sides as soon as demands on the minority become expropriatory. The existence of a middle class thus quasiautomatically corrects for both excessive inequality and equality without generating the hold-up effect of an institutional rule.In this paper, we experimentally test the composite hypothesis following from this argument that, in democratic and competitive organizations, both the existence of a middle class and institutional hurdles can protect the most able organization members from the demand of the least able for excessive income distribution policies (Protection Hypothesis); yet, setting up institutional hurdles is inferior to relying on a middle class as institutional hurdles involve efficiency losses due to bargaining impasses (Efficiency Hypothesis).In our experiment, we directly test whether a neutral middle class is as effective as an institutional rule to avoid excessive expropriation or extremely low redistribution. The second goal of the paper is to check if the existence of a middle class leads to higher efficiency than institutional hurdles.The experiment was composed of two consecutive tasks. During the first task, subjects took part in a multiple-prize rank-order contest that involved a simple cognitive ability task. The contest rewarded effort by assigning the first prize to the most able subject, the second prize to the second most able subject, and so on. Following Moldovanu and Sela [22], the contest ensured that more able subjects should expend more effort in order to win it. Hereby, we focus on the impact of the skewness of the prize scheme on effort and its interaction with ex-post income distribution. During the second task players first deliberated on sharing a surplus (using a group chat). As soon as the deliberation time had elapsed, they simultaneously and anonymously made their binding proposals for a distribution parameter. The proposal that achieved the quorum was played out and the surplus shares were added to the prize money won in the contest. If a group missed the quorum, the players received only their prizes.We find that theProtection Hypothesis is clearly supported by our data. The existence of a neutral middle class is as effective as institutional hurdles. TheEfficiency Hypothesis is also supported. Institutional hurdles come at the costs of significantly less efficiency in terms of higher default rates. The corroboration of both hypotheses allows us to give a clear recommendation for the rich. The rich should brace against the erosion of the middle class because the middle class is the efficient protection of the rich.The rest of the paper is organized as follows. Section2 links our paper to the literature. Section 3 introduces the theoretical framework of our experiment and derives testable hypotheses. Section 4 explains how the models were transferred into the experimental lab. Section 5 reports the results of the experiment. Section 6 discusses the results and concludes the paper.


## 2. Literature Review

If we assume that subjects solely follow self-interest and that self-interest is directly expressed in a social contract with a corresponding level of redistribution, we find ourself in the world of the median voter theorem [23]. Following this theory, an increasing skewness must result in larger pressure for equalization because the median voter’s income declines and hence her interest in redistribution increases [23, 24]. Disregarding the possibility of revolutionary redistribution (tax rates exceeding one), the most extreme form of equalization within a society is to implement, by means of collective decision, a measure which results in equal payoffs. This result, however, is likely to generate socially inefficient outcomes because it undermines the willingness of the more able to expend effort [25].Our paper contributes to the growing literature analyzing why the rich do not get expropriated. Besides the above-mentioned protection through institutional hurdles or the existence of a neutral middle class, another stream in the literature stresses different explanations why the poor median voter does not necessarily follow the median voter’s prediction. The “prospects of upward mobility” hypothesis [26] brings forward the argument that some voters who have an income below the mean expect that their future income will be above the mean. The expectation of these voters works against votes for high levels of redistribution. Roemer [27] and Roemer and Lee [28] show that voting about redistribution is also affected by religion and race. The more fragmented the population is with regard to both dimensions, the lower is the willingness to redistribute. Alesina and Angeletos [13] and Fong [29] show that if the poor believe that the rich are rich because they had invested high efforts and have high abilities, the pressure for redistribution is low. According to extensive empirical and experimental literature, people tend to accept some amount of inequality if it can be attributed to individual effort and ability (e.g., [30–35]). Klor and Shayo [36] find that if the poor identify themselves with the nation (rich and poor) the poor do not want to harm members of the nation and therefore do not expropriate the rich. Moreover, Glaeser et al. [18] highlight that, beyond being protected from expropriation through institutions which are maintained to enforce low levels of redistribution, the better-off are able to manipulate institutions to their own profit. Our paper adds an additional explanation of why the poor cannot enforce high levels of redistribution. We argue that the middle class acts as an uninvolved spectator not affected by redistribution that does not have an interest in excesses from either side.We contribute to a recent wave of research investigating voting on redistribution. This literature sheds some light on the voting decision by using experiments. The main methodological advantage of using experiments is that it allows us to detect how preferences affect the voting-decision. A stylized fact generated by this literature is that voters are willing to sacrifice their own payoffs in order to achieve a more equal payoff distribution, which has been explained by social preferences or social identity. Tyran and Sausgruber [37] reported supporting evidence for inequity theory [38] but emphasized the importance of being pivotal for voting on redistribution. Similarly, Höchtl et al. [39] showed that for empirically plausible cases inequality-averse voters may not matter for redistribution outcomes. Moreover, they did not observe efficiency-loving voters. Bolton and Ockenfels [40] investigated the trade-off between equity and efficiency motives in a voting game with three voters. They found that twice as many voters were willing to give up their own payoff in favor of an equal distribution as compared to a more efficient but unequal distribution. Messer et al. [41] studied the impact of majority voting on the provision of a public good. They detected substantial concerns for efficiency in the subjects’ behavior but found little support for inequality aversion and maximin preferences. Paetzel et al. [42] investigated whether voters would be willing to sacrifice their own payoff in order to implement not only an efficiency-increasing but also an inequality-increasing reform. This case can be thought of as the reverse of voting on efficiency-reducing but inequality-decreasing redistribution. They showed that efficiency preferences of potential reform-losers outweighed the inequality aversion of reform-gainers. Klor and Shayo [36] reported a trade-off between social-identity concerns and payoffs maximization: a subset of their sample systematically deviated from monetary payoff maximization towards a tax rate benefiting their group. Such deviations can neither be explained by efficiency concerns nor by inequality aversion.Recently, Balafoutas et al. [43] reported on an experiment similar to ours (heterogenous initial endowments, quiz versus random assignment, majority vote, and neutral middle player), which generated a number of interesting results. For example, the players with the highest and the lowest endowments were mainly driven by material self-interest. Low-endowment players, however, signalled their willingness to cooperate by increasing their contributions if the redistribution rate was determined by majority vote.1 Our experiment differs in various important respects: the size of the pie to be redistributed is exogenously given, our game involves a communication phase before voting on the tax, and we vary both the initial distribution of endowments and the institutional background in terms of the quorum.A bit against the trend, Esarey et al. [44] and Durante et al. [45] still found redistribution to be strongly related to the self-interest of voters. Durante et al. [45] showed that support for redistribution vanishes if taxation was associated with costs and deadweight losses and if participants earned their incomes in a real effort task.


## 3. Theoretical Framework

In this section, we introduce the theoretical framework of our experiment in order to derive testable hypotheses. The experiment was composed of two consecutive tasks, namely, a contest and a demand game. The contest is explained in the first subsection. It was used for allocating subjects’ initial endowments. The protection hypothesis presupposes that initial endowments adequately reflect subjects’ abilities. We did not induce abilities, but subjects took part in a multiple-prize rank-order contest that involved a simple knowledge test. Assuming that subjects knew their own abilities to solve the knowledge test and had a guess about the distribution of abilities within the sample, which was made up of their fellow students, the contest ensured that more able subjects would expend more effort in order to win it. Effort was rewarded by assigning the first prize to the most able subject, the second prize to the second most able subject, and so on. The theoretical setup for the contest was taken from Moldovanu and Sela [22]. Sheremeta et al. [46] showed the rank-order contest to generate higher effort than lottery and proportional contests.2The demand game is explained in the second subsection. It was used for investigating the impact of different allocations of initial endowments and institutional setups on the acknowledgment of abilities and effort, respectively. Subjects first deliberated on sharing a surplus. As soon as the deliberation time had elapsed, they simultaneously and anonymously made their binding proposals for a distribution parameter. The proposal that achieved the quorum was played out and the surplus shares were added to the prize money won in the contest. If a group missed the quorum, the subjects received only their prizes. Such coordination and bargaining games with preplay communication (also known as cheap talk) have intensively been studied in the literature (for surveys see, e.g., [47–49]). The task determined the distribution parameter by vote and required a communication phase prior to finalizing the proposals such that group members could coordinate towards a distribution parameter capable of winning the necessary majority. In the context of our experiment, the results of Roth [50, 51] are highly relevant, who showed that cheap talk focuses subjects’ attention on a small number of fairness norms in unstructured bargaining experiments (see also [52]). More specifically, subjects identify initial bargaining positions that have some special reason for being credible and these serve as focal points.In the third subjection, we derive testable hypotheses from the theoretical models. We first identify three potential focal points of the demand game, namely, the egalitarian solution, equal sharing, and proportional sharing. Then, each experimental setup is assigned its most likely sharing rule by theoretical consideration. We also analyze the possibility of disagreement. Finally, we argue by backward induction whether and how the sharing rule enacted in the demand game could impact subjects’ willingness to expend effort in the contest.


