Microeconomic education, strategic incentives, and gender: An oligopoly classroom experiment with social interaction

Accepted Manuscript Title: Microeconomic education, strategic incentives, and gender: an oligopoly classroom experiment with social interaction Authors: Jos´e Antonio Garc´ıa-Mart´ınez, Carlos Guti´errez-Hita, Joaqu´ın S´anchez-Soriano PII: DOI: Reference:

S1477-3880(18)30058-6 https://doi.org/10.1016/j.iree.2018.09.001 IREE 148

To appear in: Received date: Revised date: Accepted date:

28-6-2018 20-9-2018 21-9-2018

Please cite this article as: Garc´ıa-Mart´ınez JA, Guti´errez-Hita C, S´anchez-Soriano J, Microeconomic education, strategic incentives, and gender: an oligopoly classroom experiment with social interaction, International Review of Economics Education (2018), https://doi.org/10.1016/j.iree.2018.09.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Joaquín Sánchez-Soriano3

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José Antonio García-Martínez1 Carlos Gutiérrez-Hita2

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Microeconomic education, strategic incentives, and gender: an oligopoly classroom experiment with social interaction

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Universitas Miguel Hernández

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E-mail address: [email protected]. Phone: +34 966 658 886. E-mail address: [email protected]. Phone: +34 966 658 869.

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E-mail address: [email protected]. Phone: 966 658 715.

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Abstract

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In an oligopoly classroom experiment we study the extent to which microeconomic education, strategic incentives, and gender affect students’ profits. In our setting, students may interact in the classroom (indeed, everywhere) prior to submitting quantity bids to a virtual market. As students could submit a quantity bid over a week-long period, information exchange among students was expected to take place (as it did). This makes this experiment very useful as a pedagogical tool. Students were divided into markets. We first apply a treatment in which students’ incentives only depend on their own market performance. In the second treatment students’ incentives not only depend on their own market performance but also on performance in other markets. First, it is observed that gender does not affect the results. Second, significant education effects are found. Indeed, students’ profits differ as students reach a higher level of microeconomics education. Finally, cumulative profits depend on the treatment applied: under the first treatment students are more competitive, whereas under the second treatment students partially cooperate. Moreover, this result is related to the level of education in microeconomics.

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Keywords: classroom experiments, microeconomic education, gender, strategic incentives, quantity-setting oligopoly. JEL codes: C93, D43, I20, L13.

1. Introduction

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There is an increasing interest in the use of classroom experiments in teaching economics. The introduction of economic experiments into the classroom is an active alternative to complement traditional methods of teaching that a teacher may use to promote a more active learning environment. Moreover, in addition to the teacher’s explanations on theoretical predictions, classroom experiments allow students to learn in a more active way. In particular, those experiments run in the classroom. The use of experiments to teach economics early on began in the sixties. The growing importance of experimental economics is highlighted in Watts and Guest (2010) since this decade. They point out how important Chamberlain’s classroom experiments were for Vernon Smith when he attended classes as a doctoral student at Harvard. Indeed, in Smith (1981) the importance of experimental sessions in class as a part of students’ skills in learning economic concepts is highlighted. In recent years some economics textbooks have included supplementary materials of classroom experiments (O'Sullivan and Sheffrin (2003), Bergstrom and Miller (2000), among others). In Guest (2015) the author reflects on his 10 years’ experience of using games and experiments in the classroom. He concludes that by taking part in experiments a positive effect on increasing microeconomic theory education is shown. He also argues that low-cost paper-based games facilitate social interaction which has a positive impact on acquiring economic theory education and also to increase students’ motivation. In the classroom exercise described in Brouhler (2011), some kind of social interaction is also found. The students play the role of a firm that maximizes its profits given the behavior of other firms in a three-firms-industry. They are allowed to choose between two given prices, low and high, and they enact a prisoner dilemma. They use classroom clickers, which allow them to speed up the game. When the three participants in a market are sitting together, the social interaction appears as “threats and promises”. It increases the level of cooperation. By taking part in classroom experiments students also realize the impact of different incentive structures from their own behavior and that of their colleagues. In fact, experiments allow students to experience and actively participate in different market environments. In this line, although Kaplan and Balkenborg (2010) recognize that getting started may be difficult, they provide some stylized cases for beginners in order to introduce experimental technics in the classroom. Indeed, our experiment can be framed in their Case 1 intermediate microeconomics, in which they propose classroom markets experiments in order to explain Industrial organization topics and Game Theory concepts. There are many examples of teaching industrial organization by using classroom experiments. For instance, Gorry and Gilbert (2015) explain strategic interaction where competition takes place in quantities by using numerical simulation models to motivate students in the comprehension of economic concepts. Moreover, in Correa et al. (2016) cartel behavior is also introduced as a classroom experiment. In their setting, students had to decide OPEC (Organization of Petroleum Exporting Countries) quotas aimed at maximizing joint profits.

