Competition and Incentives. Klaus Schmidt, Lisa Fey and Carmen Thoma

Transcription

1 Competition and Incentives Klaus Schmidt, Lisa Fey and Carmen Thoma

2 Competition and Incentives Lisa Fey University of Munich Klaus M. Schmidt University of Munich, CESifo and CEPR Carmen Thoma University of Munich This version: August 24, 2015 Very preliminary. Please do not quote without permission ABSTRACT: We report on two experiments that identify the non-monetary incentive effects of competition. Our hypothesis is that competition has a direct incentive effect that is independent of the monetary incentives it provides. In the experiments we change the degree of competition exogenously keeping the monetary incentives to spend effort constant. The first experiment shows that subjects spend significantly more effort if there is competition. The second experiment shows that a duopolist reacts to a higher effort of his competitor by spending more effort himself while a monopolist reacts to a (payoff equivalent) adverse change in market conditions by spending less effort. JEL CLASSIFICATION NUMBERS: D03, L10, O31. KEYWORDS: Incentive Effects of Competition; Behavioral Industrial Organization. Financial support from the Deutsche Forschungsgemeinschaft through SFB-TR 15 and the Excellence Initiative of the German government through MELESSA is gratefully acknowledged. Department of Economics, University of Munich, Ludwigstr. 28 (Rgb.), D München, Germany. Department of Economics, University of Munich, Ludwigstr. 28 (Rgb.), D München, Germany, klaus.schmidt@lrz.uni-muenchen.de (corresponding author). Department of Economics, University of Munich, Ludwigstr. 28 (Rgb.), D München, Germany.

3 The best of all monopoly profits is a quite life (Hicks, 1935) 1. Introduction There is ample empirical and anecdotal evidence that competition induces firms and individuals to spend more effort and to engage more in innovative activities. In fact an extensive literature in empirical industrial organization shows that there is either a positive or an inverted U-shaped relationship between the degree of competition in an industry and measures of productivity and innovation (Gilbert, 2006). The theoretical literature, however, finds it surprisingly difficult to explain this phenomenon. An increase in the degree of competition affects the marginal returns of investments in cost reduction and innovation, but the effect can go in either direction. Whether an increase of competition increases or decreases the monetary incentives for cost reduction and innovation is ambiguous and depends on subtle details of the market structure (Vives, 2008). In this paper we focus on the non-monetary incentive effects of competition. Our hypothesis is that competition has a direct incentive effect that is independent of the monetary incentives it provides. This effect may explain why we so often observe a positive association between competition and effort incentives. In order to identify this effect we conduct two laboratory experiments in which we change the degree of competition exogenously keeping the monetary incentives to spend effort constant. In the first experiment (with simulataneous investments) we compare a monopoly to a duopoly and an oligopoly with four firms. Competition has a highly significant causal effect on behavior. We find that our experimental subjects engage in significantly more effort in the treatments with competition than in the monopoly treatment. Furthermore, effort falls slightly (but non-significantly) in the oligopoly treatment as compared to the duopoly treatment, which is consistent with the often observed inverted U-shaped relationship between competition and incentives. Even though in equilibrium monetary incentives are kept constant in this experiment, there are several differences between treatments. In the monopoly treatment each subject has to choose his effort level playing against nature. This is a one-person decision problem under risk with exogenously given and known probabilities. In the competition treatments 1

4 several players interact strategically. Thus, subjects have to form beliefs about the strategies taken by their opponents. Furthermore, they may care about the payoffs that their opponents receive, i.e. social preferences may play a role. The optimal strategy depends on the (possibly mistaken) beliefs about the strategies of their opponents and on their (possibly social) preferences. In order to better understand what is driving the incentive effect of competition we conduct a second experiment. In this experiment we compare a monopolist market to a duopoly. In the duopoly treatment the duopolists move sequentially, Thus, the second duopolist observes the effort choice of the first duopolist, so there is no strategic uncertainty. In the monopoly treatment the monopolist faces exogenous uncertainty about adverse market conditions. An increase of the effort chosen by the first duopolist in the duopoly treatment corresponds to an increase of the probability of adverse market conditions in the monopoly treatment. The experiment is designed such that not just the monetary incentives in equilibrium but the entire decision problem is the same for the monopolist and the second duopolist. Furthermore, the monopolist and the second duopolist have the same dominant strategy (i.e., their optimal strategies are independent of market conditions and of what the first duopolist does). The only difference is that in the duopoly treatment there is a second player with whom to interact. In this experiment the average effort level chosen by subjects in the monopoly and in the duopoly treatment are not significantly different. However, we show that in the duopoly treatment there is a strong positive reaction of the second duopolist to the effort chosen by the first duopolist, i.e. efforts are strategic complements. In contrast, in the monopoly treatment an increase in the probability of adverse market conditions (which is payoff equivalent) has a strongly negative effect on the effort chosen by the monopolist. Thus, it is indeed the case that more effort of their competitors induces subjects to work harder, while more challenging market conditions in a monopoly induces them to be more complacent. While our experimental study is conducted in a laboratory environment and uses undergraduate students as subjects, it offers several advantages over field studies. First, in our experiments we can change the degree of competition exogenously. This allows us to identify the causal effects of changes in the degree of competition. In contrast, in field 2