### 3.1. The Contest

Following Moldovanu and Sela [22], we consider a contest with three prizes πj, where π1>π2≥π3≥0. The total prize money Π=∑j=13‍πj has been exogenously fixed by the contest organizer. The set of contestants is given by K={A,B,C}. Individual effort is denoted by xi, where we set xA>xB>xC. The contest success function is perfectly discriminatory; that is, contestant A is awarded the first prize π1, contestant B is awarded the second prize π2, and contestant C is awarded the third prize π3. Making an effort involves a cost ciγ(xi).3  γ is a strictly increasing function with γ(0)=0. ci>0 is an ability parameter. The lower is ci, the higher is the ability of contestant i and the lower is the cost of effort.Individual abilities are private information. They are independently drawn from the closed interval[m,1], where m>0, and have a continuous distribution function F(c) which is common knowledge. To put it simply, we assume that ability follows a uniform distribution F(c)=(1/(1-m))c-m/(1-m)I[m,1](c)+I(1,∞)(c), where I is an indicator function taking a value of one if c is inside the stated interval and otherwise taking a value of zero. It can be shown (see Appendix C in [22]) that in the Nash equilibrium individual effort is given by(1)x(c)=γ-1∑j=13‍πj∫c1‍-1aFj′(a)da,where(2)Fj′a=3-1!j-1!3-j!1-Fa3-j-1Faj-2·F′a1-3Fa+j-1.In order to interpret (1), one has to realize that a subject’s probability of wining prize j, 1≤j≤3, given her ability a∈[m,1], can be represented by an order statistic(3)Fj(a)=(3-1)!(j-1)!(3-j)!1-Fa3-jFaj-1.This equation takes into account that subject j meets 2 competitors of whom 3-j are less able than j and j-1 are more able. Equation (2) is the first derivative of (3) with respect to ability. Hence, the payoff-maximizing equilibrium effort stated in (1) is a function of the weighted sum of the three prizes, and the weights differ from subject to subject according to their abilities c. Shaked and Shanthikumar [53] have shown that, if γ(c) is a strictly increasing function, effort is a monotonically decreasing function of the cost of ability c and is zero at c=1. Hence, the most able subject will expend the highest effort and win the first price, the medium subject will win the second prize, and the least able subject will expend the lowest effort (but not necessarily zero effort) and win the third prize. Since there is a unique relation between ability, effort, and prize, in the following we will call the most able subject the A-player, the medium able subject the B-player, and the least able subject the C-player.The bidding function (1) is too complex to be solved analytically for the “structural parameters” of the prize scheme that are of interest for us, namely, its mean, variance, and skewness. Nevertheless, clear predictions concerning subjects’ effort reactions can be derived for each parameter change by numerical simulation. In Appendix A,  we report the results of simulating a contest with c={0.4,0.6,0.8} and m=0.2, assuming linear cost functions. The predicted outcome for each prize scheme applied in the experiment is shown in Table 4. The columns list groups of three hypothetical subjects with their abilities, expected winning probabilities, expected returns, efforts, ranks, prizes, costs, and net payoffs (recall that subjects did not know the abilities of the other subjects, but supposedly only the distribution of ability). Table 5, also located in Appendix A, summarizes the information given in Table 4 by listing each prize scheme with its parametrization.4 Additionally it states the mean and the coefficient of variation of predicted effort. As can be seen from the table, predicted effort doubles if the prize money is doubled and if the coefficient of variation of the prize scheme is doubled, and it is almost halved when the prize scheme becomes right-skewed. Furthermore, within-group effort variation increases with a right-skewed prize scheme.


### 3.2. The Demand Game

The second task is a variation of the Nash demand game [54]. After awarding the prizes to the contestants, the contest organizer asks the contestants to make an arbitrary number of proposals s={sA,sB,sC} for sharing a surplus S=Π; that is, total prize money is doubled. However, the surplus is made available only if one of the proposals is supported by a qualified majority of the group of contestants. If none prevails, the contestants receive only their prizes πD={πA,πB,πC} and exit the game (default option). If one of the proposals becomes accepted, it is made binding and the contestants receive their gross payoffs πα={πA+sA,πB+sB,πC+sC}. The following restriction applies to the set of feasible distributions of S:(4)siα=απi+(1-α)23Π-πi∀i∈{A,B,C},0≤α≤1.It is straightforward to show that any feasible agreement α∈[0,1] would be weakly preferred by each contestant over the default option if si≥0 or 0≤πi≤(2/3)Π. Hence, assuming that the latter condition holds, the default option can never be a Nash equilibrium. Conversely, any agreement is a Pareto-efficient Nash equilibrium. We refer to α as the distribution parameter in the following.5This unstructured bargaining protocol, in which subjects could first freely communicate and thereafter had to submit their binding proposals forα simultaneously and anonymously, is ideal for studying the distribution of the surplus and its interaction with the contest for two reasons (for a critical survey of bargaining theories and their experimental tests, see, e.g., [55]): First, existing experimental evidence clearly suggests that subjects coordinate on a small number of focal points or fairness norms in such settings.6 Distributions that could potentially serve as focal points in our experiment are addressed below. Second, the bargaining protocol allows for studying, apart from conflict of interest, the impact of different institutional settings in terms of voting rules on the frequency of disagreement as required for testing theEfficiency Hypothesis.7 Sequential bargaining protocols such as Rubinstein’s [56] and, in its finite version, Baron and Ferejohn’s [57] are inappropriate for studying our research questions because they exhibit unique subgame perfect Nash equilibria, and they assign proposer and responder roles to the players.


### 3.3. Focal Points and Hypotheses

The demand game outlined in the previous subsection has three potential focal points which correspond to different distribution principles or fairness norms. Figure1 gives a self-explaining example for a right-skewed distribution of prizes πD=(26,12,12). Total prize money and surplus are given by Π=S=50. The “budget line” ER¯ represent the bargaining set as well as the Pareto frontier. With regard to α we can distinguish three interesting special cases. First, for α=1, we obtain a surplus distribution sR={sAR,sBR,sCR}, where siR=πi∀i∈{A,B,C}, that is proportional to the prize money earned in the contest and, thus, has a strong positive correlation with effort. In comparison to the distribution of prizes πD={πA,πB,πB} (point D) the resulting gross payoff distribution πR={2πA,2πB,2πC} (point R in the figure) preserves the degree of inequality measured by any relative (scale invariant) inequality measure. The equity standard underlying πR is well known asproportional sharing [58]. It targets the individual opportunity costs of the players [59].Figure 1
Sharing a surplus. The figure shows the gross payoffsπiα of players i=A (horizontal axis) and B and C (vertical axis) for sharing a surplus of S=Π=50 with a right-skewed distribution of prizes π={26,12,12}. ER¯ represents the bargaining set as well as the Pareto frontier. D marks the default option (no agreement). Three focal points E (egalitarian), A (equal sharing), and R (proportional sharing) are depicted together with their corresponding values of the distribution parameter α.Second, forα=0.5, surplus is shared equally siA=(1/3)Π, proportional to the size of the surplus, and uncorrelated with effort. Compared with πD the distribution πA={πA+(1/3)Π,πB+(1/3)Π,πC+(1/3)Π} does not change any absolute (translation invariant) inequality measure. The respective focal point is marked by point A in   Figure 1. Moulin [58, page 162] argued that “any symmetric solution concept would divide equally the surplus.” Theequal sharing rule rewards cooperation rather than effort.In the third case,α=0 yields siE=(2/3)Π-πi, which is proportional to the gap between the equal share in total resources (prize money and surplus) and own prize. siE is negatively correlated with effort. An equal distribution of gross payoffs πE={(2/3)Π,(2/3)Π,(2/3)Π} (point E) occurs (egalitarian solution). Here, the surplus is devoted to wiping out all inequality with regard to gross payoff by imposing a distribution principle which resembles Rawls’ [60] difference principle (though the demand game does not involve a veil of ignorance). However, if erroneously applied to gross income instead of net income, this principle penalizes effort by reversing the rank ordering produced by the contest.As regards different setups of the demand game, we have the following expectations. Theunanimity rule assigns every subject the same veto power regardless of her performance in the contest. Hence, subjects deal separately with the different tasks. In the default option of the demand game, the experimenter retains the surplus; that is, all subjects are treated alike in being given nothing. In line with the literature (see, e.g., [61]), we therefore conjecture the so-called symmetric solution, equal sharing (α=0.5), to be the only distribution standard compatible with the unanimity rule.If the demand game is played withsimple majority voting instead of the unanimity rule, we have to carefully distinguish betweensymmetric andright-skewed prize schemes. Let π¯=(1/3)Π denote the equal share. The first derivative of (4) with respect to α is given by(5)∂siα∂α=2(πi-π¯).A payoff-maximizing subject would therefore vote for α=1 if her prize money exceeds the equal share, she would vote for α=0 if her prize money falls short of the equal share, and she would be indifferent if her prize money equals π¯. In our experimental setup, right-skewed prize schemes consist of two prizes falling short of π¯ and one prize exceeding it. Hence, the B- and C-players are expected to agree on α=0, giving rise to the egalitarian solution. In contrast to this, if a symmetric prize scheme applies, the B-player is indifferent because she cannot change her personal surplus share by voting on α. The B-player’s vote on the distribution parameter might be guided by social preferences. Inequity aversion would induce the B-player to agree with the C-player on an α<0.5. On the other hand, if she acknowledges the higher ability of the A-player, she might agree with the A-player on an α>0.5. The B-player might not be interested in α at all and just randomizes between the proposals of A and C in order to prevent the default option. Since, we have no a priori information about the distribution of B’s preferences, we conjecture that any feasible agreement α∈[0,1] is equally likely. Hence, on average, we should observe that α=0.5, the equal sharing distribution standard. These considerations lead to a testable version of theProtection Hypothesis. (H1)
Both unanimity rule and simple majority voting with a symmetric prize scheme result in a moderate level of redistribution (α=0.5, equal sharing). Simple majority voting with a right-skewed prize scheme leads to the lowest possible value of the distribution parameter; namely α=0, the egalitarian solution.Recall that any agreementα∈[0,1] is a Pareto-efficient Nash equilibrium. Nevertheless, default might occur if subjects decide to veto an agreement in order to prevent “unfair” outcomes. Then, they would sacrifice potential payoff in exchange for keeping the respective prize scheme intact. Obviously, subjects’ veto power is highest if the decision mode is the unanimity rule. Furthermore, it is more difficult for three subjects to coordinate on a joint distribution standard than just for two as in the case, where α is determined by simple majority vote. These considerations lead to a testable version of theEfficiency Hypothesis.(H2)
Fixing the distribution standard by the unanimity rule involves more group disagreement in terms of default than simple majority voting and, therefore, is less efficient.Finally, we have to address the issue whether subjects change their behavior in the contest when anticipating the results of the demand game. Large distribution parameters1≥α≥0.5 definitely preserve the rank ordering determined by the contest in terms of net payoff. A risk neutral contestant would therefore plan her effort independent from the surplus sharing task. Small distribution parameters 0.5>α≥0 would punish effort and possibly reverse the rank ordering in terms of net payoff if α is sufficiently close to zero. In that case, the marginal return on effort becomes negative and effort is expected to diminish strongly. Hence, we can complement the Protection Hypothesis and theEfficiency Hypothesis by the following hypothesis.(H3)
Subjects on average expend less effort in contests with right-skewed prize schemes if the decision mode in the demand game is simple majority voting.