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The main difference of our experiment regarding those previous works in the literature is that a round is five-days long, and students can submit just a quantity bid at any time within this period. Although the predominant strand in the literature is to run experiments on computers, in recent years those experiments run manually that allow classroom interaction between students in (and outside) the classroom have proved to be interesting for teaching purposes. Following this strand, our experiment takes place outside the computer laboratory. It allows us to test how sociological concerns may influence economic strategies. Moreover, this approach has the added value of flexibility and not being dependent on the availability of computer rooms. Computerized versions of experimental games also present other disadvantages. Most games cannot progress from one round to another until all the students have made their decisions. In a classroom experiment the whole decision-making process is more transparent. Another

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disadvantage with computerized games is that they do not generate the face-to-face social interaction that occurs in classroom games. In our framework, students have the whole week to submit a quantity bid and thus for social interaction to become relevant. Carter and Emerson (2012) investigates whether students in microeconomics principles classes increase economic knowledge when they are exposed to computerized experiments as compared to students exposed to in-class manually run experiments. They compare the impact on students of using six computerized games (treatment group) as opposed to six paper-based versions of the same games (control group). Overall, they found no significant difference in student achievement of the microeconomics course between the two treatments. Nevertheless, the authors find that students exposed to classroom experiments report more favorable views of the experimental pedagogy and report higher levels of interaction with their classmates. Other examples of manually run experiments are Emerson and Taylor (2004), Dickie (2006), Durham et al. (2007), and Frank (1997).

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Some economic concepts are difficult to manage or, in other words, to fully understand for undergraduate students. Our main purpose with this work is to help students in this task. These concepts can be much more easily understood if students are able to participate in a market situation (as a complement to theoretical explanations and problem sets). In this paper we present results from a classroom experiment where students enrolled in a degree of Business Administration play an oligopoly game. This paper is part of an experimental project on teaching microeconomics. Previously, in García-Martínez et al. (2012), we made a descriptive statistical analysis on the differences of the students’ quantity bids regarding Walras, Nash, and Collusive outcomes. However, our present paper is quite different: First, we focus on the cumulative profits attained by students instead of quantity bids. Second, we use inferential statistical analysis instead of just descriptive. Finally, our goal is to study the extent to which gender, education level and strategic incentives affects students’ cumulative profits. The experiment was run with basic and medium level microeconomics students, and the market was open for a whole semester divided into 20 rounds. In our setting, students play the role of firms and may socially interact each other. Each round is one week long (Monday to Friday). Hence, students may talk to each other taking into account not only economic information but also their social relation. At any time of their choice in this round-week, students have to submit by email just one quantity bid to the virtual market. Once the email is sent, the quantity proposed cannot be modified. Finally, students were rewarded with grade incentives that depended on students’ market performance: higher cumulative profits yielded a larger reward. The instructions for students are in the Appendix.

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We consider two treatments. In the first ten rounds, we run a treatment in which students’ incentives only depend on their own market performance. In the last ten rounds a second treatment is run, in which students’ incentives not only depend on their own market performance but also on the other markets performance. In this setting, we are interested in studying the extent to which microeconomic education, strategic incentives and gender affect student profits. Therefore, our classroom experiment allows students to understand first, the extent to which strategic behavior is important in an oligopoly environment and second, how to work by being part of it. We consider that it is crucial that students have enough time to decide their strategies in each game’s stage and thus, to interact each other.