5 studies it is very difficult to identify causal effects because competition affects innovation, but innovation also affects competition. Second, by using the induced value method we can control for the monetary incentive effects of competition (the costs and the returns of the effort invested) which is much more difficult in an empirical study. Finally, we can eliminate potential selection biases that plague many empirical studies. Monopolistic companies are often either state-owned or tightly regulated, thus exhibiting different wage and pension systems than competitive firms. Thus, they may attract managers and workers with different characteristics than companies acting under competitive pressure. In our experiments subjects are randomly assigned to treatments, so there is no self-selection of individuals in more or less competitive markets. Our paper is closely related to two strands of literature the theoretical and empirical literature on competition and innovation and the experimental literature on the effects of competition and on contests. The theoretical literature on competition, investment incentives and innovation goes back at least to Schumpeter (1942) who argued that monopolies will invest more in innovation and Arrow (1962) who argued that the incentives for innovation are stronger with competition. This literature is still not conclusive. Depending on the underlying market model (Bertrand or Cournot competition, type of product differentiation, heterogeneity of firms, etc.) an increase of the degree of competition may increase or decrease the incentives of a firm to innovate and to reduce costs. 1 A different strand of models investigates the effects of competition on managerial incentives (Martin, 1993; Schmidt, 1997; Raith, 2003). In an early contribution Leibenstein (1966) claims that in the absence of competitive pressure there will be managerial slack (which he calls X-Inefficiency ). More recently Bloom and Van Reenen (2007) show that poor management practices are more prevalent when product market competition is weak. Jensen and Meckling (1976) argue that the degree of competition cannot affect managerial slack because a monopolist has the same incentives to reduce agency costs as a competitive firm, so both firms should offer the same incentive scheme. However, this argument ignores that competition changes the environment in which the firm operates and thereby the 1 See Vives (2008) and Schmutzler (2013) for an overview of this literature. 3

6 optimal incentive scheme. For example, Schmidt (1997) shows that if an increase in competition increases the probability of bankruptcy then there there is a threat-of-liquidationeffect : The increased probability of bankruptcy relaxes the manager s limited liability constraint and thereby reduces the cost to implement a higher effort level. This unambiguously increases managerial effort. But more competition also reduces profits and thereby the marginal benefits of a cost reduction for the owner. This value-of-a-cost-reduction effect is ambiguous. If the benefits of a cost reduction are sufficiently reduced the owner of the firm may induce the manager to spend less effort if competition increases. Empirical studies find either that measures of innovation and productivity increase monotonically with the degree of competition (Geroski, 1994; Nickell, 1996; Blundell et al., 1999) or that there is an inverted U-shaped relationship between competition and incentives(scherer, 1967; Aghion et al., 2005). 2 Aghion et al. (2005) argue that the inverted U- shape emerges because the competitiveness of an industry is endogenous and varies with innovative activity. Depending on the innovation level, anti- or pro-competitive effects of an increase in the innovation level dominate. However, using field data it is difficult to control for this joint endogeneity problem. Furthermore, it is difficult to disentangle whether competition has an effect on innovation because of incentive or because of selection effects. There is also a small experimental literature on the relationship between competition and innovation. Isaac and Reynolds (1992) find a positive correlation between competition and cost-reducing R&D investments. Darai et al. (2010) consider two different measures of the degree of competition. A change from Cournot to Bertrand competition increases cost-reducing investments in their experiments, while an increase from two to four players in a Cournot setting leads to lower average investments. In Sacco and Schmutzler (2011) the degree of competition is varied by the degree of product differentiation. They find weak experimental evidence for a U-shaped relationship between competition and innovation. Aghion et al. (2014) test the effect of product market competition on innovation in a dynamic step-by-step innovation model and find an encouraging effect of competition on innovation for neck-and-neck firms and a weak discouraging effect for laggard firms. In all of these papers changes in the degree of competition change the monetary incentives to 2 Gilbert (2006) gives an overview of this literature. 4

7 invest. Thus, these papers cannot disentangle the monetary effects and the non-monetary effects of competition. This is what our paper focuses on. Finally our paper is related to the experimental literature on contests and tournaments. 3 Experiments on Tullock (1980) contests (Millner and Pratt, 1989; Shogren and Baik, 1991), in which several agents exert effort to increase the probability of winning a fixed prize, have shown that the rent dissipation rate (total effort divided by the prize) is significantly higher than predicted by Nash equilibrium, i.e. contestants spend too much effort. In our experiments we also find that subjects overinvest. Furthermore, similar to these studies, we find a high variation in individual investments. However, in our setting the prize is not fixed but determined endogeneously on the market, and we focus on changes in the degree of competition keeping monetary incentives constant. The remainder of the paper is organized as follows. Section 2 reports on our first experiment with simultaneous investments and strategic uncertainty. We describe the experimental design in subsection 2.1, derive the theoretical hypotheses in subsection 2.2 and report the experimental results in subsection 2.3. Section 3 discusses the second experiment with sequential investments in which there is no strategic uncertainty. The experimental design, described in Subsection 3.1, is such that decision makers in the monopoly and the duopoly treatment face exactly the same decision problem (except for the presence of a second duopolist). We report the results of this experiment in Subsection 3.2. Section 4 concludes. 2. Simultaneous Investments 2.1. Experimental Design and Procedures We consider a manager who has to decide how much costly effort to invest into a risky project. The more he invests the higher is the probability that an innovation (a new product, an R& D project, etc.) is successful which increases the profits of the firm he works for. The manager has a monetary incentive to spend costly effort because his compensation is 3 See Dechenaux et al. (forthcoming) for a detailed overview of this literature. 5

