Endogenous managerial compensation contracts in experimental duopolies

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Endogenous managerial compensation contracts in experimental duopolies∗ Nikolaos Georgantzis†

Constantine Manasakis‡

Evangelos Mitrokostas§

Emmanuel Petrakis¶

January 2, 2009

Abstract In a Cournot duopoly, we experimentally investigate whether firms’ owners compensate their managers with contracts combining own profits and revenues or own profits and relative performance. We also explore the effects of the selected contracts on the output levels set by managers. In line with the theory, Relative Performance contracts are chosen more frequently than Profit Revenue contracts. Nevertheless, Profit Revenuecompensating owners weight own profits more than Relative Performancecompensating owners. This is in line with the theory, but only for asymmetric contract configurations. Finally, managers set quantities in an excessively pro-competitive way. Behavioral aspects are suggested as a possible explanation for the divergence between observed and predicted outcomes. Keywords: Experimental economics; Oligopoly theory; Managerial delegation; Endogenous contracts JEL Classification: D43; L21.

∗ Financial support by the Spanish Ministry of Science and Technology (SEJ 200507544/ECON) and Bancaixa are gratefully acknowledged. Part of this research was undertaken while N.Georgantzis was visiting the University of Cyprus whose hospitality is gratefully acknowledged. We are grateful to Ivan Barreda for programming and Ainhoa Jaramillo for data analysis. We would also like to thank participants at the EARIE 2008 Conference, Toulouse; the ASSET 2008 Meetings, Florence; and the Seminars Series at UADPhilEcon, Department of Economics, University of Athens, for their helpful comments and suggestions. Full responsibility for all shortcomings is ours. † GLOBE and Department of Economics, University of Granada, Campus de la Cartuja, 18011 Granada, Spain; Tel.: 0034 958249995; Fax: 0034 958249995; e-mail: [email protected]. ‡ Department of Economics, University of Crete, Rethymnon 74100, Greece; e-mail: [email protected]. § Department of Economics, University of Crete, Rethymnon 74100, Greece; e-mail: [email protected]. ¶ Department of Economics, University of Crete, Rethymnon 74100, Greece; e-mail: [email protected].

1

Introduction

It is well established that in modern firms, where ownership and management are separated (Fama and Jensen, 1983), owners choose their managers’ compensation contracts so as to motivate them to gain a competitive advantage in the market (Murphy, 1999; Jensen et al., 2004). Several corporate performance measures have been associated with managerial compensation. Jensen and Murphy (1990) and Lambert et al. (1991) report evidence according to which managerial compensation is associated with firms’ profits and size (as measured by sales or revenues). Gibbons and Murphy (1990), Joh (1999), and Aggarwal and Samwick (1999) report that a widely used practice among firms’ owners, when designing their managers’ compensation contracts, is to take into account the relative performance of own firms against their rivals’ profits. In this paper, we present experimental evidence firstly, on whether firms’ owners compensate their managers with contracts combining own profits and revenues or own profits and relative performance. And secondly, on the effects of the selected by the owners contracts on the output levels set by managers. The strategic use of managerial compensation contracts combining own profits and revenues has been introduced in the literature by Vickers (1985), Fershtman (1985), Fershtman and Judd (1987) and Sklivas (1987). In this line of research, an owner has the opportunity to delegate the output decision to his manager and by offering him an appropriate compensation contract, to direct the manager to a more aggressive behavior in the market. This forces rival firms to reduce their output. In this way, the owner has the opportunity to become a Stackelberg leader in the market, provided that the rival owners do not delegate output decisions to their managers. In equilibrium however, all owners delegate output decisions to managers, ending up in a Stackelberg warfare situation with relatively low profits for all firms. More recently, Miller and Pazgal (2001; 2002; 2005) investigate the case of relative performance contracts, according to which the manager’s compensation is a linear combination of own profits and the relative performance of own firm against its rivals’ profits. In this case too, firms end up in a Stackelberg warfare. However, firms’ profits are higher than in the case of profits-revenues contracts. We study a simple Cournot duopoly framework with symmetric firms. Each firm has an owner and a manager. In our basic three-stage scenario, in the first stage, each firm’s owner commits to one among two types of managerial compensation contracts. First, the Profit Revenue (P R) contract, according to which the manager’s compensation is a linear combination of own profits and revenues. And second, the Relative Performance (RP ) contract, according to which, the manager’s compensation is a linear combination of own profits and relative performance. In the second stage, given that the managerial contracts have become common knowledge and can not be reset, each owner sets the managerial incentive parameter, i.e. the weight of own profits and revenues or own profits and relative performance, depending on the contract type chosen in the previous stage. In the third stage, managers simultaneously set output. An alternative two-stage scenario is also considered, according to which in the 1

first stage, each owner chooses both the type of contract to compensate his manager and the respective managerial incentive parameter. In the second stage, managers set output. This latter scenario helps us to evaluate the relative importance of strategic commitment on the owners’ contract choices. The predictions of the theoretical model are as follows. First, RP contracts are always chosen in equilibrium. This equilibrium is unique in the three-stage scenario where firms’ owners commit to contract types before setting their managerial incentive parameters. Further, in the two-stage scenario where there is multiplicity of equilibria, it is the Pareto superior equilibrium which is expected to be reached via a focal point argument. The rationale behind the contract type selection is that RP contracts lead to a less competitive market behavior, resulting in higher firms’ profits than the P R contracts. Second, managerial incentive parameters are set by owners in such a way that RP -compensated managers are directed towards a less aggressive market behavior than the respective ones for P R-compensated managers. Under universal adoption of contracts, RP -compensating owners set managerial incentive parameters higher than the respective ones set by P R-compensating owners, provided that marginal production costs are low enough. When the two contract types coexist in the market, the above ranking is reversed. And third, firms’ output set under universal adoption of RP contracts is lower than the output set under universal adoption of P R contracts. In contrast, when the two contract types coexist, the above ranking is reversed. We tested the predictions of the theoretical model in the laboratory implementing the two-stage and three-stage scenarios in two respective treatments. Our experimental evidence suggests that, under both treatments, RP contracts were more frequently chosen by owners than P R contracts. This evidence is in line with the theory. We are further able to disentangle the two alternative motives offered by the theoretical analysis for the prevalence of RP contracts. The explanation based on the selection of Pareto superior equilibria receives stronger support than the alternative explanation based on the owners’ strategic commitment over contract types before setting their managerial incentive parameters. Our results also suggest that firms’ owners only rarely chose to compensate their managers so as to direct them at strict maximization of own profits. And this is in line with the theory too. Regarding the managerial incentive parameters, the experimental evidence suggests that the average parameter set by P R-compensating owners was higher than the respective one set by RP -compensating owners. This is in line with the theory but only for duopolies where both contract types coexist. We argue that, under universal adoption of contracts, P R-compensating owners set relatively high managerial incentive parameters in order to mitigate the expected decrease in profits due to the Stackelberg warfare that their contract choices would provoke. The evidence further suggests that the managerial incentive parameter set by an owner, for any given type of contract, is independent of the contract used by the rival owner and of whether the rival owner’s contract was observable, or not, before the contract terms were chosen. Finally, regarding the impact of the contracts chosen by the firms’ owners on 2