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The experiment was performed during the courses lasting the whole semester. The main concepts covered in the first year were the basics of supply and demand, consumers’ behavior, producers’ behavior, production, and competitive markets. The experiment was particularly useful to understand how markets work, and how individual decisions of several agents yield to an equilibrium price. In our setting, although experimental subjects may impact prices, students understood the concept of price taker much more easily. In addition, they were better prepared for the second course where imperfect markets are studied. The course of the second year mainly focuses on monopoly, monopolistic competition and oligopoly markets (an introduction to game theory is also provided). The experiment helped a lot of students to understand the concept of strategic behavior, the concept of equilibrium, and how an oligopoly market works. It is also relevant to understand the concept of collusion and its eventual sustainability over time. In conclusion, we use the experiment as a complementary teaching tool. It allows us to implement the topics covered in the classroom in a manually run experimental market that

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students perform every week. Moreover, the experiment was complemented with compulsory problem sets that students solved individually and presented in the classroom. The crucial point is that students have five days to take decisions in each round and to talk with other participants if they so desire.

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Therefore, the main contribution is providing an experiment in which students can interact during an unusually long time in each round, which facilitates the social interaction and the understanding of what they are playing. This makes a significant difference. Thus, they do not demonstrate chaotic behavior in spite of the fact that there are ten participants in each market; in fact, they are able to converge quite closely to theoretical equilibria. This makes this experiment very useful as a pedagogical tool. It is also relevant that it was cheap to implement, we only need an email address. In addition, we perform an extensive statistical analysis where we are able to check how gender and level of microeconomics education can have an impact on results under two different strategic incentives (treatments 1 and 2).

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Sociological conflicts are relevant in economic experiments. In Treatment 1, a student’s payoffs depends only on his/her behavior and that of the members of his/her own market (as usual). However, under Treatment 2, the student’s payoffs depend also on the behavior and payoffs of the members of other markets. The later environment is related to group selection models, in which the subject has to balance these two opposite incentives in order to maximize his/her utility. Such models were developed in biology (Wilson, 1983), and some economic applications are outlined by Vega-Redondo (1993) and Sjöström and Weitzman (1995). In group selection models, populations (or markets) are fragmented into locally isolated groups with independent evolutions. Within each group, there is some kind of individual selection or competition, but there is also selection or competition between groups. Thus, more efficient groups have an advantage over less efficient groups. The basic result is that group selection may outweigh the effect of individual selection. A similar result is found in our environment: it is better for students to promote internal cooperation than maximize individual profits when groups compete with each other.

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The literature on oligopoly experiments is also extensive. Many papers have followed Milgrom and Roberts (1991) approach, known as adaptive learning in order to study students’ dynamic interaction to test the robustness of oligopoly models. Rassenti et al (2000) analyze some versions of Milgrom and Roberts' setting. They seek to explore whether a repeated play by privately informed subjects converge to a unique, static, non-cooperative Nash-Cournot equilibrium. It is found that this repeated interaction partially converges. Our oligopoly experiment has an educational objective. In this strand, Dickie (2006) studies the extent to which classrooms experiments affect learning in microeconomics. He used a pre-test-post-test control-group design to test whether grade incentives affect learning. Although experiments without incentives are associated with higher post-test scores and greater improvement over pre-test scores, he concludes that experiments increase learning no matter whether the grade incentives are introduced or not. It is also clear that as long as students are motivated by grades, a grade incentive for profits might cause experimental outcomes to match more closely theoretical predictions and thus, could make it easier to use classroom experiments as a teaching tool. Literature in oligopoly classroom experiments include, among others, DeYoung (1993) where it is emphasized that there are many advantages to working in a controlled laboratory environment when teaching market structures in economics. In this strand, in particular concerning repeated oligopoly games, in Bigoni and Fort (2013) experimental subjects play a repeated Cournot oligopoly with limited a priori information. Results suggest that learning plays an important role, as subjects favor strategies that have yielded higher profits in the past. Moreover, Offerman et al. (2002) also examines behavioral dynamics in a quantitysetting triopoly experiment. Three information treatments are employed. Overall, the results are consistent with the hypothesized relationships between treatments, behavioral rules, and outcomes. We should emphasize that our classroom experiment is manually run and that our rewards are related to the grade that student achieved in the subject. Davis and Holt (1993) note that salient incentives to test behavior of experimental subjects against predictions of economic theory are fundamental in experimental economics. Gächter et al. (2006) presents a computerized Cournot game divided in two treatments: fixed number of competitors and free entry and exit among markets. In the first treatment (fixed number of competitors) theoretical predictions are almost met. In the second treatment students enter profitable markets. Hence, students’ profits decrease as the number of competitors increases and profits equalize across