## 3.1. The Contest

Following Moldovanu and Sela [22], we consider a contest with three prizes πj, where π1>π2≥π3≥0. The total prize money Π=∑j=13‍πj has been exogenously fixed by the contest organizer. The set of contestants is given by K={A,B,C}. Individual effort is denoted by xi, where we set xA>xB>xC. The contest success function is perfectly discriminatory; that is, contestant A is awarded the first prize π1, contestant B is awarded the second prize π2, and contestant C is awarded the third prize π3. Making an effort involves a cost ciγ(xi).3  γ is a strictly increasing function with γ(0)=0. ci>0 is an ability parameter. The lower is ci, the higher is the ability of contestant i and the lower is the cost of effort.Individual abilities are private information. They are independently drawn from the closed interval[m,1], where m>0, and have a continuous distribution function F(c) which is common knowledge. To put it simply, we assume that ability follows a uniform distribution F(c)=(1/(1-m))c-m/(1-m)I[m,1](c)+I(1,∞)(c), where I is an indicator function taking a value of one if c is inside the stated interval and otherwise taking a value of zero. It can be shown (see Appendix C in [22]) that in the Nash equilibrium individual effort is given by(1)x(c)=γ-1∑j=13‍πj∫c1‍-1aFj′(a)da,where(2)Fj′a=3-1!j-1!3-j!1-Fa3-j-1Faj-2·F′a1-3Fa+j-1.In order to interpret (1), one has to realize that a subject’s probability of wining prize j, 1≤j≤3, given her ability a∈[m,1], can be represented by an order statistic(3)Fj(a)=(3-1)!(j-1)!(3-j)!1-Fa3-jFaj-1.This equation takes into account that subject j meets 2 competitors of whom 3-j are less able than j and j-1 are more able. Equation (2) is the first derivative of (3) with respect to ability. Hence, the payoff-maximizing equilibrium effort stated in (1) is a function of the weighted sum of the three prizes, and the weights differ from subject to subject according to their abilities c. Shaked and Shanthikumar [53] have shown that, if γ(c) is a strictly increasing function, effort is a monotonically decreasing function of the cost of ability c and is zero at c=1. Hence, the most able subject will expend the highest effort and win the first price, the medium subject will win the second prize, and the least able subject will expend the lowest effort (but not necessarily zero effort) and win the third prize. Since there is a unique relation between ability, effort, and prize, in the following we will call the most able subject the A-player, the medium able subject the B-player, and the least able subject the C-player.The bidding function (1) is too complex to be solved analytically for the “structural parameters” of the prize scheme that are of interest for us, namely, its mean, variance, and skewness. Nevertheless, clear predictions concerning subjects’ effort reactions can be derived for each parameter change by numerical simulation. In Appendix A,  we report the results of simulating a contest with c={0.4,0.6,0.8} and m=0.2, assuming linear cost functions. The predicted outcome for each prize scheme applied in the experiment is shown in Table 4. The columns list groups of three hypothetical subjects with their abilities, expected winning probabilities, expected returns, efforts, ranks, prizes, costs, and net payoffs (recall that subjects did not know the abilities of the other subjects, but supposedly only the distribution of ability). Table 5, also located in Appendix A, summarizes the information given in Table 4 by listing each prize scheme with its parametrization.4 Additionally it states the mean and the coefficient of variation of predicted effort. As can be seen from the table, predicted effort doubles if the prize money is doubled and if the coefficient of variation of the prize scheme is doubled, and it is almost halved when the prize scheme becomes right-skewed. Furthermore, within-group effort variation increases with a right-skewed prize scheme.


## 3.2. The Demand Game

The second task is a variation of the Nash demand game [54]. After awarding the prizes to the contestants, the contest organizer asks the contestants to make an arbitrary number of proposals s={sA,sB,sC} for sharing a surplus S=Π; that is, total prize money is doubled. However, the surplus is made available only if one of the proposals is supported by a qualified majority of the group of contestants. If none prevails, the contestants receive only their prizes πD={πA,πB,πC} and exit the game (default option). If one of the proposals becomes accepted, it is made binding and the contestants receive their gross payoffs πα={πA+sA,πB+sB,πC+sC}. The following restriction applies to the set of feasible distributions of S:(4)siα=απi+(1-α)23Π-πi∀i∈{A,B,C},0≤α≤1.It is straightforward to show that any feasible agreement α∈[0,1] would be weakly preferred by each contestant over the default option if si≥0 or 0≤πi≤(2/3)Π. Hence, assuming that the latter condition holds, the default option can never be a Nash equilibrium. Conversely, any agreement is a Pareto-efficient Nash equilibrium. We refer to α as the distribution parameter in the following.5This unstructured bargaining protocol, in which subjects could first freely communicate and thereafter had to submit their binding proposals forα simultaneously and anonymously, is ideal for studying the distribution of the surplus and its interaction with the contest for two reasons (for a critical survey of bargaining theories and their experimental tests, see, e.g., [55]): First, existing experimental evidence clearly suggests that subjects coordinate on a small number of focal points or fairness norms in such settings.6 Distributions that could potentially serve as focal points in our experiment are addressed below. Second, the bargaining protocol allows for studying, apart from conflict of interest, the impact of different institutional settings in terms of voting rules on the frequency of disagreement as required for testing theEfficiency Hypothesis.7 Sequential bargaining protocols such as Rubinstein’s [56] and, in its finite version, Baron and Ferejohn’s [57] are inappropriate for studying our research questions because they exhibit unique subgame perfect Nash equilibria, and they assign proposer and responder roles to the players.