the output levels set by managers, the evidence suggests that managers typically behaved in an excessively pro-competitive way, far beyond the theoretical predictions. This is in line with findings by Huck et al. (1999), whose experimental quantity-setting markets have also yielded output levels above the theoretical predictions. Finally, we observe that output levels are rarely monotonically responsive, in the predicted direction, to the contract types and the managerial incentive parameters. Overall, the experimental evidence suggests that the contracts chosen by the firms’ owners result in Stackelberg warfare between managers, in line with the theoretical predictions. Nevertheless, managers realize that the only way to signal their dissatisfaction to their firms’ owners for been compensated with excessively pro-competitive contracts is by producing excessive output levels, resulting in lower profits, despite the fact that their own compensation is seen reduced too. In turn, this evidence may imply that managers’ behavior is affected by fairness and reciprocity considerations rather than directed by absolute own utility maximization alone, as assumed in the theoretical model.1 We thus believe that our results should be perceived within a more general set of findings from experiments on asymmetric bargaining situations, like for example ultimatum games.2 In this literature, it is usually found that the subjects’ behavior is not driven by mere maximization of own utility, but it is also affected by fairness considerations, which can be explained as the result of other-regarding preferences. As a consequence, weaker agents tend to reject unfair offers, despite the fact that this leaves them with lower payoffs. This seems to be the case in our experiment as well. Such a loss of utility from excessively competitive environments has been reported in many different contexts, but, to the best of our knowledge, this is the first time it is being reported in a managerial delegation context. Huck et al. (2004) is the only previous experimental study on strategic managerial compensation contracts in oligopoly. The authors adopt a discrete strategy space where owners choose among two different contracts. The first contract (No-Delegation) gives managers incentives for strict own profit-maximization, while the second contract (Delegation) gives an additional sales bonus. Given the owners’ choices, managers choose output from a discrete strategy space. Their experimental evidence suggests that owners direct their managers towards mere profit-maximization, with a relative frequency of more than 66% in all their treatments. Contrary to Huck et al. (2004), in our experiment owners choose from a continuous strategy space the managerial incentive parameters of their compen1 Yet,

this is in line with the experimental evidence presented by Rigdon (2008). In a principal-agent framework, Rigdon (2008) experimentally investigates the impact of ex post incentives on informal contracts in bargaining environments where there are gains from exchange. She observes that when the principal is more generous to his agent in the first stage of the contracting game, the agent is much more likely to reciprocate by fulfilling the terms of the exchange in the second stage. 2 Since the seminal ultimatum experiment by G¨ uth et al. (1982), we know that an agent receiving an unequal proposal of sharing a given profit with another agent may prefer earning nothing than earning an unfairly low amount of money.

3

sation contracts. Moreover, our managers select output also from an (almost) continuous strategy space. By doing so, we test not only whether owners direct their managers away from strict own profit-maximization, but also the effects of the selected contracts on output levels. Our findings are far more supportive for the main theoretical prediction regarding the use of managerial objectives other than mere profit-maximization. The rest of the paper is organized as follows. Section 2 discusses the theoretical framework and presents the testable hypotheses. Section 3 presents the experimental design. Section 4 reports and discuss the experimental results. Finally, Section 5 concludes.

2

The theoretical framework

We consider a homogenous good industry where two firms, denoted by i, j = 1, 2, i 6= j compete in quantities. The (inverse) demand function for the final good is given by P (Q) = A − Q, with A > 0 and Q = q1 + q2 is the aggregate output. Firms are endowed with constant returns to scale technologies and have identical marginal (and unitary) production cost c. 3 Then firm i’s profits are given by: Πi = (A − qi − qj − c)qi

(1)

In this industry, each firm has an owner and a manager. Following Fershtman and Judd (1987), owner is a decision maker whose objective is to maximize the profits of the firm. This could be the actual owner, a board of directors, or a chief executive officer. Managers are agents hired by owners to make real time operating decisions. Following Straume (2006), we consider that each manager chooses the firm’s output so as to maximize his compensation, according to a contract provided by the owner. Each owner compensates his firm’s manager according to one among two alternative types of contracts. The first is the Profit Revenue (P R) contract. Following Fershtman and Judd (1987) and Sklivas (1987), under this type of contract, the compensation scheme takes a particular form: manager i is paid in proportion to a linear combination of firm i’s profits and revenues. More formally, under this type of contract, manager i’s compensation is given by: R PR CiP R = aP i Πi + (1 − ai )Ri

(2) R aP i

where Πi and Ri are firm i’s profits and revenues respectively, and is the R PR managerial incentive parameter under the P R contract, 0 ≤ aP ≤ 1. If a < i i 1, firm i’s owner directs his manager away from strict profit-maximization towards including consideration of revenues and thus, manager i becomes a more R aggressive seller in the market. If aP = 1, manager i’s behavior coincides with i owner i’s objective for strict profit-maximization. The second type of contract is the Relative Performance (RP ) one. Following Miller and Pazgal (2001; 2002; 2005), under this type of contract, firm 3 To

guarantee interior solutions in all cases, we will assume that

4

c A

≥

1 . 6

i’s owner compensates his manager according to a scheme that puts a weight aRP on own profits and a weight (1 − aRP i i ) on the difference between own and rival firm’s profits, with 0 ≤ aRP ≤ 1. Under this type of contract, manager i’s i compensation is given by: RP CiRP = aRP i Πi + (1 − ai )(Πi − Πj )