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markets. They also use the experiment to explain to students some economic concepts such as Nash equilibrium, the relation between the number of competitors and profits, and tacit collusion (they use parameters as in Huck et al. (2004)). These concepts are also educational objectives in our experiment. The rest of the paper is structured as follows. Section 2 describes the experiment. Section 3 presents statistical evidence and experiment results. Finally, discussion and conclusion are in Section 4. 2. Experimental design

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The experiment was run during a semester with students of Business Administration Bachelor (University Miguel Hernández, Spain). These students follow face to face courses from Monday to Friday. They are mostly local residents and for that reason most of them live with their families and commute to the university every day. Therefore, they interact each other mainly at the university between classes and in their free hours. In particular, the students of our experiment are enrolled in basic and medium level of microeconomics (Level 1, and Level 2 respectively). We had 70 students per level divided into 7 markets of 10 players each. Table 1 shows the participants by gender, level, and market. They were assigned to each market in alphabetical order at each level. Those students were asked to participate in a symmetric quantity-setting oligopoly. We assign to each student an alphanumeric code, so we work with hidden identities. However, they were able to learn identities as a result of social interaction. In each given market, interaction took place 20 times and this was commonly known. Students have to submit only one quantity by email at any time in each trading round (student were able to communicate with each other). Each trading round comprised five days per week, from Monday, 10 a.m. to Friday, 11.59 p.m. Finally, on Saturday the market cleared and each student in his/her corresponding market knew the market price, aggregate output and also his/her own and rivals’ profits. This information was stored and shown throughout the trials. The instructions for students are provided in the Appendix.

Table 1. Experimental subjects by gender, level and market. MARKETS OF LEVEL 1

MARKETS OF LEVEL 2

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A1 B1 C1 D1 E1 F1 G1 A2 B2 C2 D2 E2 F2 G2 FEMALES

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Students were provided with the following information: the inverse market demand function and the cost structure, all the players being equal. Inverse market demand is

P(Qt )  1000  i1 qit , where P is the market price, and Qt  i1 qit is the aggregate 10

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production of players 𝑖 = 1,2, . . ,10 at round t. Quantities could be chosen from a finite grid between 0 and 100 with 0.01 as the smallest step. 1 The cost function for each economic subject is Ci (qit )  qit / 2  100qit  50. 2

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Two different treatments were applied. Rounds one to ten are under Treatment 1, whereas rounds eleven to twenty are under Treatment 2. Treatment 1 In this setting, each student’s profits are accumulated over these ten rounds and a per-market final ranking is obtained (i.e. 7 rankings by level). In each market, the best accumulated profits were normalized to 0.5 and the worst normalized to zero. The rest of the students were ranked by a linear combination between zero and 0.5 depending on the profits earned. We obtain a different ranking for each market. Hence, in each ranking of profits the winner receives 0.5 extra points and the worst qualified player none at all. Notice that in this environment the payoff of a given player depends solely upon their own market competitiveness.

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Treatment 2 As in the previous treatment, each student’s profits are accumulated over these ten rounds. However, in this case there is only a ranking per level, and a level is comprising by seven markets (as we have pointed out before). The best per level accumulated profits was normalized to 0.5 and the worst normalized to zero. The rest of the students were ranked again by a linear combination. In this setting, the student’s payoffs depend also on the behavior and payoffs of the members of other markets. Thus, they have to decide between cooperative behavior or maximize their own profits (cheating from an eventual cooperation). In other words, students need to take into account the results (profits) obtained by their competitors in their own market but they also compete with the rest of the students enrolled in markets at their same educational level.