## 3.3. Focal Points and Hypotheses

The demand game outlined in the previous subsection has three potential focal points which correspond to different distribution principles or fairness norms. Figure1 gives a self-explaining example for a right-skewed distribution of prizes πD=(26,12,12). Total prize money and surplus are given by Π=S=50. The “budget line” ER¯ represent the bargaining set as well as the Pareto frontier. With regard to α we can distinguish three interesting special cases. First, for α=1, we obtain a surplus distribution sR={sAR,sBR,sCR}, where siR=πi∀i∈{A,B,C}, that is proportional to the prize money earned in the contest and, thus, has a strong positive correlation with effort. In comparison to the distribution of prizes πD={πA,πB,πB} (point D) the resulting gross payoff distribution πR={2πA,2πB,2πC} (point R in the figure) preserves the degree of inequality measured by any relative (scale invariant) inequality measure. The equity standard underlying πR is well known asproportional sharing [58]. It targets the individual opportunity costs of the players [59].Figure 1
Sharing a surplus. The figure shows the gross payoffsπiα of players i=A (horizontal axis) and B and C (vertical axis) for sharing a surplus of S=Π=50 with a right-skewed distribution of prizes π={26,12,12}. ER¯ represents the bargaining set as well as the Pareto frontier. D marks the default option (no agreement). Three focal points E (egalitarian), A (equal sharing), and R (proportional sharing) are depicted together with their corresponding values of the distribution parameter α.Second, forα=0.5, surplus is shared equally siA=(1/3)Π, proportional to the size of the surplus, and uncorrelated with effort. Compared with πD the distribution πA={πA+(1/3)Π,πB+(1/3)Π,πC+(1/3)Π} does not change any absolute (translation invariant) inequality measure. The respective focal point is marked by point A in   Figure 1. Moulin [58, page 162] argued that “any symmetric solution concept would divide equally the surplus.” Theequal sharing rule rewards cooperation rather than effort.In the third case,α=0 yields siE=(2/3)Π-πi, which is proportional to the gap between the equal share in total resources (prize money and surplus) and own prize. siE is negatively correlated with effort. An equal distribution of gross payoffs πE={(2/3)Π,(2/3)Π,(2/3)Π} (point E) occurs (egalitarian solution). Here, the surplus is devoted to wiping out all inequality with regard to gross payoff by imposing a distribution principle which resembles Rawls’ [60] difference principle (though the demand game does not involve a veil of ignorance). However, if erroneously applied to gross income instead of net income, this principle penalizes effort by reversing the rank ordering produced by the contest.As regards different setups of the demand game, we have the following expectations. Theunanimity rule assigns every subject the same veto power regardless of her performance in the contest. Hence, subjects deal separately with the different tasks. In the default option of the demand game, the experimenter retains the surplus; that is, all subjects are treated alike in being given nothing. In line with the literature (see, e.g., [61]), we therefore conjecture the so-called symmetric solution, equal sharing (α=0.5), to be the only distribution standard compatible with the unanimity rule.If the demand game is played withsimple majority voting instead of the unanimity rule, we have to carefully distinguish betweensymmetric andright-skewed prize schemes. Let π¯=(1/3)Π denote the equal share. The first derivative of (4) with respect to α is given by(5)∂siα∂α=2(πi-π¯).A payoff-maximizing subject would therefore vote for α=1 if her prize money exceeds the equal share, she would vote for α=0 if her prize money falls short of the equal share, and she would be indifferent if her prize money equals π¯. In our experimental setup, right-skewed prize schemes consist of two prizes falling short of π¯ and one prize exceeding it. Hence, the B- and C-players are expected to agree on α=0, giving rise to the egalitarian solution. In contrast to this, if a symmetric prize scheme applies, the B-player is indifferent because she cannot change her personal surplus share by voting on α. The B-player’s vote on the distribution parameter might be guided by social preferences. Inequity aversion would induce the B-player to agree with the C-player on an α<0.5. On the other hand, if she acknowledges the higher ability of the A-player, she might agree with the A-player on an α>0.5. The B-player might not be interested in α at all and just randomizes between the proposals of A and C in order to prevent the default option. Since, we have no a priori information about the distribution of B’s preferences, we conjecture that any feasible agreement α∈[0,1] is equally likely. Hence, on average, we should observe that α=0.5, the equal sharing distribution standard. These considerations lead to a testable version of theProtection Hypothesis. (H1)
Both unanimity rule and simple majority voting with a symmetric prize scheme result in a moderate level of redistribution (α=0.5, equal sharing). Simple majority voting with a right-skewed prize scheme leads to the lowest possible value of the distribution parameter; namely α=0, the egalitarian solution.Recall that any agreementα∈[0,1] is a Pareto-efficient Nash equilibrium. Nevertheless, default might occur if subjects decide to veto an agreement in order to prevent “unfair” outcomes. Then, they would sacrifice potential payoff in exchange for keeping the respective prize scheme intact. Obviously, subjects’ veto power is highest if the decision mode is the unanimity rule. Furthermore, it is more difficult for three subjects to coordinate on a joint distribution standard than just for two as in the case, where α is determined by simple majority vote. These considerations lead to a testable version of theEfficiency Hypothesis.(H2)
Fixing the distribution standard by the unanimity rule involves more group disagreement in terms of default than simple majority voting and, therefore, is less efficient.Finally, we have to address the issue whether subjects change their behavior in the contest when anticipating the results of the demand game. Large distribution parameters1≥α≥0.5 definitely preserve the rank ordering determined by the contest in terms of net payoff. A risk neutral contestant would therefore plan her effort independent from the surplus sharing task. Small distribution parameters 0.5>α≥0 would punish effort and possibly reverse the rank ordering in terms of net payoff if α is sufficiently close to zero. In that case, the marginal return on effort becomes negative and effort is expected to diminish strongly. Hence, we can complement the Protection Hypothesis and theEfficiency Hypothesis by the following hypothesis.(H3)
Subjects on average expend less effort in contests with right-skewed prize schemes if the decision mode in the demand game is simple majority voting.


## 4. Experimental Design

The experiment was held in the experimental economics laboratory at the University of Bremen and the University of Oldenburg using z-Tree [62].8 In total, 216 subjects participated in 12 sessions in the 90-minute long experiments. Subjects were recruited using the recruitment system ORSEE [63]. About half of the subjects were female (45.6%). 37% of the participants were students of economics, 18% were students of social sciences, and the rest came from all other fields. Participants were on average in the sixth semester. At the outset, subjects were drawn from the subject pool and randomly assigned to a single session. No subject was allowed to take part more than once. We used anonymous random matching of the subjects assigned to a certain treatment into their respective groups. Hence, individual decisions should be independent from one another.


### 4.1. Treatment and Round Structure

The experiment involved four treatments that differed in(i)
the way subjects were allocated their initialendowmentsπD (contest, random);(ii)
thequorum required for fixing the distribution parameter α (majority, unanimity).Our Baseline treatment is contest × majority. Subjects first took part in a contest and then determined the distribution parameter for sharing the surplus by majority vote.9 In the Veto treatment unanimity was required, that is, every contestant was given the same veto power. We additionally conducted Baseline and Veto without a contest in the first step. Here, initial endowments were randomly allocated to the subjects (Control-B and Control-V treatments). Each treatment involved eight rounds. Rounds differed as to the first three moments (mean, variance, and skewness) of the prize schemes. In each round, the prize scheme was presented to the subjects before the knowledge test started.Given the structure of our experiment, treatment effects regarding the impact of the quorum and endowment allocation procedure are investigated at the between-subjects level. Treatment effects regarding the impact of the shape of the prize scheme are investigated at the within-subjects level. This procedure was chosen, on the one hand, in order not to confuse subjects with different voting and allocation mechanisms and, on the other hand, to study the impact of the variation of the moments of the prize scheme on the subjects’ effort and distribution preferences. Apart from this argument, the number of subjects needed for the experiment shrunk by a factor of eight.


### 4.2. First Task: Knowledge Test

Subjects participated under time pressure in a contest. More specifically, they were presented ten questions differing in complexity which had been taken from an intelligence test. Questions were displayed in sequential order. Participants had a time restriction of 15 seconds per question. Going back and forth between questions was not possible.10 For each right (wrong) answer they obtained (lost) one point. Questions that remained unanswered after the time limit of 150 seconds yielded zero points. After having completed the test, subjects were randomly matched with two other subjects into groups of three. A subject’s success in terms of points collected determined his or her rank i∈{A,B,C} in the group. A random number drawn from the unit interval was added to the number of collected points in order to avoid ties. Participants were informed about the procedure but were not informed whether they were actually affected.In each round, each rank was endowed with a prize in tokens exchangeable for money at the end of the experiment. The respective amount was taken from the left of Table1. Note that the number stated in the first column of the table is given for reference purposes only. The prize schemes were presented in randomized order to each group.11 After the end of the quiz, subjects learned their own ranks and the ranks of the other group members, and received their prize money according to the relevant prize scheme.12 They did not receive information about the absolute number of correctly solved tasks of any group member. The group assignment was renewed in every round (stranger design) in order to avoid supergame effects.13Table 1
Set of prize schemes.
Number
Rank
Parameters
A
B
C
Coefficient of
Mean
Variation
Skewness
1
33
17
0
l
h
s
2
67
33
0
h
h
s
3
25
17
8
l
l
s
4
50
33
17
h
l
s
5
36
7
7
l
h
r
6
72
14
14
h
h
r
7
26
12
12
l
l
r
8
52
24
24
h
l
r
Note. L: low, h: high, s: symmetric, and r: right-skewed.An important feature of the set of prize schemes is that symmetric prize schemes render theB-player “neutral” because her final payoff is independent of α. To see this, we plug πB=(1/3)Π into (4), which yields sBα=(1/3)Π for all α∈[0,1]. Hence, it is only her “impartial” distribution attitude, which decides whether or not to agree, later on in the surplus-sharing task, with player A or C on a specific α, and not self-interest. As opposed to this, right-skewed prize schemes discriminate against the B-player by allocating the same prize money to her and C. Since B tried harder than C, it is likely that her net payoff from the contest will fall below C’s. Regardless of that, B’s expected utility is higher than C’s because she is more able and; therefore, she will expend more effort.If subjects were assigned to the Control treatments their ranksi∈{A,B,C} were determined by a random number generator instead of a contest. Everything else, in particular the parametrization of the rounds, stayed the same.