(3)

where aRP is the managerial incentive parameter under the RP contract. The i lower the aRP is, the higher is the weight that owner i puts on relative peri formance, directing thus his manager to become a more aggressive seller in the market. If aRP = 1, the manager’s behavior coincides with the owner’s objective i for strict profit-maximization. To investigate which types of managerial compensation contracts will prevail in equilibrium, we consider a three-stage game scenario with observable actions. In the first stage, each firm’s owner commits to one among the two types of contracts D, D = P R, RP for compensating his manager. In the second stage, given that the types of contracts have become common knowledge and can not be reset, each owner sets the respective managerial incentive parameter aD i . In the third stage, managers compete a l` a Cournot. An alternative two-stage game scenario is also considered according to which, in the first stage, each owner chooses both the type of contract and the respective managerial incentive parameter. And in the second stage, managers compete a l` a Cournot. This alternative scenario captures the case in which there is no ex-ante commitment over the type of contract that each owner offers to his manager. This is reasonable whenever the type of contract that each owner sets is unobservable by the rival owner, before the setting of contract terms is everywhere completed. This alternative scenario helps us to evaluate the relative importance of the owners’ strategic commitment over the types of contracts. The equilibrium concept employed to solve the above games is the subgame perfect equilibrium. We consider first the three-stage scenario. There are three possible subgames in this case that are briefly presented below.4 First, the Universal Profit Revenue subgame, in which both firms’ owners choose a P R contract to compensate their managers. Standard backwards induction gives the equilibrium managerial incentive parameters, output levels and profits:

R aP = i

2(A − c) 2(A − c)2 −A + 6c R ; qiP R = ; ΠP = , i = 1, 2 i 5c 5 25

(4)

Second, the Universal Relative Performance subgame, in which both firms’ owners choose a RP contract. The respective equilibrium outcome is: aRP = i

2 3(A − c) 3(A − c)2 ; qiRP = ; ΠRP = , i = 1, 2. i 3 8 32

(5)

4 Analytical results and formal proofs for both scenarios are presented and discussed in detail in Manasakis et al. (2007).

5

Finally, the Coexistence of the two types of contracts subgame, in which owner i compensates his manager with a P R contract, while the rival owner offers an RP contract to his manager. The equilibrium outcome in this case is: pr apr i = 1; qi =

A−c (A − c)2 ; Πpr , i, j = 1, 2, i 6= j i = 4 16

(6)

A−c (A − c)2 ; Πrp , i, j = 1, 2, i 6= j (7) j = 2 8 It is then easy to see that whenever owners are able to commit to contract types, before setting their managerial incentive parameters, each owner has a dominant strategy to choose the RP contract in the first stage. Thus, under the three-stage scenario, there is a unique equilibrium in which both firms’ owners choose RP contracts. The intuition behind the emergence of RP contracts goes as follows. An RP contract makes a manager’s behavior less susceptible to strategic manipulation by rivals. Less scope for strategic manipulation gives to the rival owner less reason to provide incentives for aggressive behavior to his manager. This implies that the owner who chooses the RP contract for his manager obtains a competitive advantage in the market, for any contract choice of the rival owner. This makes the selection of an RP contract each owner’s best response to whatever the rival owner’s choice is. Turning next to the two-stage scenario, one can check that in the absence of owners’ commitment over contract types, there is a multiplicity of equilibria. There are symmetric equilibria where both firms’ owners choose the same type of contract (either P R or RP ) and asymmetric ones where the two types of contracts coexist. Moreover, the symmetric equilibria are Pareto ranked in terms of firms’ profits. Then considering that symmetric equilibria are the most reasonable outcomes of a symmetric game and selecting, via a focal point argument, the Pareto superior equilibrium, it turns out that both firms’ owners choose RP contracts to compensate their managers in equilibrium. In fact, rival owners realize that it is in their mutual interest to move towards the equilibrium that ensures them the highest profits.5 We now formalize the hypotheses that will be tested with our experimental design. First, as regards the owners’ choices over the contract types with which they will compensate their managers in equilibrium, our theoretical findings lead to the following testable hypothesis: TESTABLE HYPOTHESIS 1: (H1.1) Relative Performance contracts are expected to be preferred over Profit Revenue contracts by firms’ owners and (H1.2) If the strategic commitment motivation for the prevalence of Relative Performance contracts is stronger than the focal point alternative, the frequency of Relative Performance contracts is expected to be higher when firms’ rp arp j = 0; qj =

5 Note

that if both owners set the managerial incentive papameters equal to 1, equilibrium (A−c)2

(A−c)

output level and profits are qiN = 3 and ΠN respectively. In the strategy space i = 9 of Huck et al. (2004), this is equivalent to the “No-Delegation” case where owners themselves decide over the output levels.

6

owners commit to contract types before choosing their managerial incentive parameters. Turning to the equilibrium managerial incentive parameters, our theoretical findings suggest that under universal adoption of contracts and as long as c is low enough,6 RP -compensating owners will set higher managerial incentive parameters than those of the P R-compensating owners. While under coexistence of the two contract types, the RP -compensating owner will set a lower managerial incentive parameter than the rival P R-compensating owner. As will see below, in our experimental design c is relatively low, and thus we have the following testable hypothesis: TESTABLE HYPOTHESIS 2: (H2.1) Under universal adoption of contracts, Relative Performance-compensating owners are expected to set managerial incentive parameters at a level higher than that set by Profit Revenue- compensating owners and (H2.2) Under coexistence of the two contract types, the aforementioned ranking is expected to be reversed. Finally, regarding the equilibrium output, our theoretical findings suggest that it is higher under universal adoption of P R contracts rather than under universal adoption of RP contracts. While the opposite ranking holds for firms’ profits. On the other hand, under coexistence of the two types of contracts, an RP -compensated manager sets output at a level higher than that set by his P R-compensated rival manager. The above are summarized in the following testable hypothesis: TESTABLE HYPOTHESIS 3: (H3.1) Output is expected to be higher under universal Profit Revenue contracts than under universal Relative Performance contracts and (H3.2) When the two contract types coexist, an RP -compensated manager is expected to set output at a level higher than that set by his P R-compensated rival manager.