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Summarizing, under Treatment 1 a student’s final reward (extra points) only depends on her own cumulative profits and those earned by members of her market. However, under Treatment 2 such a final reward also depends on the cumulative profits earned by students of all the markets at her educational level.

max P  qit  Ci (qit ),

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We now present the economic theory solutions for this particular market. Walrasian behavior (perfect competition) and the Nash-Cournot equilibrium are, respectively, the solutions of the following problems,2

max P(Qt )qit  Ci (qit ). qit

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The cooperative outcome (the monopoly outcome) is found when firms maximize joint profits (alternatively when they minimize total industry costs),

max P(Qt )i 1 qit  i 1 Ci (qit ) 10

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We also characterize the one-shot output in the case where a subject deviates from the cooperative equilibrium. If a given firm deviates, it takes the static optimal best response 𝑞𝑖𝑡 = ∗ 𝑅𝑖 (∑10 𝑖≠𝑗 𝑞𝑗𝑡 ) evaluated at the full cooperative output and chooses the optimal deviation strategy, yielding deviated profits 𝜋 𝐷 = 36378. Table 2 reports cumulative equilibrium profits3 arising from the above non cooperative environments. Table 2. Theoretical cumulative profits. Walras Nash-Cournot 𝝅𝑾 = 32970,9 𝝅𝑵𝑪 = 8387,5

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Cooperation 𝝅𝑪 = 19235,7

3. Statistical analysis and educational results

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In this section we analyze the results obtained over the 20 rounds played by the students in both educational levels. Table 3 summarizes cumulative average profits by level and treatment and the corresponding differences with the theoretical equilibria reported in Table 1. Standard deviation has been included to test to what extent the mean is informative regarding students’ average cumulative profits.

Table 3. Profits differences: theoretic vs experimental results. Level-Treatment

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𝝅𝑪 − 𝝅 ̅

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47399

21539

-14428

36476

144958

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40269

7326

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43606

152088

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94375

49088

-61404

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97982

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149364

L2T2

34801

-116393

-65489

42993

Notes: 𝝅 ̅ =Experimental average cumulative profits.

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Overall, under Treatment 1 in both educational levels, students were closer to the Walrasian profit. Besides, under Treatment 2 those students in Level 1 tend to behave as Cournot competitors although some cooperative behavior can be observed. In fact, some groups approach a somewhat perfect collusion during some rounds but this behavior was erratic as many students broke cooperation many times. However, those students in Level 2 are closer to the theoretical cooperative profits. Moreover, in Level 2 standard deviations were lower than in Level 1. This can be interpreted as the effect of a higher microeconomic education and maybe social interaction.

In order to extract more information from our experimental results we run a generalized linear model (GLM) and a multifactor ANOVA analysis for cumulative profits as dependent variable. The GLM for cumulative profits as dependent variable is,

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𝐶𝑖 = 𝛼 + 𝛾𝐺 · 𝐺𝑖 + 𝛾𝐿 · 𝐿𝑖 + 𝛾𝑇 · 𝑇𝑖 + 𝜀𝑖 ,

where independent variables are dummies taking the following values,

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−1 𝑖𝑓 𝑚𝑎𝑙𝑒 1 𝑖𝑓 𝑙𝑒𝑣𝑒𝑙 1 −1 𝑖𝑓 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 1 𝐺𝑖 = { 𝐿𝑖 = { 𝑇𝑖 = { 1 𝑖𝑓 𝑓𝑒𝑚𝑎𝑙𝑒 −1 𝑖𝑓 𝑙𝑒𝑣𝑒𝑙 2 1 𝑖𝑓 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 2.

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By using the GLM model, the quantitative impact on cumulative profits by each independent variable (factors) is analyzed. Table 4 summarizes properties of the estimated model. Gender factor has a little impact in cumulative profits compared with factors level and treatment (12% and 3.8%, respectively) with p-value over 0.5 so we will remove it from the model in a further step. Hence, no matter the level of education or treatment applied, gender does not alter results. It seems that strategic interaction takes place with no discrimination by gender.

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̂𝒊 = 𝜶 ̂+𝜸 Table 4. Estimated model 𝑪 ̂ 𝑮 · 𝑮𝒊 + 𝜸 ̂ 𝑳 · 𝑳𝒊 + 𝜸 ̂ 𝑻 · 𝑻𝒊 . Variable Estimation F-Statistic P-value Constant 82999.8 Gender -1481.09 0.45 0.5010 Level -12282.0 31.54 0.0000 Treatment 39018.0 333.76 0.0000 R-Square: 56.982. Adjusted R-Square: 56.515

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Figure 1 completes the analysis of the Gender factor. Looking at the Box-Plot one can see that both, females and males cumulative profits are similar (mean and median take almost the same value). Thus, at aggregate level there are no significant differences by gender.