8 increasing in the profits of his company. We want to identify the incentive effects of competition that are not due to changes in monetary incentives. In order to do so we compare three treatments: In the MONO- POLY treatment there is only one manager and one firm. The firm s profit depends only on whether its manager is successful. In the DUOPOLY treatment there are two firms and two managers. Each firm s profit depends not only on the effort of its own manager, but also on the success (or failure) of the competing firm. Finally, in the OLIGOPOLY treatment four firms are competing with each other and the profit of each firm depends on the success of its own manager and on how many other firms have been successful. In order to keep the monetary incentives constant across treatments we chose the bonus payments that the manager receives as a function of the profit of his firm such that in the unique Nash equilibrium a risk neutral manager chooses the same effort level in all treatments. Note that in the experiment managers compete only by choosing their effort levels. Product market competition is modeled in reduced form and affects the managers decision problems only via their payoff functions. In all treatments each manager i has to chose a discrete effort level e i. The larger his effort, the larger is the probability that his project is successful. The cost of effort is linear and given by c(e i ) = 2 e i. The benefit of effort is an increased probability of success. Table 1 shows the relationship between investment and probability of success. 4 Effort e Probability of success (in %) p(e) Table 1: Relationship between effort and probability of success The sequence of events is as follows. In each period managers have to choose their effort levels simultaneously. A random mechanism determines success or failure of each firm according to the chosen probabilities. In the monopoly treatment the manager learns whether he was successful and what his payoff in this period is. In the two competition 4 The numbers in the table have been derived from the quadratic function e(p) = 133.3p 2. Note also that the maximal probability of success is 86%, so success cannot be guaranteed. 6

9 treatments the manager learns not only about his own success, but also whether the competing managers have been successful and what the monetary payoffs of each of the competing managers are. In all treatments, the game is repeated over 20 periods with re-matching in the competitive treatments in each period. We used a between-subject design in which each participant attended only one session. Before the experiment began, the instructions were read aloud and the subjects had to answer several control questions. 5 After the last period, subjects answered questions regarding their risk, loss and ambiguity aversion, and filled in a standard questionnaire with demographic information. We conducted the experiments at MELESSA of the University of Munich in 2012/13. We had two sessions per treatment with subjects in each session. 6 A total of 130 subjects participated in the experiments. In each duopoly treatment we had three matching groups with six subjects each and one matching group with four subjects. In each oligopoly treatment we had one matching group with 12 and one with 8 subjects. About 61% of all participants were female and the average age was 24.6 years. Sessions lasted for about 75 minutes. We elicited the participants risk, loss and ambiguity aversion in order to control for possible correlations between effort choices and these characteristics. 7 Subjects were paid their earnings of all periods plus the outcome of the subsequent tests. On average subjects earned EUR (about USD 26 at the time of the experiment), including a showup fee of EUR 4. During the experiment payoffs where expressed in points (500 points = 1 Euro). 5 The instructions of the experiment are included in Appendix??. 6 The experiment was computerized using the software z-tree (Fischbacher, 2007) and subjects were recruited using ORSEE (Greiner, 2004). 7 The test we used for the elicitation of risk aversion is based on Dohmen et al. (2010) and Holt and Laury (2002), the test for loss aversion is based on Gaechter et al. (2010) and Fehr and Goette (2007) and the test for ambiguity aversion is a modified version of Ederer and Manso (2013). For each participant one of the lotteries was randomly chosen for payment at the end of the experiment. The tests can be found in Appendix??. 7

10 2.2. Theoretical Predictions and Hypotheses In this section we derive the optimal effort choices in the experiments assuming that managers are fully rational, only interested in their own monetary payoff, and risk neutral. MONOPOLY Treatment In the MONOPOLY treatment the monetary payoff function of the manager is given by π M = B M 2e (1) where the bonus payment B M depends on whether or not the manager is successful: π M 290 if success = 0 if no success (2) Thus, the managers expected payoff is E[π M (e)] = p(e) 2e. (3) Lemma 1. The optimal effort level in the MONOPOLY treatment is given by e M = 40. Proof. See Appendix A.1. DUOPOLY Treatment In the DUOPOLY treatment the payoff of manager i depends not only on his own success, but also on whether the competing firm is successful or not. He gets the highest payoff if he is the only one who is successful. If both managers are successful his payoff is higher than if no manager is successful. His payoff is lowest if the other firm is successful while he is not. In the experiment manager i s payoff function is given by πi D = Bi D 2e i, (4) where the bonus payment Bi D depends on the success and failure of managers i and j, i, j {1, 2}, i = j: 8