3

Experimental design

We have tested the predictions of the theoretical framework outlined above in a laboratory experiment. A total of 144 subjects participated in the sessions. They were volunteers recruited among 2nd and 3rd year students enrolled in the Business and Human Resources degrees at the Universitat Jaume I (Castell´ on, Spain) according to standard protocols used in the Laboratori d’Economia Experimental (LEE). Each session lasted approximately 100 minutes and average earnings per subject were slightly below 20 euros. The experiment was organized under two treatments. A total of four 36subject sessions were run, two under each treatment. In the first treatment, labeled as 3-stage game, the choice of contract types precedes the choice of their 6 More

specifically, if

c A

<

3 . 8

7

managerial incentive parameters. Then managers set output. In the second treatment, labeled as 2-stage game, owners choose simultaneously both the type of contract to compensate their managers and the respective managerial incentive parameter, before managers decide on their firms’ output. Incentive parameters were chosen between 0 and 1 (inclusive) using up to two decimal digits, whereas output was chosen among the integers in the range between 0 and 500. The experiment was programmed using the z-Tree toolbox (Fischbacher, 2007). At the beginning of each session, each subject was randomly assigned the role of an owner or a manager and written instructions specific to each role were distributed to them. All remaining questions were privately answered by one of the organizers. Eighteen owner-manager pairs, labeled as firms, were randomly formed at the beginning of each session. These pairs were kept fixed throughout the 50 periods of the session in order to encourage the development of a cooperative relation between the agents who formed each firm. In order to facilitate learning in the quantity-setting stage, owners could change their managers’ compensation contract every 3 periods, during the first 30 periods of the session and in every period, during the last 20 periods. Nine duopolies were randomly formed in each period using a strangers matching protocol in order to preserve the one-shot nature of the market game. In order to increase the number of completely independent observations per session, matching occurred within three groups of 6 owner-manager pairs (firms), that is three independent matching groups of 12 subjects each. However, this precise detail was not known by the subjects who would have a further difficulty to guess the total group size and assess the likelihood of being re-matched with the same firm in two different periods, given that the computer network of the LEE is installed in two distant rooms between which there is no possibility of visual contact. No significant difference was found across matching groups within each treatment and, thus, data from the same treatment were pooled together. Following this design, a total of three totally independent observations per session is guaranteed by the fact that strategies and the history experienced by each subject were never contaminated nor did they contaminate decision making within the other two matching groups. Therefore, in a very strict statistical sense, our conclusions are based on behavior within six totally independent groups per treatment. The four independent sessions were run in two occasions on subsequent dates (18-19/12/2006 and 29-30/05/2007). The order between 2-stage and 3-stage treatment was changed across the two occasions to control for any undesirable “social learning” across sessions creating misleading false treatment effects. Therefore, sessions 1 and 4 correspond to the 3-stage treatment, while sessions 2 and 3 belong to the 2-stage treatment. The total cost for subject payoffs was 2, 739 euros which implies slightly above 19 euros per subject earnings, ranging between 7.3 and 29.6 euros (an owner subject in a 3-stage treatment and an owner-subject in a 2-stage treatment respectively). Subjects in the 3-stage treatment receive slightly lower payments than in the 2-stage one (18.7 and 19.3 euros respectively). To compensate for excessively low earnings, a show-up fee of 10 euros was 8

given to each subject and it was uniformly distributed over the 50 periods in the form of a fixed amount f = 20, 000 U M EX (Experimental Currency Units) per period. An exchange rate of 1 euro per 80, 000 U M EX was used. Following closely the contracts studied in the theoretical model, the contract schemes for the experiment were designed after a series of pilot sessions in order to guarantee that subjects with different roles could earn similar expected rewards. In particular, the P R contract took the following formula: 20.000 U M EX as a fixed salary plus a half of a linear combination between the profits and the revenues of the firm. The respective formula for the RP contract was: 20.000 U M EX as a fixed salary plus a half of a linear combination between the firm’s profits and the difference between the firm’s profits and the profits of the rival firm.7 The theoretical model’s parameter values implemented in the experiment were A = 1000 and c = 200. Under this set of parameters, in the Universal R P R equilibrium, our theoretical model predicts aP = 0.2 and qiP R = 320. i The respective values in the Universal RP equilibrium are aRP = 0.666 and i qiRP = 300. The equilibrium managerial incentive parameters and output levels owner i chooses the P R contract while owner j chooses the RP one are: when rp pr rp  = [1, 0, 200, 400]. apr , a , q , q i j i j A strict test of the theoretical model should aim at comparing the observed data on contract types, contract terms and outputs to the aforementioned theoretical predictions. However, any experimentalist would immediately recognize the difficulties associated with such a strict test of the theory, given that, unlike the usual theoretical assumption of perfectly informed human decision makers with unlimited calculus capacity and perfect foresight, real subjects learn from trial-and-error strategies and often commit systematic mistakes due to a number of reasons.8 Thus, we will focus on the test of the predictions provided in a qualitative form by the testable hypotheses H1 − H3 stated in the previous section.

4

Experimental results

In this section we present our experimental results. 7 For

the instructions given to subjects, see the Appendix. vast literature has been dedicated to various factors that may be responsible for observed shortcomings of human behavior in complex environments, such as misperception of feedback (Paich and Sterman, 1993; Sterman, 1994), limitations in subjects’ learning when exposed to strategic complexity (Richards and Hays, 1998), or multitask decision making (Kelly, 1995). A number of factors that favor subjects’ improvement of performance have also been identified. For example, trial-and-error algorithms have been shown to facilitate convergence of the strategies played by uninformed subjects toward symmetric, full-information equilibrium predictions, as shown in Garcia-Gallego (1998) for the case of a price-setting oligopoly. While full convergence near the theoretical single-product symmetric benchmark is obtained in settings such as that outlined in Garcia-Gallego (1998), the introduction of a slightly more complex task in the multiproduct oligopolies in Garcia-Gallego and Georgantzis (2001) or the asymmetry in Garcia-Gallego et al. (2004) provide a sufficiently unfavorable environment for the hypothesis based on the corresponding theoretical prediction to be rejected. 8A

9

4.1

Overall descriptive statistics

We start with the presentation of the overall descriptive statistics of our experiment. Table 1 provides overall sample (sessions 1-4) descriptive statistics for contract types, managerial incentive parameters and firms’ outputs. Table 1: Overall sample descriptive statistics Treatment 2-Stage 3-Stage Both Variable Mean St. Dev. Mean St. Dev. Mean St. Dev. Contract Type 1.733 0.442 1.709 0.454 1.721 0.448 Incentive Parameter 0.498 0.261 0.523 0.285 0.510 0.274 Quantity 357.00 97.99 354.43 91.97 355.72 95.02 Profit-Revenue: Contract Type=1, Relative Performance: Contract Type=2