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FIGURE 1: Profits by Gender. The black line stands for mean whereas the white line stands for the median. The white diamond stands for confidence interval for the mean.

F-Ratio

P-Value

5,79873E8 4,02784E10 4,26272E11 1,27717E9

0,45 31,54 333,76

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Mean Square

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Table 5. Analysis of variance for cumulative profits. Source Sum of Squares Df MAIN EFFECTS GENDER 5,79873E8 1 LEVEL 4,02784E10 1 TREATMENT 4,26272E11 1 RESIDUAL 3,52499E11 276 TOTAL (CORRECTED) 8,19434E11 279

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The ANOVA analysis determines which factors have a statistically significant effect on the dependent variable. It also tests for significant cross effects among factors. Table 5 shows the results.

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Within Table 5 the variability of cumulative profits is decomposed into contributions due to Gender, Level, and Treatment. The contribution of each factor is measured having removed the effects of all other factors. In viewing p-values, at 95% of confidence level, gender has no statistical significance, whereas the other two factors have a positive impact on cumulative profits.

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Having as significant factors Level and Treatment the second step in the analysis is to run a Multiple Range Test4 (MRT). This is a multiple comparison procedure to determine the extent to which means are significantly different from each other within each factor. Tables 6 and 7 show MRT results.

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Table 6. MRT for cumulative profits by level. LEVEL Count LS Mean LS Sigma Homogeneous mean X 1 140 70717,8 3030,8 X 2 140 95281,9 3098,3 Notes: 95% confidence level. Method: Fisher’s LSD.

Table 7. MRT for cumulative profits by treatment. TREATMENT Count LS Mean LS Sigma Homogeneous mean X 1 140 43981,9 3028,36 X 2 140 122018, 3028,36 Notes: 95% confidence level. Method: Fisher’s LSD.

In Table 6 at the right hand side, 2 homogenous groups in terms of means are identified. Means in each market at the same educational level are not statistically different, whereas means by educational level are (X appears in a different column). The estimated difference between each pair of means (-24564.1) is statistically significant at the 95.0% confidence level. It reveals that students enrolled in Level 2 attained a higher level of cumulative profits. This fact can be related to a higher knowledge of microeconomic concepts. It seems that this social cohesion may yield in Treatment 2 a more stable cooperation and thus, higher cumulative profits. Table 7 has a

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similar analysis as Table 6. On the right hand side, 2 homogenous groups in terms of means are identified, in this case in terms of treatments. Means in each market in the same treatment are not statistically different, whereas means between treatments are (X appears in a different column). The estimated difference between each pair of means (-78035.9) is statistically significant at the 95.0% confidence level. Thus, no matter which level the student belongs to, under Treatment 2 cumulative profits are higher than those under Treatment 1.

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As Gender is not statistically significant, we have explored how level and treatments have impacted in cumulative profits through strategic interaction. When we run the GLM and multifactor ANOVA analysis for cumulative profits as dependent variable, taking as factors level and treatment, we obtain almost the same statistical significant effects on the dependent variable.5

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One step further in our analysis is to study the cross effect of level and treatment. In Table 8 the ANOVA procedure decomposes the variability of cumulative profits into contributions due to cross factor level and treatment. Since p-value is less than 0.05, the cross contribution has a statistically significant effect on cumulative profits at the 95.0% confidence level. Moreover, we present the MRT for cumulative profits by factors level and treatment. Table 9 shows a multiple comparison procedure to determine which means are significantly different from which others.

P-Value 0,0000

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Table 8. Analysis of Variance for cumulative profits. Multiplicative model. Source Sum of Squares Df Mean Square F-Ratio MAIN EFFECTS LEVEL * TREATMENT 5,33885E11 3 1,77962E11 172,01 RESIDUAL 2,85549E11 276 1,0346E9 TOTAL (CORRECTED) 8,19434E11 279

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Table 9. MRT for cumulative profits by level*treatment. LEVEL*TREATMENT Count LS Mean LS Sigma Homogeneous mean L1*T1 70 47399,0 3844,47 X L2*T1 70 40268,5 3844,47 X X L1*T2 70 94375,1 3844,47 X L2*T2 70 149364, 3844,47 Notes: 95% confidence level. Method: Fisher’s LSD.