11 480 if i succeeds and j fails Bi D 200 if i and j both succeed = 80 if i and j both fail 0 if j succeeds and i fails (5) Thus, manager i s expected monetary payoff is given by E[π D (e i, e j )] = p(e i )(1 p(e j )) + 200p(e i )p(e j ) + 80(1 p(e i ))(1 p(e j )) 2e i (6) The two managers have to choose their effort levels independently. Note that effort levels are strategic substitutes, i.e., the more manager j invests the smaller is the investment incentive for manager i. Lemma 2. The unique Nash equilibrium in the DUOPOLY treatment is for each manager i, i {1, 2}, to choose ei D = 40. Proof. See Appendix A.1. OLIGOPOLY Treatment Finally, in the OLIGOPOLY treatment there are four managers competing with each other. The monetary payoff of each manager i, i = 1, 2, 3, 4 is given by πi D = Bi O 2e i, (7) where the bonus payments Bi O depend on the success and failure of manager i and on how many other managers have been successful: 760 if i succeeds and all others fail 350 if i and one other manager succeed Bi O 190 if i and two other managers succeed = (8) 90 if all managers succeed 40 if all managers fail 0 if i fails and at least one other manager succeeds 9

12 Thus, manager i s expected monetary payoff is given by E[πi O (e i, e j, e k, e l )] = [p i (1 p j )(1 p k )(1 p l )] [p i p j (1 p k )(1 p l ) + p i p k (1 p j )(1 p l ) + p i p l (1 p j )(1 p k )] +190 [p i p j p k (1 p l ) + p i p l p k (1 p j ) + p i p j p l (1 p k )] +90 [p i p j p k p l + 40 (1 p i )(1 p j )(1 p k )(1 p l ) 2e i. (9) Again, the investments of the four managers are strategic substitutes. Lemma 3. The unique Nash equilibrium in the OLIGOPOLY treatment is for each manager i, i {1, 2, 3, 4} to choose e i = 40. Proof. See Appendix A.1. Lemmas 1 to 3 show that the optimal investment in the MONOPOLY treatment and the Nash equilibrium investments in the DUOPOLY and in the OLIGOPOLY treatment are identical. In equlilibrium the monetary incentives to spend effort are independent of the degree of competition. The equality of the optimal investments across treatments allows us to directly compare the non-monetary effects of different degrees of competition. Hypothesis 1. The investments in the R&D project are the same in the MONOPOLY, DUOPOLY and OLIGOPOLY treatment Results Comparing the average effort levels over all periods across treatments shows significant differences between treatments and between treatments and the Nash equilibrium prediction. The average effort level in the MONOPOLY treatment is 50.4 points. In the DUOPOLY treatment, the average effort is 63.5 points and 59.5 points in the OLIGOPOLY treatment. Figure 1 shows the average effort levels per treatment with 95% confidence interval error bars. Average efforts from period 5 20 are very similar to the average over all periods. Result 1. In all treatments, subjects invest significantly more effort than predicted by Nash equilibrium. 10

13 Figure 1: Average effort invested by treatment The result that subjects exert too much effort compared to the profit-maximising equilibrium prediction is highly significant in all three treatments (sign tests, p-values < 0.001). Result 2. The average effort invested in the DUOPOLY treatment and the average effort invested in the OLIGOPOLY treatment are significantly higher than the average effort invested in the MONO- POLY treatment. A Wilcoxon rank-sum test on the equality of investments (on subject averages) yields a p-value< comparing the MONOPOLY and the DUOPOLY treatment and a p-value of comparing the MONOPOLY and the OLIGOPOLY treatment. We also find that the average investment is lower in the OLIGOPOLY treatment than in the DUOPOLY treatment which is consistent with the often observed inverse U-shaped relationship between competition and incentives. However, this difference is not statistically significant (Wilcoxon rank-sum test, p = ). The treatment difference between the MONOPOLY treatment and the competition treat- 11

14 (1) (2) Investment Investment Duopoly (3.308) (3.450) Oligopoly (3.786) (3.637) Female (3.166) Age (0.277) Risk aversion (1.271) Risk aversion quest (0.959) Loss aversion (0.987) Ambiguity aversion (1.705) p (2.313) Constant (2.161) (11.59) Observations Adjusted R Standard errors in parentheses test line 1 test line 2 p < 0.10, p < 0.05, p < Notes: The table reports coefficients of OLS regressions. Robust standard errors are clustered by subject and reported in parentheses. In regression (2), only the dummy for period 1 is significant. p < 0.10, p < 0.05, p < Table 2: Determinants of the investment in the R&D project 12