The following observations are in order. First, regarding the types of contracts chosen by the owners, our experimental evidence suggests that, on average, RP contracts (Contract Type=2) were more frequently chosen than P R contracts (Contract Type=1). This holds for both treatments (2-stage and 3stage) and is in line with the predictions of our theoretical model. Second, regarding the managerial incentive parameters, a first glance at the overall sample reveals some “attraction” towards the focal value of 0.5, which lies between the predictions of both the two symmetric equilibrium configurations R (aRP = 0.2 and aP = 0.666) and the prediction of the asymmetric one (apr i i i = 1, rp aj = 0). A third and quite interesting observation is that, within both treatments and for all contract type configurations, the quantities set were, on average, significantly higher than those predicted by the theoretical analysis. This result implies that our subjects behaved in an excessively pro-competitive way, far beyond the one predicted by the theoretical model. We shall pay special attention to this finding in subsection 4.4. Finally, our evidence suggests an equal split of the experimental earnings in the overall sample and within each treatment. More specifically, owners’ earnings were exactly 50% of total earnings in both the overall sample and the subsamples under treatments 1 and 2. Small variations of these percentages were observed across sessions (51% in session 1; 52% in session 2; 47% in session 3 and 48% in session 4).

4.2

Types of contracts

Our experimental data analysis leads to a number of interesting findings regarding the owners’ choices of contract types to compensate their managers. This evidence is presented in Table 2. First, the evidence suggests that RP contracts were more frequently chosen by owners than P R contracts under both treatments. More specifically, RP 10

vs. P R contracts were chosen 1320 vs. 480 times in the 2-stage treatment and 1277 vs. 523 times in the 3-stage treatment. This is in line with the theoretical predictions. Table 2: Owners’ choices of contract types Treatment i, j = P R i, j = RP i = P R; j = RP 2-stage 148 988 332; 332 3-stage 178 932 345; 345 Total 326 1920 677; 677

Total 1800 1800 3600

Interestingly, the owners’ choices of contract types in our 900 experimental duopolies were as predicted by the theoretical analysis too. As shown in Table 2, more than half of our experimental duopolies took place under Universal RP contracts. This holds for both the 2-stage (494/900 = 54.9%) and the 3stage (466/900 = 51.8%) treatments. In contrast, the Universal P R contracts configuration received scarce, if any, support (74/900 = 8.2% for the 2-stage and 89/900 = 9, 9% for the 3-stage treatment). In fact, the frequency of Universal P R is approximately one quarter of the frequency of the “out of equilibrium” Coexistence of the two contract types, which is 332/900 = 36.9% for the 2-stage and 345/900 = 38.3% for the 3-stage treatment.9 Another significant finding is that firms’ owners only rarely chose to compensate their managers in a way directing them to strict profit maximization. In fact, only in 4% (6%) of the contracts in the 3-stage (2-stage) treatment, owners set the managerial incentive parameter equal to 1. This result comes in sharp contrast with the experimental evidence of Huck et al. (2004). The authors find that the “No-Delegation” strategy is chosen with a relative frequency of more than 66% in all their treatments. Therefore, our experimental results clearly confirm the first part (H1.1) of the Testable Hypothesis 1. Regarding its second part (H1.2), our findings suggest that there is no statistical difference in the frequency of RP contracts across treatments.10 We thus find no evidence in favor of the owners’ ability to commit over specific contract types. In contrast, and against H1.2, there is some evidence suggesting that RP contracts are chosen because these contracts lead to Pareto superior (in terms of firms’ profits) outcomes. We can thus state the following result: RESULT 1: 1. Under both the 2-stage and 3-stage treatments, Relative Performance contracts are significantly more frequent than Profit Revenue contracts. 2. The relatively higher frequency of Relative Performance contracts does not depend on whether owners commit to contract types before contract terms 9 A χ2 test (p < 0.001) has been used to confirm the significance of the difference between the aforementioned observed frequencies and a random distribution of strategy pairs uniformly across the corresponding outcomes of the game in the contract stage. 10 The difference in the frequency of RP contracts across treatments (2-stage vs 3-stage) is rejected by a Mann-Whitney test comparing the number of RP contracts obtained within each independent matching group (p = 0.243).

11

are chosen. The latter result indicates that the prevalence of the Universal RP configuration over its Universal P R counterpart could be explained by the subjects’ selection of the Pareto-dominant equilibrium and not by the subjects’ ability to commit to a specific contract type. Surprisingly, the strategic commitment over contract types motivation seems to lose ground against the rational selection of a Pareto-dominant equilibrium.

4.3

Managerial incentive parameters

We next present our findings regarding the owners’ choices of managerial incentive parameters. We present our evidence in Table 3. Table 3: Owners’ choices of managerial incentive parameters Treatment i, j = P R i, j = RP i = P R; j = RP 2-stage Mean a 0.579 0.471 0.571; 0.472 St. dev. 0.242 0.254 0.285; 0.247 3-stage Mean a 0.611 0.485 0.620; 0.485 St. dev. 0.278 0.277 0.292; 0.276 Regarding the symmetric configurations of contracts, our experimental evidence leads to the following observations. First, under both treatments, the average managerial incentive parameter set by P R-compensating owners was higher than the predicted one; while the opposite was true for the RP -compensating R owners (Recall that our theoretical model predicts aP = 0.2 and aRP = 0.666). i i This implies that P R-compensating (RP -compensating) owners’ intention towards profit-maximization was stronger (weaker) than predicted. Note also that, in absolute values, the deviation of observed managerial incentive parameters from their respective predicted values for P R contracts was twice the deviation for RP contracts. Surprisingly, within each treatment, P R-compensating owners set, on average, managerial incentive parameters higher than those set by the RP -compensated owners.11 This is in contrast to the theory’s predictions and implies that P R-compensated managers were directed towards a relatively more aggressive behavior in the market, as compared to the RP -compensated managers. Note also that for both contract types, the difference in incentive parameters across treatments (2-stage vs. 3-stage) is not statistically significant.12 The evidence regarding the relatively higher managerial incentive parameters set by P R-compensating owners can be rationalized as follows. P Rcompensating owners, anticipating the intense competition that their contract 11 Within each treatment, the difference in managerial incentive parameters across contract types is significant as shown by a Mann-Whitney test comparing averages of independent groups (p = 0.033 for the 2-stage treatment and p = 0.025 for the 3-stage treatment). 12 Given a P R contract, the statistical significance of the difference in incentive parameters across treatments (2-stage vs 3-stage) is rejected by a Mann-Whitney test comparing the populations of independent group averages (p = 0.25). The respective test for an RP contract rejects the statistical significance of the difference in incentive parameters across treatments too (p = 0.48).