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Two main insights can be inferred. Firstly, under Treatment 1, in which students have no incentives to coordinate, both levels have no statistical differences in means. In other words, after ten rounds, students obtain on average similar results which are close to the Walrasian equilibrium. However, in Figure 2 we can observe that students’ profits have more dispersion in Level 1 than in Level 2. This difference seems to come from the different students’ economic education. Thus, students in Level 1 follow a more trial and error strategy than those in Level 2. Secondly, under Treatment 2 the microeconomic education seems to be more important. Levels are different by comparison with Treatment 1 but also they are different within Treatment 2. The intuition arising from this is that students enrolled in the second year of microeconomic have attained sufficient microeconomic education that allows them to have a better understanding of cooperation and thus, maintain loyalty to the agreement. This means that one can argue that microeconomic education plays an important role and thus, learning effects are not negligible. Taking into account the above information a number of observations can be made. First, rules (i.e. market regulation) may favor different groups depending on the microeconomic education. Assuming that each treatment can be seen as a particular market regulation, under Treatment 1 there are no significant differences on average between educative levels. However, as we discuss below, the dispersion of the cumulative profits is quite different (see Figure 2). In Treatment 2, students in Level 2 with a higher microeconomic education are benefited. In this case, the dispersion is also different between educational levels (see Figure 3).

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Figure 2: Profits by Treatment 1

Figure 3: Profits by Treatment 2

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The black line stands for mean; White line stands for the median; White diamond stands for confidence interval for the mean.

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It is interesting to note that, as the microeconomic education increases, average profits become higher as the incentives to cooperate increase. Moreover, profits are homogenized across students. These facts suggest that education may reduce inequality. This is consistent with the empirical finding in macroeconomics studies, see for example Martins and Pereira (2004) and De Gregorio and Lee (2002).

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The level of education is relevant. We observe that standard deviation and mean by level are different. Concerning dispersion, it seems that trial and error is common under Level 1 whereas students in Level 2 seem to behave more strategically. As a result, applying both treatments, in Level 1 students’ profits have a higher dispersion. The intuition appears to be that microeconomic education and social interaction (classmates have met for a shorter time) are stronger under Level 2 than under Level 1. Secondly, in terms of mean, cumulative profits are similar under Level 1 and 2 when only inner competitiveness is encouraged; however, when cooperation is enhanced, students in Level 2 are benefited. The insight behind this seems to be that the regulatory framework may induce differences in the level of profits depending on the educational level. Our Treatment 1 encourages individualism and thus, students only take care of their own profits. Treatment 2 also encourages cooperation (notice that the incentives under Treatment 1 do not disappear). In this setting, students in Level 2 benefit probably as a result of a higher economic education and thus, attain larger cumulative profits.

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Taking into account the above insights, we can conclude that heterogeneity could be reduced because of education. This result of the experiment provides an excellent way in which to explain two important ideas to our students. First, education has a positive effect in reducing inequality. Second, the regulatory framework is also relevant. As we have seen, it has a different impact depending on the level of education. Indeed, education homogenizes profits (by reducing dispersion) and also provides better rewards for individuals when cooperation is enhanced. Notice that for students with low level of economic education, profits under Treatment 2 are lower. 4. Discussion and conclusion

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In this experiment, we endeavor to explore the extent to which microeconomic education, strategic incentives and gender affects student economic profits in an oligopoly environment.6 Students may socially interact in the classroom (and also outside). They were asked to submit a quantity to a virtual market each week and then, market cleared and outputs were revealed. In our experiment one of the interesting issues is that students can interact during the whole business week in order to decide how to bid. By opening the market for five days, students might interact allowing us to test how profit-oriented decisions may be altered by reputation/social concerns. Hence, it was possible for students to take into account not only economic information but also sociological concerns that modified the final output decision. By means of our approach, a central difference from other oligopoly experiments is that students had a long time period to decide his/her strategy. Usually, in oligopoly experiments students play rounds within some second or minutes without any kind of social interaction. As an example of this kind of interaction we present four anecdotes. First, during Treatment 2 some students declared pressures concerning the opportunity to deviate from the cartel when