15 ments is also significant in an OLS regression in which we compare efforts across treatments. Table 2 reports the regression results. The results of regression (1) show that subjects in the DUOPOLY treatment invest on average points more than in the MONOPOLY treatment (p < 0.001) and that subjects in the OLIGOPOLY treatment invest 9.12 points more than in the MONOPOLY treatment (p = 0.017). 8 The treatment difference between the MONOPOLY treatment and the competition treatments stays significant when we control for gender, age, risk aversion, loss aversion and ambiguity aversion in regression (2). 9 The only marginally significant control variable is age, which has a positive effect on effort. None of the period dummies included in regression (2) is significant, i.e. there does not seem to be a time trend or end game effect. Figure 4 in Appendix A.1 shows average investments per treatment over periods and also does not indicate a time trend in any of the treatments. The main results also do not change if we consider only the investments in period 1, the average investment over periods or if we cluster the standard errors on matching groups instead of on subjects (see Table 5 in Appendix A.1). Based on Result 2 we can reject Hypothesis 1. Investments differ significantly between the MONOPOLY treatment and the competition treatments. To examine the differences in the average investments in more detail, Figure 2 displays the distribution of investments in the R&D project. We observe that investments are dispersed over the whole range in all treatments. Some subjects invest nothing of their endowment in the project, others invest their whole endowment of 100 points. High investments of 80 or more points are chosen in only 13.6% of all cases in the MONOPOLY treatment, but in 32.5% of all cases in the DUOPOLY and in 30.1% of all cases in the OLIGOPOLY treatment. The highest possible investment was chosen in less than 2% of all cases in the MONOPOLY treatment compared to 14.3% and 16.8% in the DUOPOLY and the OLIGOPOLY treatment. What explains the difference in behavior in the monopoly and in the competition treatments? Even though we kept the monetary incentives to invest equal in all treatments, there are several other differences. 8 The difference between the DUOPOLY and the OLIGOPOLY treatment is also not significant in a F-test of the dummy coefficients in regression (1) of Table 2 (p = ). 9 See 7 for the description of the tests we used for the elicitation of risk, loss and ambiguity aversion (included in Appendix??). Points range from 0 to 10 in the risk self-assessment and 0 to 7 in the tests. Higher values imply a higher degree of aversion against risk, loss or ambiguity. 13

16 Relative frequency in % Monopoly Duopoly Oligopoly Investment in R&D Figure 2: Frequencies of chosen investments in the R&D project by treatment First of all, the manager in the monopoly treatment faces exogneous uncertainty with known objective probabilities. In contrast, managers in the competition treatments have to form beliefs about the strategies chosen by their opponents. Thus, a possible explanation for difference in behavior could be that subjects in the competition treatments form mistaken beliefs. Recall that investments are strategic substitutes. In the competition treatments treatment the average effort invested is about 60 points. For an investment level greater or equal than 60 to be a best response a subject would have to believe that the expected investment of his opponent is below 20 in the DUOPOLY treatment and below 30 in the OLIGOPOLY treatment. If this was the case, subjects should have seen over time that this belief is mistaken, that the actual investment levels of their opponents are much higher, and they should have lowered their own effort levels over time. However, we do not observe any time trend in the data. Nevertheless, we cannot rule out that mistaken beliefs did have some effect. 14

17 Second, the payoff structure in the competition treatments are more complex. There are only two possible payoffs in the MONOPOLY treatment but four (six, respectively) different payoffs in the DUOPOLY and the OLIGOPOLY treatment. Furthermore, payoffs in the competition treatments had a higher variance and exposed the decision maker to more risk. This may affected behavior if subjects are risk averse or suffer from loss aversion. If parties are risk averse they should provide less effort than predicted by Lemmas 1 to 3. Furthermore, because there is more uncertainty in the DUOPOLY and in the OLIGOPOLY treatment than in the MONOPOLY treatment, a risk averse decision maker should work less hard if there is competition, the exact opposite of what we observe. The regression analysis in Table 3 shows that neither risk aversion nor loss aversion are significantly correlated with the chosen effort levels. Thus, it seems unlikely that risk and/or loss aversion are driving our results, but again, the current experiment does not allow us to rule out this possibility completely. Finally, the competition treatments involve social interaction, while managers in the MONOPOLY treatment face a one-person decision problem. If parties have social preferences this may affect their behavior if subjects are envious, inequity averse, or reciprocal. The literature on contests claims that subjects spend too much effort as compared to the Nash prediction because there is a joy of winning. In our experiments subjects could win in all treatments, but it is possible that they enjoy winning more if they win against another subject than if they win against nature. In the real world all of these effects do play a role. Competition involves strategic interaction and requires the formation of (possibly mistaken) beliefs of the opponents, competitive situations are more complex and more risky than situations without competition, and competition involves social interactions. In order to better understand how these effects affect behavior we conduct a second experiment in which we control for all of these effects except for the social interaction. 15

18 3. Sequential Investments In the second experiment we control for the differences between monopolistic and competitive markets. The design of the second experiment is similar to the design of the monopoly and the duopoly treatment in the first experiment, but in the new duopoly treatment subjects invest sequentially. After manager D1 chose his effort level, manager D2 observes the effort chosen by his competitor before choosing his own effort level. In this way we can control the beliefs of manager D2. He knows the probability with which his competitor will be successful. Furthermore, we add some randomness in the monopoly treatment in such a way that the decision problems in the new duopoly treatment (DUO-SEQ) and in the new monopoly treatment (MONO-SEQ) are identical. We tell the manager M in the MONO-SEQ treatment that his bonus payment depends on two factors: First, on whether he is successful which depends probabilistically on the effort he chooses, and second on whether market conditions are adverse or favorable. His bonus payment if he is successful and the market is favorable is the same as the bonus payment of manager D2 in the DUO-SEQ treatment if this manager is successful and manager D1 fails. His bonus payment if he is successful and market conditions are adverse is the same as the bonus payment of manager D2 in the DUO-SEQ treatment if both managers are successful, and so on. In the MONO-SEQ treatment manager M is informed that the probability of adverse market conditions in period t is equal to p t. We conducted the DUO-SEQ treatment first and used the probabilities chosen by the first manager in period t as the probability of adverse market conditions p t in the corresponding MONO-SEQ treatment. Thus, the managers in the MONO-SEQ treatment faced exactly the same payoffs and the same probabilities as the corresponding second movers in the DUO-SEQ treatment. The only difference is that in the DUO-SEQ treatment the bad state of the world is that the competing manager is successful, while in the MONO-SEQ treatment the bad state is an unfavorable market. Finally, in order to simplify the decision problems we let managers choose the probabilities of success directly and we adjusted the bonus payments such that the optimal effort level is independent of the effort chosen by the competitor (independent of the probability 16