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choices would give rise to, might realize that it is in their mutual interest to diR rect their managers towards a relatively less aggressive behavior (higher aP i ), in terms of output expansion, so as to increase their profits. Thus, in order to mitigate the anticipated Stackelberg warfare, they set relatively high managerial incentive parameters, directing their managers to a less aggressive behavior than RP -compensating owners did. Regarding the configurations where the two contract types coexist, three observations are in order. First, under both treatments, the average incentive parameter set by P R-compensating owners was lower than the predicted one; while the opposite was true for the RP -compensating owners (Recall that in asymmetric contract configurations, our theoretical analysis predicts apr i = 1 and arp = 0). Second, P R-compensating owners set, on average, managerial j incentive parameters higher than those set by the RP -compensating owners.13 This holds for both treatments and is in line with the theoretical predictions. Third, for both contract types, the difference in managerial incentive parameters across treatments (2-stage vs. 3-stage) is not statistically significant.14 In fact, the managerial incentive parameters under the coexistence of contract types are strikingly close to those reported under universal adoption of contract types.15 The most striking pattern observed in the evidence reported so far is that given a contract type, owners set very similar managerial incentive parameters across treatments. More specifically, P R-compensating owners set the managerial incentive parameter around 0.57 − 0.62, while RP -compensating owners set it around 0.47 − 0.485. In fact, these value intervals do not vary with either the contract type used by the rival owner or the observability, or not, of the rival owner’s contract (3-stage vs. 2-stage treatment). This can be seen as further evidence regarding the subjects’ selection of the Pareto-dominant equilibrium against the strategic commitment motivation. We summarize our findings in the following result: RESULT 2: 1. Under universal adoption of contracts: (a) there is a systematic deviation of observed managerial incentive parameters from their respective theoretically predicted values, upwards for Profit Revenue contracts and downwards for Relative Performance contracts. (b) the theoretical prediction concerning the relatively higher managerial incentive parameters (i.e., lower aggressiveness) set by Relative Performance-compensating owners, over their Profit Revenue rivals, is not confirmed. 2. Under coexistence of the two contract types: (a) there is a systematic deviation of observed managerial incentive parameters from their respective theoretically predicted values, downwards for Profit Revenue contracts and upwards 13 Within each treatment, the difference in managerial incentive parameters across contract types is significant as shown by a Mann-Whitney test comparing averages of independent groups (p = 0.038 for the 2-stage treatment and p = 0.019 for the 3-stage treatment). 14 The significance of the corresponding differences is rejected by the respective MannWhitney tests obtaining p − values such that p > 0.5 in all cases. 15 The significance of the corresponding differences is rejected by the respective MannWhitney tests obtaining p − values such that p > 0.5 in all cases.

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for Relative Performance contracts. (b) the theoretical prediction concerning the relatively lower incentive parameters (i.e., higher aggressiveness) set by Relative Performance-compensating owners, over their Profit Revenue rivals, is confirmed. 3. The managerial incentive parameter set by an owner is independent both of (i) the contract used by the rival owner and (ii) whether the rival owner’s contract was observed, or not, before the contract terms were chosen.

4.4

Output levels

Finally, we focus on the effects of contract types and managerial incentive parameters chosen by firms’ owners on output levels set by managers. We present our evidence in Table 4. The theoretical analysis predicts that, under symmetric contract configurations, a P R-compensated manager sets output at a level higher than that set by an RP -compensated manager. While under asymmetric configuration of contracts the ranking is reversed (Recall that our theoretical analysis predicts qiRP = 300, qiP R = 320, qipr = 200 and qjrp = 400). We firstly observe that the output levels set in our experiment exceed the theoretically predicted ones. This holds for all cases except for the output level set by RP -compensated managers in the case of asymmetric contract configurations. Table 4: Managers’ choices of output levels Treatment i, j = P R i, j = RP i = P R; 2-stage Mean q 364.608 358.725 359.241; St. dev. 106.741 98.922 95.029; 3-stage Mean q 347.905 359.505 343.177; St. dev. 99.829 90.662 94.548;

j = RP 346.271 93.334 355.357 87.498

The evidence further suggests that the output exhibited little, if any, responsiveness to variations of contract type configurations within each treatment.16 Interestingly, output has remained relatively invariant within each contract type across treatments too.17 This finding seems to be in line with previous research suggesting that learning in Cournot experimental markets exhibits modest degrees of convergence towards the corresponding theoretical predictions due to 16 Regarding the symmetric configurations of contracts, within each treatment, the difference in output levels across contract types is not significant as shown by a Mann-Whitney test comparing averages of independent groups (p = 0.187 for the 2-stage treatment and p = 0.284 for the 3-stage treatment). Under coexistnece of the two types of contracts too, within each treatment, the Mann-Whitney test reveals that the difference in output levels across contract types is not significant, as shown by the respective Mann-Whitney test comparing averages of independent groups (p = 0.111 for the 2-stage treatment and p = 0.124 for the 3-stage treatment). 17 The statistical significance of treatment differences in output levels obtained within each contract type is rejected by Mann-Whitney tests comparing within each contract type independent group output averages across treatments (in all cases, p > 0.005).

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excessively competitive behavior and strategy volatility.18 A remaining question concerns the response of output to a given contract type and a specific managerial incentive parameter. The experimental evidence suggests that under symmetric contract configurations, only in the 2-stage treatment the P R-compensated managers set output levels higher than those set by the RP -compensated managers, in line with the theory. Under asymmetric contract configurations, only in the 3-stage treatment our manager subjects’ behavior was in line with the theoretical predictions. The theory also predicts that the higher the managerial incentive parameter is, the lower is the output, for both types of contracts. We investigate whether our experimental results support the above hypothesis by examining specific patterns of individual managers’ responses to their owners’ managerial incentive parameter decisions. In particular, we consider four intervals of the incentive parameter: [0, 0.25), [0.25, 0.5), [0.5, 0.75), [0.75, 1]. In each market, we have obtained average output and counted the number of duopolies in which average output obtained within each one of the aforementioned intervals exhibits the expected response to the managerial incentive parameter, labeling the response as Monotonic (M ). All other patterns, including non monotonic fluctuations of average output across the four intervals, as well as responses which go in the opposite direction to the predicted one, are labeled as Non-Monotonic (N ).19 Table 5 presents the patterns of output responses to contract terms in each contract configuration.