### 4.3. Second Task: Surplus Sharing

The second task involved a phase of preplay communication. Subjects were allowed to chat with their group mates about the distribution parameter to be fixed. For this purpose, we arranged a separate chat room for each group. A calculator for the gross payoff distribution was available during the whole task. The chat was available for three minutes at maximum. Afterwards, subjects were prompted to type in, simultaneously and anonymously, their preferred distribution parameter. The subjects were informed that if there was no agreement on a distribution parameter according to the necessary quorum, they would only receive their prize money. In Baseline at least two group members had to type in exactly the same distribution parameter. In Veto all group members had to type in exactly the same distribution parameter in order to find an agreement. Note that the parametrization of the experiment secured that the distribution of the surplus for a given prize scheme was equivalent to redistributing half of total income (the sum of prize money and surplus). Each distribution standard α corresponded to a specific level of redistribution τ=1-α.14 For example, the egalitarian distributional standard α=0 corresponded to full redistribution τ=100 percent. We favored the design of the experiment as a distributional problem over its presentation as a redistribution task because the chosen design highlights that in case of group default subjects are left alone with their individual outcomes from the contest and nobody can benefit from belonging to a group or society.At the end of the experiment, after the eighth round had been played, one round was randomly selected for payoff. The distribution parameter agreed upon by the group was applied for calculating the gross payoff. If subjects failed to reach an agreement in the surplus sharing task, they received only their prizes. Finally, tokens were converted at a rate of 4 : 1 into Euros. All payments were made in cash and in private. The minimum and the maximum possible payoffs were zero and 36 Euros, respectively. On average, subjects earned €12.01 (≈US$ 13.67) plus a show-up fee of €5 (≈US$ 5.69) for about 90 minutes of work.


## 4.1. Treatment and Round Structure

The experiment involved four treatments that differed in(i)
the way subjects were allocated their initialendowmentsπD (contest, random);(ii)
thequorum required for fixing the distribution parameter α (majority, unanimity).Our Baseline treatment is contest × majority. Subjects first took part in a contest and then determined the distribution parameter for sharing the surplus by majority vote.9 In the Veto treatment unanimity was required, that is, every contestant was given the same veto power. We additionally conducted Baseline and Veto without a contest in the first step. Here, initial endowments were randomly allocated to the subjects (Control-B and Control-V treatments). Each treatment involved eight rounds. Rounds differed as to the first three moments (mean, variance, and skewness) of the prize schemes. In each round, the prize scheme was presented to the subjects before the knowledge test started.Given the structure of our experiment, treatment effects regarding the impact of the quorum and endowment allocation procedure are investigated at the between-subjects level. Treatment effects regarding the impact of the shape of the prize scheme are investigated at the within-subjects level. This procedure was chosen, on the one hand, in order not to confuse subjects with different voting and allocation mechanisms and, on the other hand, to study the impact of the variation of the moments of the prize scheme on the subjects’ effort and distribution preferences. Apart from this argument, the number of subjects needed for the experiment shrunk by a factor of eight.


## 4.2. First Task: Knowledge Test

Subjects participated under time pressure in a contest. More specifically, they were presented ten questions differing in complexity which had been taken from an intelligence test. Questions were displayed in sequential order. Participants had a time restriction of 15 seconds per question. Going back and forth between questions was not possible.10 For each right (wrong) answer they obtained (lost) one point. Questions that remained unanswered after the time limit of 150 seconds yielded zero points. After having completed the test, subjects were randomly matched with two other subjects into groups of three. A subject’s success in terms of points collected determined his or her rank i∈{A,B,C} in the group. A random number drawn from the unit interval was added to the number of collected points in order to avoid ties. Participants were informed about the procedure but were not informed whether they were actually affected.In each round, each rank was endowed with a prize in tokens exchangeable for money at the end of the experiment. The respective amount was taken from the left of Table1. Note that the number stated in the first column of the table is given for reference purposes only. The prize schemes were presented in randomized order to each group.11 After the end of the quiz, subjects learned their own ranks and the ranks of the other group members, and received their prize money according to the relevant prize scheme.12 They did not receive information about the absolute number of correctly solved tasks of any group member. The group assignment was renewed in every round (stranger design) in order to avoid supergame effects.13Table 1
Set of prize schemes.
Number
Rank
Parameters
A
B
C
Coefficient of
Mean
Variation
Skewness
1
33
17
0
l
h
s
2
67
33
0
h
h
s
3
25
17
8
l
l
s
4
50
33
17
h
l
s
5
36
7
7
l
h
r
6
72
14
14
h
h
r
7
26
12
12
l
l
r
8
52
24
24
h
l
r
Note. L: low, h: high, s: symmetric, and r: right-skewed.An important feature of the set of prize schemes is that symmetric prize schemes render theB-player “neutral” because her final payoff is independent of α. To see this, we plug πB=(1/3)Π into (4), which yields sBα=(1/3)Π for all α∈[0,1]. Hence, it is only her “impartial” distribution attitude, which decides whether or not to agree, later on in the surplus-sharing task, with player A or C on a specific α, and not self-interest. As opposed to this, right-skewed prize schemes discriminate against the B-player by allocating the same prize money to her and C. Since B tried harder than C, it is likely that her net payoff from the contest will fall below C’s. Regardless of that, B’s expected utility is higher than C’s because she is more able and; therefore, she will expend more effort.If subjects were assigned to the Control treatments their ranksi∈{A,B,C} were determined by a random number generator instead of a contest. Everything else, in particular the parametrization of the rounds, stayed the same.


## 4.3. Second Task: Surplus Sharing

The second task involved a phase of preplay communication. Subjects were allowed to chat with their group mates about the distribution parameter to be fixed. For this purpose, we arranged a separate chat room for each group. A calculator for the gross payoff distribution was available during the whole task. The chat was available for three minutes at maximum. Afterwards, subjects were prompted to type in, simultaneously and anonymously, their preferred distribution parameter. The subjects were informed that if there was no agreement on a distribution parameter according to the necessary quorum, they would only receive their prize money. In Baseline at least two group members had to type in exactly the same distribution parameter. In Veto all group members had to type in exactly the same distribution parameter in order to find an agreement. Note that the parametrization of the experiment secured that the distribution of the surplus for a given prize scheme was equivalent to redistributing half of total income (the sum of prize money and surplus). Each distribution standard α corresponded to a specific level of redistribution τ=1-α.14 For example, the egalitarian distributional standard α=0 corresponded to full redistribution τ=100 percent. We favored the design of the experiment as a distributional problem over its presentation as a redistribution task because the chosen design highlights that in case of group default subjects are left alone with their individual outcomes from the contest and nobody can benefit from belonging to a group or society.At the end of the experiment, after the eighth round had been played, one round was randomly selected for payoff. The distribution parameter agreed upon by the group was applied for calculating the gross payoff. If subjects failed to reach an agreement in the surplus sharing task, they received only their prizes. Finally, tokens were converted at a rate of 4 : 1 into Euros. All payments were made in cash and in private. The minimum and the maximum possible payoffs were zero and 36 Euros, respectively. On average, subjects earned €12.01 (≈US$ 13.67) plus a show-up fee of €5 (≈US$ 5.69) for about 90 minutes of work.


## 5. Results

We present the results of our experiment in three steps. First, we investigate individual and group effort, then we compare the default rates between different treatments and prize schemes, and, finally, we report the results of testing the hypotheses regarding the outcome of the vote and relate them to effort choice. Furthermore, the outcome of the surplus sharing task after the contest is compared with a setup where the contest was replaced by a random generator.


### 5.1. Effort

Baseline and Veto were conducted each with 72 subjects, randomly forming 72×8/3=192 groups. We start off with the analysis of individual effort expended in the contest. The results of running separate fixed effects (FE) regressions for both treatments are presented in Table 2. We regressed individual effort on the parameters of the prize schemes, mean (0=low, 1=high), variance (0=low, 1=high), and skewness (0=symmetric, 1=rightskewed). The expected signs of their coefficients are given in the last column of the table. The fit of these regressions is very low, which is not too surprising given the usual noise in experimental data and given the fact that we did not induce abilities. Varying mean and variance did not have a significant influence on individual effort.15 For skewness, we obtain a rather interesting pattern. In Baseline, subjects behaved as expected by significantly reducing effort with right-skewed prize schemes. As opposed to this, in Veto subjects increased effort as compared to symmetric prize schemes. In the following, we will therefore concentrate on skewness, quorum, and their interaction.Table 2
Individual effort by treatment.
Coefficient
SE
P
Expected sign
Baseline
Mean
−0.281
0.231
0.228
+
Variance
0.038
0.209
0.855
+
Skewness
−0.552
0.194
0.006
−
Constant
3.170
0.200
0.000
R
2
0.0132
F
3.76
0.015
Veto
Mean
−0.313
0.208
0.137
+
Variance
−0.063
0.181
0.731
+
Skewness
0.375
0.222
0.095
-
Constant
2.729
0.180
0.000
R
2
0.008
F
1.96
0.128
Note. Fixed effects regression (n=72 in both regressions). Endogenous variable: effort. SE: robust standard errors. Subject and period dummies. P: significance level of a two-tailed t-test.Mean group effort across all treatments is 8.25 points. Figure2 shows how group effort varied between treatments and prize schemes, each bar representing 96 group observations. As indicated by the FE regression, the mean difference between Veto and Baseline is negative and insignificant (−0.13, SE: 0.51, P=0.399).16 Due to the opposing effect of skewness between treatments, the mean effort difference between symmetric and right-skewed prize schemes is insignificant too (0.27, SE: 0.51, P=0.300). In fact, mean group effort, like individual effort, decreases by 1.66 points (SE: 0.68) in Baseline, which is highly significant (P≤0.01), while it increases by 1.13 points (SE: 0.77) in Veto, which is significant at the 10% level (P=0.065).Figure 2
Mean effort. The figure shows mean group effort in points by treatment and prize scheme.n=96 for each bar.We conclude that hypothesisH3 is clearly supported by our data both at the individual and at the group level. Subjects expended less effort in contests with right-skewed prize schemes when the surplus sharing task involved the simple majority rule. Additionally, we observed the opposite effect for the Veto treatment, though the effect was less pronounced. In order to analyze our subjects’ effort reactions to the anticipation of surplus distribution in the second part of the experiment more closely, we compiled the respective information on mean effort, separated by rank and treatment, in Table 6 in Appendix A. First focusing on simple majority voting, it becomes apparent that the decline of group effort was mainly due to the less able subjects B and C who expended significantly less effort when the contest involved a right-skewed prize scheme (B-player: P=0.004; C-player: P=0.043), while the most able subject A also showed a negative but insignificant reaction (P=0.326). The unanimity rule induced all subjects to expend a bit more effort when the contest involved a right-skewed prize scheme, but all differences are insignificant (A-player: P=0.167; B-player: P=0.216; C-player: P=0.114). Hence, we refrain from speculating about the reasons for this effect.