19 of adverse market conditions, respectively) Experimental Design and Parameters Each subject has an initial endowment of 100 points in each period. Subjects choose the probability of success according to the function displayed in Table 3: 10 Probability of success in % p Effort cost e Table 3: Relationship between probability of success and effort cost In the DUO-SEQ treatment the sequence of events in each period t is as follows: First, manager D1 chooses his probability of success p1 t and thereby how much effort to invest. Then manager D2 learns which probability was chosen. Finally manager D2 decides on his success probability p t 2 (and thus his effort investment. The probabilities pt 1 and pt 2 are stochastically independent. Both managers learn the outcomes of both projects and both of their bonus payments. In the MONO-SEQ treatment there is only one manager M. Before choosing his effort level the manager is informed that the probability of adverse market conditions in this period t is equal to p t. We have chosen p t = p1 t, i.e., equal to the probability of success chosen by a corresponding manager D1 in the DUO-SEQ treatment in period t. Furthermore, the bonus payments in the MONO-SEQ treatment are equal to the corresponding bonus payments in the DUO-SEQ treatment. Thus, the manager in the MONO-SEQ treatment faces the same probabilities, the same payoffs, and the same information as the corresponding manager D2 in the DUO-SEQ treatment. At the end of each period the manager learns whether he was successful and whether market conditions were favorable or not. The experiment runs for 20 periods with random rematching in the DUO-SEQ treatment. We take the complete history of probabilities {p1 t } of one first moving manager in the DUO- SEQ treatment and use them as the probabilities {p t } of one manager M in the DUO-SEQ treatment. Figure 3 illustrates the sequence of events in the duopoly (upper part) and the 10 The table is derived from the quadratic effort cost function e(p) = 125p 2. 17

20 monopoly (lower part) treatment in each period. Duopoly: manager D1 chooses p 1 manager D2 gets to know p 1 manager D2 chooses p 2 managers learn both outcomes Monopoly: probability of adverse market conditions is p = p 1 manager M gets to know p manager M chooses p manager M learns both outcomes Figure 3: Sequence of events in the DUO-SEQ and MONO-SEQ treatments t.. We conducted nine sessions for this experiment in 2013, three with the MONO-SEQ treatment and six with the DUO-SEQ treatment. Between 22 and 24 subjects participated in each session, a total of 210 subjects over all sessions. In the DUO-SEQ sessions we had either three matching groups with eight subjects or 2 groups with 8 subjects and 1 group with 6 subjects. Half of the participants in each DUO-SEQ sessions were chosen to be first movers (manager D1), the other ones second movers(manager D2). 11 On average, subjects earned EUR 16.44, including a show-up fee of EUR 4. During the experiment, payments were expressed in points (25 points = 1 Euro) Theoretical Predictions and Hypotheses DUO-SEQ Treatment Equation (10) shows the payoff function π D i i = j in the DUO-SEQ treatment. of subject i = 1, 2 with π D i = B D i e i (10) 11 The experiment was computerized using the software z-tree (Fischbacher, 2007) and subjects were recruited using ORSEE (Greiner, 2004). About 61% of all participants were female and average age was 24 years. Sessions lasted about 90 minutes. Subjects were paid their earnings of one period chosen randomly out of the 20 periods plus the outcome of one randomly chosen test in which we elicited subjects risk, loss and ambiguity aversion. See 7 and 9 for a description of the tests. The tests are included in Appendix??. 18

21 where the bonus payment Bi D depends on manager i s own success and on whether or not the other manager was succesful: 200 if i succeeds and j fails Bi D 100 if i and j succeed = (11) 100 if i and j fail 0 if j succeeds and i fails Manager i s payoff function can be rewritten π D i (p i, p j ) = p i (1 p j )200 + p i p j (1 p i )(1 p j ) p 2 i = p i 100p j 125p 2 i (12) Lemma 4. In the DUO-SEQ treatment it is a dominant strategy for each manager i, i {1, 2}, to choose p i = 0.4. Thus, the unique Nash equilibrium is (p1, p 2 ) = (0.4, 0.4). Proof. See Appendix A.2. MONO-SEQ Treatment The payoff function π M of a manager in the MONO-SEQ treatment is given by π M = B M e (13) where 200 if manager is successful and favorable market conditions B M 100 if manager is successful and adverse market conditions = 100 if manager is and favorable market conditions 0 if manager is and adverse market conditions (14) Equation (13) can be rewritten as π M (p M, p) = p M (1 p L )200 + p M p L (1 p M )(1 p L )100 p2 M = p M 100p 125p 2 M (15) Lemma 5. In the MONO-SEQ treatment the optimal strategy of manager M is independent of the 19