Universal PR 2-Stage 3-Stage

Universal RP 2-Stage 3-Stage

Coexistence 2-Stage 3-Stage PR RP PR RP M N M N M N M N 1 8 2 7 2 7 0 9

M N M N M N M N 1 8 1 8 2 7 3 6 Table 5: Monotonic (M) and Non-Monotonic (N) responses of the average

output per market due to increases in the managerial incentive parameter.

Observe that the most frequent pattern is, by far, N , implying that in most of our experimental duopolies average output has exhibited at least one kink, revealing non-linear patterns of individual managers’ response to their owners’ behavior. Interestingly, non-monotonic responses of output can be described by 18 See, for example, the sharp difference in the results obtained by Garcia-Gallego (1998) on learning in Bertrand oligopolies and those reported by Huck et al. (1999) on learning in experimental Cournot markets. 19 We have also tested the theory’s prediction through the sign of β in a linear regression 0 + β 1 ∗ alpha equation of the following type: qiD = βiD iD + εi , D = P R, RP . Although iD mixed evidence is obtained, this approach ignores the non-monotonic and, thus, non-linear patterns of output responses to the alpha incentive parameters, which are found to dominate our data.

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a threshold value of the managerial incentive parameter beyond which the manager “counteracts” to the owner’s pretended “advice” (via extreme deviations from strict profit-maximization) for excessively competitive behavior. We summarize our findings in the following result: RESULT 3: 1. Within each treatment, output levels remain invariant across contract types. 2. Given any contract configuration, output has remained invariant across treatments. 3. Output levels set by managers are not monotonically responsive (in the predicted direction) to the managerial incentive parameters chosen by firms’ owners. We may interpret our results within the context of a more general set of findings from experiments on asymmetric bargaining situations, like for example ultimatum games.20 In this literature, it is usually found that the subjects’ behavior, rather than simply maximizing absolute own utility, is affected by fairness considerations which can be explained as the result of other-regarding preferences. As a consequence, weaker agents tend to reject unfair offers, despite the fact that this leads them to lower payoffs. In our experiment, managers are the “weak agents” since they have no bargaining power over the types of contracts and the managerial incentive parameters. Furthermore, they can neither express their opinion or preferences regarding the contracts they are offered, that moreover result in Stackelberg warfare between managers. In this context, a manager realizes that the only way to signal his dissatisfaction to his firm’s owner, concerning the imposition of such a contract, is by producing an excessive output level that results in relatively low profits. Of course, this reduces the manager’s compensation too, but the message is clear: “I do not like compensation contracts that lead to excessively competitive markets”. Such a loss of utility from excessively competitive environments has been reported in many different contexts, but, to our knowledge, this is the first time it is being reported in the context of managerial delegation. An alternative way to accommodate our experimental results into the otherregarding preferences framework is by considering managers’ compliance with their owners’ preferred objectives, as a reciprocal behavior aiming at rewarding their firms’ owners for choosing a contract that does not put excessive procompetitive pressure on the managers while taking their output decisions.21 In 20 Since

the seminal ultimatum experiment by G¨ uth et al. (1982), an influential strand of literature emerged on economic behavior which is driven by other motives than pure short-run own utility maximization. A sample of representative contributions from a plethora of recent papers is Andreoni (1988, 1990), Andreoni and Croson (2008), Berg et al. (1995), Camerer and Thaler (1995), Charness (2004), Cochard et al. (2004), Croson (2000), Dufwenberg et al. (2001), Dufwenberg and Kirchsteiger (2004), Fehr and G¨ achter (1998), Fehr et al. (1998a,b), Fehr and Schmidt (1999), G¨ achter and Falk (2002), Gneezy et al. (2000), G¨ uth et al. (1997, 2001), Hoffman et al. (1994, 1996), Levine (1998), McCabe et al. (2000, 2003), McCabe and Smith (2000) and Rabin (1993). 21 An extensive literature exists on positive and negative reciprocity in many different contexts. Without pretending an exhaustive list, some representative examples are studies by

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any event, a serious but not surprising deviation of experimental results from the theoretical framework is the little, if any, frequency of totally symmetric strategy profiles (including contract types, managerial incentive parameters and output choices), a fact that sharply contrasts with the theoretical predictions of total symmetry. Therefore, one should have in mind that, for instance, in all the occasions of a Universal RP configuration, there is a subject which receives a penalization (negative variable compensation contingent on relative profits) that might trigger regret and feelings of loss to the looser of the “output race” he is forced to participate.

5

Conclusions

In this paper, we have experimentally investigated firstly, whether firms’ owners compensate their managers with contracts combining own profits and revenues or own profits and relative performance and secondly, the effects of the selected by the owners contracts on the output levels set by managers. Our envisaged product market was a homogenous good Cournot duopoly with symmetric firms. Our first key finding is that Relative Performance contracts were more frequently chosen by owners than Profit Revenue contracts. This result does not depend on whether owners commit to contract types before they set the managerial incentive parameters. This seems to imply that the Pareto dominance selection criterion is sufficient to explain the prevalence of RP contracts, while the strategic commitment to contract types, before the managerial incentive parameters are set, seems to lose ground for this prevalence. A second key finding is that the average managerial incentive parameter set by P R-compensating owners was higher than the respective set by RP compensating owners. This is in line with the theory but only for duopolies in which both contract types coexist. Moreover, the managerial incentive parameter set by an owner is found to be independent of the contract chosen by the rival owner and of whether the rival owner’s contract was observed, or not, before the contract terms were set. Finally, output is not monotonically responsive, in the predicted direction, neither to the contract type, nor to the managerial incentive parameters set by firms’ owners. A possible explanation for the managers’ behavior may be the fact that they often counteract to excessively pro-competitive compensation contracts as a means of punishing their owners for “using” them. In this way, the resulting loss of present earnings aims at increasing the probability of receiving more manager-friendly compensation contracts in the future, in the same way in which rejections in repeated ultimatum games aim at increasing offers in the future. This is certainly an underinvestigated behavioral aspect of managerial Andreoni (1988, 1990), Berg et al. (1995), Bolton and Ockenfels (2000), Boyd and Richerson (1989), Cochard et al. (2004), Dufwenberg et al. (2001), Dufwenberg and Kirchsteiger (2004), Engelmann and Fischbacher (2002), Fehr and G¨ achter (1998), Fehr et al. (1998b), G¨ achter and Falk (2002), G¨ uth et al. (2001), McCabe et al. (2003). More similar to our intrafirm relations context is the study by Charness (2004).