### 5.2. Default

Before moving on to analyzing the distribution parameter, we have to filter out those groups that failed to come to an agreement. The overall default rate is 10.2%. Figure3 shows the default rates by treatment and prize scheme. As expected by theEfficiency Hypothesis, the unanimity requirement for α made default more likely in Veto than in Baseline (mean difference: 16.1%, SE: 3.0%, P≤0.01). At first sight, default rates also seem to be lower for right-skewed prize schemes, but the difference turned out to be insignificant at usual significance levels (3.6%, SE: 3.1%, P=0.119). Applying the test separately to each treatment does not change the result (Baseline: 2.1%, SE: 2.1%, P=0.157; Veto: 5.2%, SE: 5.6%, P=0.176). We conclude thatH2 is clearly supported by the data. Note that groups that failed at finding an agreement on α exhibited significantly lower group effort (0.769 points, SE: 0.276, P=0.003). Default was not associated with higher within-group effort variation (mean difference: -7.0%, SE: 51.2%, P=0.554).Figure 3
Default rates. The figure shows the default rate by treatment and prize scheme.n=96 for each bar.


### 5.3. Distribution

After excluding groups that defaulted, 345 group observations remained, 188 (93/95) in Baseline (symmetric/right-skewed) and 157 (76/81) in Veto. The mean of the distribution parameter across all groups is 0.366; that is, the average distribution attitude is a mixture between equal sharing (point A in Figure 1) and the difference principle (pointE). However, the black bars in Figure 4 show αs of around 0.5 (equal sharing) for all situations except for Baseline (majority) combined with right-skewed prize schemes. There, α is very close to zero, that is, the egalitarian distribution standard. Comparing means between treatments (Veto versus Baseline: 0.142, SE: 0.029, P≤0.01) and between prize schemes (symmetric versus skewed: 0.236, SE: 0.027, P≤0.01) supports theProtection Hypothesis that unanimity requirement and symmetric prize schemes make strong (re)distribution less likely. The effect of skewness is more extreme in Baseline but significant in both treatments (Baseline: 0.400, SE: 0.038, P≤0.01; Veto: 0.043, SE: 0.029, P=0.069).Figure 4
Distribution parameter. The figure shows the mean of the distribution parameterα by treatment and prize scheme. Black bars represent Baseline and Veto (contest); n=93, 95, 76, and 81 group observations. White bars represent Control (random endowment); n=48, 48, 47, and 41 group observations.We conclude thatH1 is clearly supported by the data. Additionally, we take a glance at the final proposals for α submitted by the different players (the respective figures can be taken from the right panel of Table 6 in Appendix A). As implied by theProtection Hypothesis, it is mainly the B-player who is responsible for this result. When moving from symmetric to right-skewed prize schemes, her α drops from 0.51 – punctuating her neutrality – to 0.10 (P≤0.01). It is also interesting to see that both the A-player and the B-player made concessions: when moving to a right-skewed prize scheme the A-player “offered” α=0.4 instead of α=0.59 (P≤0.01); when moving to a symmetric prize scheme the B-player “offered” α=0.41 instead of α=0.1 (P≤0.01). In the Veto treatment, we observe significant differences between symmetric and right-skewed prize schemes with regard to the submitted α too (A-player: P=0.052; B-player: P=0.026; C-player: P=0.032). Although all results are relatively close to equal sharing (α=0.4), subjects seem to have perceived the right skewed prize scheme less fair than the symmetric and, therefore, were willing to compensate the losers with a slightly larger share of the surplus. Finally, we would like to note that the dispersion of submitted distribution parameters was highest in Baseline with right-skewed prize schemes, pointing to huge friction within the respective groups.One could argue that theα-values represented by the black bars do not relate to subjects’ approval of individual effort or ability in the contest, but to their acceptance of the prize-schemes specified by the experimenter. In order to check for that objection, we set up the Control treatment, where subjects were randomly endowed with the same set of “prizes” as in Baseline and Veto. 72 subjects participated in Control. The white bars in Figure 4 represent the mean α-values of the groups that did not default. There are two striking observations. First, the average height of the white bars is significantly lower than the black ones (0.247 versus 0.366, mean difference: −0.119, SE: 0.025, P≤0.01). This means that randomly endowing subjects gave rise to a more egalitarian distribution attitude. Groups strove towards wiping out inequality caused by chance rather than effort. Second, the white bars seem to replicate the black-bar pattern produced by the contest. The situation with majority vote and right-skewed initial endowment exhibits the lowest distribution parameter of only 0.03.Table3 gives the difference of the group mean of α between contest and random endowment by quorum and prize scheme. All mean differences exhibit the expected sign and are significantly greater than zero at least at the 5 percent level. Figure 4 and Table 3 indicate that the difference between contest and random endowment is largest for situations involving symmetric endowments/prize schemes and majority vote. This conjecture is supported by the data, the difference of the mean differences of α between symmetric × majority and symmetric × unanimity is 0.147 (SE: 0.069, P=0.017), right-skewed × majority is 0.087 (SE: 0.068, P=0.100), and right-skewed × unanimity is 0.139 (SE: 0.064, P=0.015). All other pairwise difference tests are insignificant. In other words, if at all, individual effort in terms of success in a contest is acknowledged by a group majority only if the prize scheme is symmetric and the distribution of the surplus is determined by the majority vote. Despite the general acceptance of the outcome of the contests, groups on average agreed on a distribution parameter close to 0.5, making equal sharing the dominant distribution motive. This setup was also associated with highest group effort (9.15, see Figure 2). The acceptance of the outcome of the contest shrunk dramatically with a right-skewed prize scheme. In this situation the majority agreed willingly on counteracting ex-ante inequality by imposing the difference principle. Hence, default rates shrunk, but at the cost of lower effort. The unanimity requirement obviously shifted the focus away from effort towards cooperation in order to obtain the surplus. In that situation groups geared themselves to equal sharing combined with a small correction for ex-ante inequality. The respective α-values fall below 0.5 and are almost independent from the shape of the prize scheme/endowment distribution.Table 3
Contest versus random endowment.
Prize scheme
Quorum
Majority
Unanimity
0.218
0.071
Symmetric
(0.057)
(0.035)
P
≤
0.01
P
=
0.022
0.079
0.131
Right-skewed
(0.029)
(0.031)
P
≤
0.01
P
≤
0.01
Note. First row: mean difference of α between contest and random. Second row: standard errors. Third row: significance level of a one-tailed t-test.Table 4
Predictions for the contest.
Prizescheme
Player
Ability
Expected winning   probabilities (%)
Expected return
Effort
Rank
Prize
Cost
Net payoff
i
c
i
1st
2nd
3rd
E
(
π
i
)
x
i
j
π
j
1
0.4
56.2
37.5
6.2
10
38
A
33
15
18
1
2
0.6
25.0
50.0
25.0
4
21
B
17
13
4
3
0.8
6.2
37.5
56.2
1
9
C
0
8
−8
1
0.4
56.2
37.5
6.2
19
77
A
67
31
36
2
2
0.6
25.0
50.0
25.0
8
42
B
33
25
8
3
0.8
6.2
37.5
56.2
2
18
C
0
15
−15
1
0.4
56.2
37.5
6.2
13
20
A
25
8
17
3
2
0.6
25.0
50.0
25.0
10
11
B
17
7
10
3
0.8
6.2
37.5
56.2
8
5
C
8
4
4
1
0.4
56.2
37.5
6.2
27
38
A
50
15
35
4
2
0.6
25.0
50.0
25.0
21
21
B
33
12
21
3
0.8
6.2
37.5
56.2
18
9
C
17
7
10
1
0.4
56.2
37.5
6.2
12
29
A
36
11
25
5
2
0.6
25.0
50.0
25.0
8
10
B
7
6
1
3
0.8
6.2
37.5
56.2
7
2
C
7
2
5
1
0.4
56.2
37.5
6.2
24
57
A
72
23
49
6
2
0.6
25.0
50.0
25.0
16
20
B
14
12
2
3
0.8
6.2
37.5
56.2
14
4
C
14
3
11
1
0.4
56.2
37.5
6.2
14
14
A
26
6
20
7
2
0.6
25.0
50.0
25.0
13
5
B
12
3
9
3
0.8
6.2
37.5
56.2
12
1
C
12
1
11
1
0.4
56.2
37.5
6.2
29
28
A
52
11
41
8
2
0.6
25.0
50.0
25.0
25
10
B
24
6
18
3
0.8
6.2
37.5
56.2
24
2
C
24
2
22
Note. Predictions for a 3-player contest with linear cost functions and maximum ability, m=0.2.Table 5
Predicted effort by prize scheme.
Prize scheme
Mean
Coefficientof variation
Skewness
Effort
Mean
Variation
1
0
1
0
22.9
.6
2
1
1
0
45.9
.6
3
0
0
0
11.9
.6
4
1
0
0
22.5
.6
5
0
1
1
13.6
1.0
6
1
1
1
27.2
1.0
7
0
0
1
6.6
1.0
8
1
0
1
13.1
1.0
Note. 0 = low/symmetric, 1 = high/right-skewed. Effort predictions according to Table 4.Table 6
Effort and distribution proposal by treatment.
Prize scheme
Subject’s rank
Effort
α
A
B
C
A
B
C
Simple majority voting
Symmetric
4.39
3.14
1.63
0.59
0.51
0.41
(0.22)
(0.20)
(0.32)
(0.03)
(0.03)
(0.03)
Right-skewed
4.26
2.38
0.85
0.40
0.10
0.10
(0.17)
(0.20)
(0.30)
(0.04)
(0.02)
(0.02)
Unanimity rule
Symmetric
3.92
2.55
1.16
0.48
0.49
0.47
(0.21)
(0.21)
(0.31)
(0.02)
(0.02)
(0.02)
Right-skewed
4.24
2.80
1.72
0.43
0.41
0.43
(0.26)
(0.22)
(0.35)
(0.02)
(0.03)
(0.02)
Note. The figures give the subjects’ mean scores in the intelligence test (per round) and the mean of the distribution parameter α typed in after the chat phase. Standard errors are in parentheses.