22 probability of adverse market conditions and given by p M = 0.4. Proof. See Appendix A.2. Note that the decisions problems of managers M and D2 are (almost) identical. Adverse and favorable market conditions have the same effect on manager M s payoff as the success or failure of manager D1 has on manager D2. Furthermore, the probabilities of these states are the same, the two managers have the same cost functions and the information structure is the same across treatments. The only difference is that there is a second duopolist in DUO-SEQ which is not the case in MONO-SEQ. Thus, it is not surprising that the standard neoclassical model predicts the same investments. Note further that in both treatments it is a dominant strategy to choose a probability of success of 40%, independent of p 1 and p L. Hypothesis 2. Manager D2 in the DUO-SEQ treatment and manager M in the MONO-SEQ treatment choose the same effort level, p 2 = p M = 40%. Furthermore, the effort of manager D2 is independent of the probability of success chosen by manager D1 and the effort of manager M is independent of the probability of adverse market conditions Results The average chosen probability of success is 53.6% for subject 2 in the DUO-SEQ treatment and 52.6% for the subject in the MONO-SEQ treatment. As in the experiment with simultaneous investments, we observe that subjects invest more than the equilibrium prediction in both treatments (sign tests, p-values< 0.001). The dominant strategy of p = 0.4 is chosen in only 12.5% of all investment decisions in the MONO-SEQ treatment and in 9.5% of all investment decisions in the DUO-SEQ treatment. Result 3. In both treatments, subjects on average invest significantly more than predicted by Hypothesis 2. The effort chosen by the manager in the monopoly treatment is somewhat lower in the MONO-SEQ treatment than in the DUO-SEQ treatment, but the difference is small. A 20

23 Wilcoxon rank-sum test on equality of the chosen probability of success in the MONO- SEQ treatment and the DUO-SEQ treatment cannot be rejected (average over periods and subjects in a treatment, p = 0.47). This is confirmed by the simple OLS regression (1) reported in Table 4 where we regress the chosen success probabilities on the treatment variable monopoly only. However, a Chi-test on independence of the distributions of the probabilities of success p M and p 2 between the treatments rejects the hypothesis of equal investment distributions across treatments (p < 0.001). Furthermore, the treatment difference becomes significant in OLS regression (2) where we control for the probability of success of subject 1, respectively the probability of adverse market conditions. Regression (2) in Table 4 shows that the treatment variable monopoly has a highly significant and positive effect on the chosen probability. At the same time monopoly interacted with p has a highly significant negative impact. Regression (3) shows that the difference in the investment behaviour with and without competition is still significant and almost unchanged if we control for other characteristics. Only the control variable female has a marginally significant and positive effect on the chosen probability. The other characteristics age, risk aversion, risk aversion questionnaire, loss aversion and ambiguity aversion do not have a significant effect on subjects investment decision.controlling for period effects does not affect the results and there does not seem to be an end-game effect. Figure 5 in Appendix A.2 shows average investments per treatment over periods. The main results of the regressions do not change if we consider only the investments in period 1 or if we cluster the standard errors on matching groups (see Table 10 in Appendix A.2). Result 4. Subjects in both treatments do not choose the dominant investment strategy. The probability of success of subject 2 depends positively on the probability of success of subject 1 in the DUO-SEQ treatment. The probability of success of subject M depends negatively on the probability of a bad market development in the MONO-SEQ treatment. In the experiment with simultaneous investments we found that subjects in the competition treatments invest on average significantly more than subjects in the MONOPOLY treatment (see Result 2). By controlling for the differences in the complexity of the invest- 21

24 Probability of success of the R&D project in % (subject M and 2) (1) (2) (3) Monopoly (2.647) (4.754) (4.722) Prob. of subject 1/ Prob. of bad market development (0.0545) (0.0527) Monopoly Prob. of subject 1/ Prob. of bad market development (0.0809) (0.0801) Female (2.615) Age (0.241) Risk aversion (1.149) Risk aversion quest (0.861) Loss aversion (0.793) Ambiguity aversion Period dummies (1.617) yes Period 1 Period 2 Period (2.211) (2.144) (2.197) Constant (1.933) (3.418) (10.10) Observations Adjusted R Notes: The table reports coefficients of OLS regressions. Robust standard errors are clustered by subject and reported in parentheses. All probabilities are expressed in percent. In regression (3), of the 20 period dummies only the listed ones are significant. p < 0.10, p < 0.05, p < Table 4: Determinants of the investment in the R&D project in the SEQ-experiment 22