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compensation contracts. Hopefully, this is a good opportunity for a re-consideration of managerial incentives in oligopoly theory towards frameworks inspired by the rapidly growing behavioral economics literature on other-regarding preferences. Our experimental evidence gives rise to several natural extensions. First, a theoretical model with behavioral considerations like fairness and reciprocity, might be helpful in order to bring the theoretical framework closer to real world markets. Second, controlling for some of the behavioral factors described above could require designing a more complex environment, accounting for managers’ willingness to sacrifice present earnings in order to cause their firms’ owners to adopt more manager-friendly contracts. We plan to undertake these tasks in the future.

6 6.1

Appendix: Experimental instructions (translated from Spanish) Owner Instructions

2-stage treatment Your decisions in this experiment will help us study human behavior in specific economic contexts. The experiment is financed by public research funds. Read these instructions carefully, taking into account that a better understanding of the decision making context will help you earn more money and generate more reliable and, thus, useful data. You are the owner of one of the two firms selling a given product. You will delegate the output decision of your firm to a manager whom you have hired for this purpose. You will have to decide on the compensation method which your firm will adopt to remunerate your firm’s manager. Your decisions in each period will become public information to all agents involved in the same market before output decisions are made. Managers will have to take these decisions as given and then fix their firm’s output. Contracts may be of the following types: Contract Type 1: 20.000 experimental currency units (UMEX) as a fixed salary plus half of a linear combination between the firm’s profits and the firm’s revenues. Choosing the value of alpha you can vary the weight given by your firm to each of these two objectives (profit and revenue) in the variable compensation of the firm’s manager. Contract Type 2: 20.000 experimental currency units (UMEX) as a fixed salary plus half of a linear combination between the firm’s profits and the difference between your firm’s and the rival’s profits. Choosing the value of alpha you can vary the weight given by your firm to each of these two objectives (profit and revenue) in the variable compensation of the firm’s manager.

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When choosing the contract terms you should take into account that your earnings will be: a fixed amount of 20.000 UMEX plus the firm’s profit. The market will take place for 50 subsequent periods. In each one of them, following your choice of contract and that of the rival firm’s owner managers will make output decisions simultaneously choosing output levels between 0 and 500 product units. You may change your manager’s compensation method every 3 periods during the first 30 periods and every period after period 30. The manager of your firm will be randomly assigned to you once and will be kept fixed throughout the experiment. In each period, you will form a market with a (different) single rival firm which will be chosen randomly among the firms formed by the participants of this experiment in the same way as your firm. Your objective is to maximize your cumulative compensation. The more UMEX you earn the higher will be your payment in cash at the end of the session. We give you a fixed initial payment of 100.000 UMEX which will be added to your earnings from the experiment. The exchange rate is 1 euro for every 80,000 UMEX. Only for the 3-stage treatment Only for the 3-stage treatment: You and the owner of the rival firm will first know the contract chosen by each one of you and then you will decide on the value of alpha. Only after these two decisions have been made by owners, the managers receive information on contract types and alpha’s chosen in order to make their firms output decisions. Thank you for your participation and remember that, once these instructions are read, any communication or action which is not controlled by the organizers is prohibited until payments in cash have been made at the end of the experiment.

6.2

Manager Instructions (both treatments)

Your decisions in this experiment will help us study human behavior in specific economic contexts. The experiment is financed by public research funds. Read these instructions carefully, taking into account that a better understanding of the decision making context will help you earn more money and generate more reliable and, thus, useful data. You are the manager of one of the two firms selling a product in the market. The owner of the firm has hired you in order to delegate to you the decisions concerning the output of the firm. The method with which you will be compensated which you will have to take as given may be of either type: Contract Type 1: 20.000 experimental currency units (UMEX) as a fixed salary plus a half of a linear combination between the profits and the revenues of the firm.

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By choosing the value of alpha, the owner can vary the weight given to each one of the two aforementioned objectives in the variable part of your compensation. Contract Type 2: 20.000 experimental currency units (UMEX) as a fixed salary plus a half of a linear combination between the firm’s profits and the difference between the firm’s profits and the profits of the rival firm. By choosing the value of alpha, the owner can vary the weight given to each one of the two aforementioned objectives in the variable part of your compensation. When receiving this information you should have in mind that the owner’s earnings will be a fixed amount of 20.000 UMEX plus the firm’s profit. The market will take place during 50 periods in each one of which you will have to make the decision of your firm’s output. The contract concerning your compensation may be changed every three periods during the first 30 periods and every period after period 30. You will be assigned to a firm’s owner who will be randomly chosen once at the beginning of the experiment. This matching will be kept constant throughout the session. The firm with which your firm will be matched to form a market will be determined randomly in each period among the rest of the firms formed by the participants in this session in the same way as your firm. Your objective is to maximize your cumulative compensation. The more UMEX you earn the higher will be your payment in cash at the end of the session. We give you a fixed initial payment of 100.000 UMEX which will be added to your earnings from the experiment. The exchange rate is 1 euro for every 80,000 UMEX. Thank you for your participation and remember that, once these instructions are read, any communication or action which is not controlled by the organizers is prohibited until payments in cash have been made at the end of the experiment. References Aggarwal RK, Samwick AA. Executive compensation, strategic competition, and relative performance evaluation: theory and evidence. Journal of Finance 1999; 54; 1999-2043. Andreoni J. Why free ride? Strategies and learning in public good experiments. Journal of Public Economics 1988; 37; 291-304. Andreoni J. Impure altruism and donations to public goods: A theory of warm-glow giving. Economic Journal 1990; 100; 464-477. Andreoni J, Croson R. Partners versus strangers: Random rematching in public goods experiments. In: Plott C, Smith V (Eds.), Handbook of experimental economics results, vol.1. North-Holland: Amsterdam; 2008. p. 776-783. Berg, J., Dickhaut, J., McCabe, K., 1995. Trust, reciprocity, and social history. Games and Economic Behavior 10, 122-142. Bolton GE, Ockenfels A. ERC: A theory of equity, reciprocity and competition. American Economic Review 2000; 90; 166-193. 20

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