## 5.1. Effort

Baseline and Veto were conducted each with 72 subjects, randomly forming 72×8/3=192 groups. We start off with the analysis of individual effort expended in the contest. The results of running separate fixed effects (FE) regressions for both treatments are presented in Table 2. We regressed individual effort on the parameters of the prize schemes, mean (0=low, 1=high), variance (0=low, 1=high), and skewness (0=symmetric, 1=rightskewed). The expected signs of their coefficients are given in the last column of the table. The fit of these regressions is very low, which is not too surprising given the usual noise in experimental data and given the fact that we did not induce abilities. Varying mean and variance did not have a significant influence on individual effort.15 For skewness, we obtain a rather interesting pattern. In Baseline, subjects behaved as expected by significantly reducing effort with right-skewed prize schemes. As opposed to this, in Veto subjects increased effort as compared to symmetric prize schemes. In the following, we will therefore concentrate on skewness, quorum, and their interaction.Table 2
Individual effort by treatment.
Coefficient
SE
P
Expected sign
Baseline
Mean
−0.281
0.231
0.228
+
Variance
0.038
0.209
0.855
+
Skewness
−0.552
0.194
0.006
−
Constant
3.170
0.200
0.000
R
2
0.0132
F
3.76
0.015
Veto
Mean
−0.313
0.208
0.137
+
Variance
−0.063
0.181
0.731
+
Skewness
0.375
0.222
0.095
-
Constant
2.729
0.180
0.000
R
2
0.008
F
1.96
0.128
Note. Fixed effects regression (n=72 in both regressions). Endogenous variable: effort. SE: robust standard errors. Subject and period dummies. P: significance level of a two-tailed t-test.Mean group effort across all treatments is 8.25 points. Figure2 shows how group effort varied between treatments and prize schemes, each bar representing 96 group observations. As indicated by the FE regression, the mean difference between Veto and Baseline is negative and insignificant (−0.13, SE: 0.51, P=0.399).16 Due to the opposing effect of skewness between treatments, the mean effort difference between symmetric and right-skewed prize schemes is insignificant too (0.27, SE: 0.51, P=0.300). In fact, mean group effort, like individual effort, decreases by 1.66 points (SE: 0.68) in Baseline, which is highly significant (P≤0.01), while it increases by 1.13 points (SE: 0.77) in Veto, which is significant at the 10% level (P=0.065).Figure 2
Mean effort. The figure shows mean group effort in points by treatment and prize scheme.n=96 for each bar.We conclude that hypothesisH3 is clearly supported by our data both at the individual and at the group level. Subjects expended less effort in contests with right-skewed prize schemes when the surplus sharing task involved the simple majority rule. Additionally, we observed the opposite effect for the Veto treatment, though the effect was less pronounced. In order to analyze our subjects’ effort reactions to the anticipation of surplus distribution in the second part of the experiment more closely, we compiled the respective information on mean effort, separated by rank and treatment, in Table 6 in Appendix A. First focusing on simple majority voting, it becomes apparent that the decline of group effort was mainly due to the less able subjects B and C who expended significantly less effort when the contest involved a right-skewed prize scheme (B-player: P=0.004; C-player: P=0.043), while the most able subject A also showed a negative but insignificant reaction (P=0.326). The unanimity rule induced all subjects to expend a bit more effort when the contest involved a right-skewed prize scheme, but all differences are insignificant (A-player: P=0.167; B-player: P=0.216; C-player: P=0.114). Hence, we refrain from speculating about the reasons for this effect.


## 5.2. Default

Before moving on to analyzing the distribution parameter, we have to filter out those groups that failed to come to an agreement. The overall default rate is 10.2%. Figure3 shows the default rates by treatment and prize scheme. As expected by theEfficiency Hypothesis, the unanimity requirement for α made default more likely in Veto than in Baseline (mean difference: 16.1%, SE: 3.0%, P≤0.01). At first sight, default rates also seem to be lower for right-skewed prize schemes, but the difference turned out to be insignificant at usual significance levels (3.6%, SE: 3.1%, P=0.119). Applying the test separately to each treatment does not change the result (Baseline: 2.1%, SE: 2.1%, P=0.157; Veto: 5.2%, SE: 5.6%, P=0.176). We conclude thatH2 is clearly supported by the data. Note that groups that failed at finding an agreement on α exhibited significantly lower group effort (0.769 points, SE: 0.276, P=0.003). Default was not associated with higher within-group effort variation (mean difference: -7.0%, SE: 51.2%, P=0.554).Figure 3
Default rates. The figure shows the default rate by treatment and prize scheme.n=96 for each bar.