25 ment decision and the exposure to risk we find that subjects in the DUO-SEQ treatment do not invest on average significantly more than in the MONO-SEQ treatment. We find that subject 2 and subject M both do not choose the dominant strategy which is independent of the probability of success of subject 1 and the probability of a bad market development, respectively. Instead we find that subjects react differently to the exogenous uncertainty. Regression (2) of Table 4 predicts the following reaction functions p 2 (p 1 ) of subject 2 and p M (p) of subject M, which are depicted in Figure 3: p 2 (p 1 ) = p 1 (16) p M (p) = p (17) chosen probability p 2 (p 1 ), p M (p B ) competition Duopoly Monopoly monopoly p 1 =p B probability of of the the other other player/probability of of bad market outcome Figure 3: Reaction functions p 2 (p 1 ) and p M (p) In the DUO-SEQ treatment, a high investment of the competitor reduces the subject s expected profit. The marginal effect of the investment remains unaffected but the higher probability of success of the competitor has a negative wealth effect on the subject s profit. The same holds true for the subjects in the MONO-SEQ treatment: An increase in the probability of a bad market development imposes a negative wealth effect on a subject s profit, 23

26 keeping the marginal effect of the investment unaffected. However, subjects in the DUO- SEQ and in the MONO-SEQ treatment react differently. In the DUO-SEQ treatment, the exogenous decrease in the expected profit motivates subject 2 to increase his investment. This effect is reversed in the MONO-SEQ treatment, in which subject M is discouraged by a low expected profit and therefore invests less. Our findings reveal, that in our experiment with sequential investments, the difference in the average investment disappears. But we find that subjects in the DUO-SEQ and the MONO-SEQ treatment have a significantly different investment strategy. Even though the experiment with sequential moves controls for several factors that are prevalent in competitive markets such as exogenous uncertainty, strategic interaction, beliefs and complex decision-making, subjects incentives to invest still differ with and without competitive pressure. 4. Conclusions Our experiments confirm that the degree of competition has an effect of behavior that goes beyond the monetary incentives that are provided by competition. The first experiment with simultaneous investment decision shows that subjects invest more if there is competition than in a monopolistic situation. However, competition changes a situation in several respects. There is strategic interaction, so agents have to form beliefs about the strategies of their opponents. Furthermore, the decision problem becomes more complex and more risky. Finally, there is a social interaction between competitors that is absent in the monopoly case. In a second experiment with sequential investments we control for all of these differences except for the social interaction. We find that in this case competition does not induce more effort per se. Rather, in a competitive situation investments are strategic complements, that is subjects invest more effort the more effort is invested by the competitor. In contrast, in a monopoly situation subjects invest less if the probability of adverse market conditions increases, even though this is payoff equivalent to a higher investment of a competitor in the duopoly market. Thus, the challenge of a competitor induces subjects to try harder, while the challenge of an unfavorable market induces a monopolist to become 24

27 more complacent. So far these non-monetary incentive effects of competition have been largely ignored. However, they could play an important role for our understanding of why there is a positive or an inverted U-shaped relationship between competition and measures of productivity and innovation in many markets. Furthermore, if these non-monetary incentive effects play an important role they have to be considered in the optimal design of managerial compensation schemes. Our results are clearly only a first step. Much more research is required in order to better understand how competition affects behavior and how these effects can be modelled. 25

28 A. Appendix A.1. Experiment with Simultaneous Investments A.1.1. Supplementary Tables and Figures Figure 4 shows the average over subjects investment per period and treatment. In all treatments and periods, the investments are above the Nash equilibrium prediction of 40 (solid grey line). The investments of the DUOPOLY and OLIGOPOLY treatment are in each period above the investments of the MONOPOLY treatment. There does not seem to be a time trend of endgame effect. Investments in R&D project Period MONOPOLY DUOPOLY OLIGOPOLY Figure 4: Per period investments by treatment in the experiment with simultaneous investments Table 5 reports regressions on the determinants of the investment in the R&D project additional to Table 2. Regression (1) shows that subjects invest significantly more in the DUOPOLY and the OLIGOPOLY treatments compared to the MONOPOLY treatment if we restrict the data to the first period. Regression (2) and (3) show that repeating regressions (1) and (2) of Table 2, but clustering on matching groups instead of on subjects, slightly 26

29 decreases the standard errors. It does not affect the significance of the results. The effect of the oligopoly treatment dummy is significant at the 1% level instead of the 5% level. In regression (4) we use the mean of the investments over all periods (which reduces the observations to 130). Again, all results stay significant and the oligopoly treatment dummy is even significant at the 1% level. 27

30 Investment in R&D project (1) (2) (3) (4) Duopoly (4.602) (2.924) (3.284) (3.373) Oligopoly (3.173) (2.559) (2.274) (2.336) Female (3.133) (3.218) Age (0.304) (0.312) Risk aversion (1.077) (1.106) Risk aversion quest (1.069) (1.098) Loss aversion (0.988) (1.015) Ambiguity aversion Restrict to period 1 yes (1.769) (1.817) Period dummies yes Period (2.249) Constant (1.225) (2.171) (10.93) (11.86) Observations Adjusted R Notes: The table reports coefficients of OLS regressions with robust standard errors in parentheses. Regression (1) is restricted to period 1 and standard errors are clustered by session. In regression (2) and (3) standard errors are clustered by matching groups instead of subjects. In regression (3), only the dummy for period 1 is significant. Regression (4) regresses the subject mean over periods of the investment in the R&D project, standard errors are clustered by matching groups. p < 0.10, p < 0.05, p < Table 5: Experiment with simultaneous investments: Additional results on the determinants of the investment in the R&D project 28