## 5.3. Distribution

After excluding groups that defaulted, 345 group observations remained, 188 (93/95) in Baseline (symmetric/right-skewed) and 157 (76/81) in Veto. The mean of the distribution parameter across all groups is 0.366; that is, the average distribution attitude is a mixture between equal sharing (point A in Figure 1) and the difference principle (pointE). However, the black bars in Figure 4 show αs of around 0.5 (equal sharing) for all situations except for Baseline (majority) combined with right-skewed prize schemes. There, α is very close to zero, that is, the egalitarian distribution standard. Comparing means between treatments (Veto versus Baseline: 0.142, SE: 0.029, P≤0.01) and between prize schemes (symmetric versus skewed: 0.236, SE: 0.027, P≤0.01) supports theProtection Hypothesis that unanimity requirement and symmetric prize schemes make strong (re)distribution less likely. The effect of skewness is more extreme in Baseline but significant in both treatments (Baseline: 0.400, SE: 0.038, P≤0.01; Veto: 0.043, SE: 0.029, P=0.069).Figure 4
Distribution parameter. The figure shows the mean of the distribution parameterα by treatment and prize scheme. Black bars represent Baseline and Veto (contest); n=93, 95, 76, and 81 group observations. White bars represent Control (random endowment); n=48, 48, 47, and 41 group observations.We conclude thatH1 is clearly supported by the data. Additionally, we take a glance at the final proposals for α submitted by the different players (the respective figures can be taken from the right panel of Table 6 in Appendix A). As implied by theProtection Hypothesis, it is mainly the B-player who is responsible for this result. When moving from symmetric to right-skewed prize schemes, her α drops from 0.51 – punctuating her neutrality – to 0.10 (P≤0.01). It is also interesting to see that both the A-player and the B-player made concessions: when moving to a right-skewed prize scheme the A-player “offered” α=0.4 instead of α=0.59 (P≤0.01); when moving to a symmetric prize scheme the B-player “offered” α=0.41 instead of α=0.1 (P≤0.01). In the Veto treatment, we observe significant differences between symmetric and right-skewed prize schemes with regard to the submitted α too (A-player: P=0.052; B-player: P=0.026; C-player: P=0.032). Although all results are relatively close to equal sharing (α=0.4), subjects seem to have perceived the right skewed prize scheme less fair than the symmetric and, therefore, were willing to compensate the losers with a slightly larger share of the surplus. Finally, we would like to note that the dispersion of submitted distribution parameters was highest in Baseline with right-skewed prize schemes, pointing to huge friction within the respective groups.One could argue that theα-values represented by the black bars do not relate to subjects’ approval of individual effort or ability in the contest, but to their acceptance of the prize-schemes specified by the experimenter. In order to check for that objection, we set up the Control treatment, where subjects were randomly endowed with the same set of “prizes” as in Baseline and Veto. 72 subjects participated in Control. The white bars in Figure 4 represent the mean α-values of the groups that did not default. There are two striking observations. First, the average height of the white bars is significantly lower than the black ones (0.247 versus 0.366, mean difference: −0.119, SE: 0.025, P≤0.01). This means that randomly endowing subjects gave rise to a more egalitarian distribution attitude. Groups strove towards wiping out inequality caused by chance rather than effort. Second, the white bars seem to replicate the black-bar pattern produced by the contest. The situation with majority vote and right-skewed initial endowment exhibits the lowest distribution parameter of only 0.03.Table3 gives the difference of the group mean of α between contest and random endowment by quorum and prize scheme. All mean differences exhibit the expected sign and are significantly greater than zero at least at the 5 percent level. Figure 4 and Table 3 indicate that the difference between contest and random endowment is largest for situations involving symmetric endowments/prize schemes and majority vote. This conjecture is supported by the data, the difference of the mean differences of α between symmetric × majority and symmetric × unanimity is 0.147 (SE: 0.069, P=0.017), right-skewed × majority is 0.087 (SE: 0.068, P=0.100), and right-skewed × unanimity is 0.139 (SE: 0.064, P=0.015). All other pairwise difference tests are insignificant. In other words, if at all, individual effort in terms of success in a contest is acknowledged by a group majority only if the prize scheme is symmetric and the distribution of the surplus is determined by the majority vote. Despite the general acceptance of the outcome of the contests, groups on average agreed on a distribution parameter close to 0.5, making equal sharing the dominant distribution motive. This setup was also associated with highest group effort (9.15, see Figure 2). The acceptance of the outcome of the contest shrunk dramatically with a right-skewed prize scheme. In this situation the majority agreed willingly on counteracting ex-ante inequality by imposing the difference principle. Hence, default rates shrunk, but at the cost of lower effort. The unanimity requirement obviously shifted the focus away from effort towards cooperation in order to obtain the surplus. In that situation groups geared themselves to equal sharing combined with a small correction for ex-ante inequality. The respective α-values fall below 0.5 and are almost independent from the shape of the prize scheme/endowment distribution.Table 3
Contest versus random endowment.
Prize scheme
Quorum
Majority
Unanimity
0.218
0.071
Symmetric
(0.057)
(0.035)
P
≤
0.01
P
=
0.022
0.079
0.131
Right-skewed
(0.029)
(0.031)
P
≤
0.01
P
≤
0.01
Note. First row: mean difference of α between contest and random. Second row: standard errors. Third row: significance level of a one-tailed t-test.Table 4
Predictions for the contest.
Prizescheme
Player
Ability
Expected winning   probabilities (%)
Expected return
Effort
Rank
Prize
Cost
Net payoff
i
c
i
1st
2nd
3rd
E
(
π
i
)
x
i
j
π
j
1
0.4
56.2
37.5
6.2
10
38
A
33
15
18
1
2
0.6
25.0
50.0
25.0
4
21
B
17
13
4
3
0.8
6.2
37.5
56.2
1
9
C
0
8
−8
1
0.4
56.2
37.5
6.2
19
77
A
67
31
36
2
2
0.6
25.0
50.0
25.0
8
42
B
33
25
8
3
0.8
6.2
37.5
56.2
2
18
C
0
15
−15
1
0.4
56.2
37.5
6.2
13
20
A
25
8
17
3
2
0.6
25.0
50.0
25.0
10
11
B
17
7
10
3
0.8
6.2
37.5
56.2
8
5
C
8
4
4
1
0.4
56.2
37.5
6.2
27
38
A
50
15
35
4
2
0.6
25.0
50.0
25.0
21
21
B
33
12
21
3
0.8
6.2
37.5
56.2
18
9
C
17
7
10
1
0.4
56.2
37.5
6.2
12
29
A
36
11
25
5
2
0.6
25.0
50.0
25.0
8
10
B
7
6
1
3
0.8
6.2
37.5
56.2
7
2
C
7
2
5
1
0.4
56.2
37.5
6.2
24
57
A
72
23
49
6
2
0.6
25.0
50.0
25.0
16
20
B
14
12
2
3
0.8
6.2
37.5
56.2
14
4
C
14
3
11
1
0.4
56.2
37.5
6.2
14
14
A
26
6
20
7
2
0.6
25.0
50.0
25.0
13
5
B
12
3
9
3
0.8
6.2
37.5
56.2
12
1
C
12
1
11
1
0.4
56.2
37.5
6.2
29
28
A
52
11
41
8
2
0.6
25.0
50.0
25.0
25
10
B
24
6
18
3
0.8
6.2
37.5
56.2
24
2
C
24
2
22
Note. Predictions for a 3-player contest with linear cost functions and maximum ability, m=0.2.Table 5
Predicted effort by prize scheme.
Prize scheme
Mean
Coefficientof variation
Skewness
Effort
Mean
Variation
1
0
1
0
22.9
.6
2
1
1
0
45.9
.6
3
0
0
0
11.9
.6
4
1
0
0
22.5
.6
5
0
1
1
13.6
1.0
6
1
1
1
27.2
1.0
7
0
0
1
6.6
1.0
8
1
0
1
13.1
1.0
Note. 0 = low/symmetric, 1 = high/right-skewed. Effort predictions according to Table 4.Table 6
Effort and distribution proposal by treatment.
Prize scheme
Subject’s rank
Effort
α
A
B
C
A
B
C
Simple majority voting
Symmetric
4.39
3.14
1.63
0.59
0.51
0.41
(0.22)
(0.20)
(0.32)
(0.03)
(0.03)
(0.03)
Right-skewed
4.26
2.38
0.85
0.40
0.10
0.10
(0.17)
(0.20)
(0.30)
(0.04)
(0.02)
(0.02)
Unanimity rule
Symmetric
3.92
2.55
1.16
0.48
0.49
0.47
(0.21)
(0.21)
(0.31)
(0.02)
(0.02)
(0.02)
Right-skewed
4.24
2.80
1.72
0.43
0.41
0.43
(0.26)
(0.22)
(0.35)
(0.02)
(0.03)
(0.02)
Note. The figures give the subjects’ mean scores in the intelligence test (per round) and the mean of the distribution parameter α typed in after the chat phase. Standard errors are in parentheses.


## 6. Conclusion

In this paper, we experimentally test if both the existence of a middle class and institutional hurdles can protect the most able members of the society from the demand of the least able for excessive income distribution policies (Protection Hypothesis). We operationalized the institutional rule by the quorum needed for a group decision (majority versus unanimity) and the social structure by the existence of a middle class in contrast to a winner-take-all society. Moreover, we have argued that setting up institutional hurdles is inferior to relying on a middle class as institutional hurdles involve efficiency losses due to bargaining impasses (Efficiency Hypothesis).The experiment directly tests our main hypotheses. We find that theProtection Hypothesis is clearly supported by our data. The existence of a neutral middle class is as effective as institutional hurdles to protect the rich from being expropriated. Hereby, the middle class balances the interests of the poor and the rich. The middle class does not have an interest in excesses from one side because redistribution shifts money from the rich to the poor. We argue that the middle class can be interpreted as an uninvolved spectator who has no interest to favor one group over another. TheEfficiency Hypothesis is also supported. Institutional hurdles come at the cost of significantly less efficiency in terms of higher default rates. Hereby, a higher default rate means that the payoff for both the rich and the poor is lower. Even, at the individual level, we could observe that subjects expend more effort if the prize scheme involved a moderating middle player. The corroboration of both hypotheses allows us to draw the conclusion that the middle class is the efficient protection of the rich.We contribute to the literature about why the rich do not get expropriated. Leaving aside the branch of the literature which summarizes the reasons of why the poor do not expropriate the rich (e.g., beliefs, identity, and social preferences of the poor), we study a constellation in which the rich can actively protect themselves from being expropriated. Although any extrapolation of our laboratory results has to be done carefully, we note that our finding that collective decisions have been less equalizing and more efficient under the majority rule with a neutral middle player than in groups with a right-skewed prize structure resonates well with the empirical data, supporting the warnings about the impact of rising inequality on societal stability and economic growth in contemporary societies. Coming back to the empirical findings in the introduction: not only the middle class itself but also the rich should have an interest in bracing against the erosion of the middle class.



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*Source: 303912-2015-09-01.xml*