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the rest of their mates followed it. Second, sometimes students requested the opportunity to change his/her quantity in a given round because he/she had noticed the rest of quantities of their mates. Third, within each market students were able to find out progressively the real identities of the other market-members. For instance, a curious case occurred in one group. Students started to collude, but two of them played quantities that ruined collusion. Somehow, they were able to find out their identities except those who did not follow collusion. Then, those students under the collusive agreement asked one of the teachers the identity of those two unknown members. They declared without any qualms that they wanted to coerce them into following collusion. Although the identities were not revealed, they eventually found out and persuaded them to collude at least for a while. Finally, in a given market, one of the student declared that he persuaded the rest of the members of their group to collude. Then, he cheated and broke the deal. He declared that he was able to repeat this strategy as many time as he wanted. This evidence proves that the experiment is a useful pedagogical tool.

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There is some evidence that using experimental games may have a positive impact on the students acquiring microeconomic theory education. Nevertheless, this kind of experiments is not yet widely employed in the classroom. In this research, we introduce an oligopoly classroom experiment with a particular manually run design. Two treatments are run over two educational levels (basic and intermediate microeconomic theory).

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Our experiment provides three main insights. First, no matter the student’s gender, results are statistically the same regardless of the level and treatment applied, which is a relevant lesson to be learnt by our students. Second, microeconomic education modifies students’ profits. Indeed, depending on the level of microeconomic education, the standard deviation and mean of the students’ profits differ. In particular, in Level 2 standard deviation is lower than in Level 1 under both treatments. It seems that students in Level 1 use the trial and error strategy whereas those students in Level 2 have a better knowledge of microeconomic concepts. Third, the treatment is also important, i.e., market rules matter. Under Treatment 1, where competitiveness is enhanced, profits attained in Level 2 are similar on average to those under Level 1. However, under Treatment 2, profits are higher in Level 2 than in Level 1. This result is related to the strategic incentives underlying each treatment. Under Treatment 1, cooperation is not encouraged, and we found that the part played by the educational level is not relevant. However, in Treatment 2, when the market rules favor cooperation, students in Level 2 obtain significant higher profits. Once again, a better knowledge of microeconomic concepts takes on an important role.

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To sum up, gender does not affect students’ cumulative profits (quantitative results are statistically the same). Concerning the effect of the level of economic education (on microeconomic foundations classes) it is found that those students enrolled in Level 2 (second year of the bachelor) perform different to those in Level 1 (first year of the bachelor). Hence, we obtain that a better knowledge of microeconomic concepts has an effect on the profits attained by the students. Strategic interaction also depends on the treatment applied. Treatment 2 involves an externality: the payoff of a student depends not only on the behavior in his/her own market but also on the behavior in other markets. In other words, the strategic decision adopted by a given student is affected by those taken not only in his/her market, but also in other markets. This externality may encourage collusion if students engage in coordination one way or another. That is, students may be encouraged to feel that by taking part in a collusive agreement they can improve their profits.

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As a result of taking part in the experiment, students have learnt two important ideas. The first is that, in our oligopoly environment, microeconomic education may play an important role to achieve success in competitive scenarios. The second is that, in our framework, gender is not related to the level of the individual’s success. Finally, we would like to point out that our experiment was run in a particular environment (students enrolled in a Business Administration degree at the same university, all of them attending microeconomic courses, a particular cost function and demand specification). Although it is an obvious limitation of the research, our results contribute to a better understanding of oligopoly competition by students. Future experiments in this strand may include heterogeneities between subjects, a different number of students by market and also different sociological conditions (commuter students versus those located near the campus,

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students belonging to fraternities…).These aspects can alter and enhance the results although it requires a better definition of the experiment environment. It constitutes a challenge and an opportunity to go further in using classroom experiments in order to improve the students’ economic education.

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REFERENCES

Bergstrom, T., and Miller, J., 2000. Experiments with economic principles: Microeconomics. 2 nd ed. Boston, MA: Irwin McGraw-Hill. Bigoni, M., and Fort, M., 2013. Information and learning in oligopoly: An experiment. Games Econ. Behav. 81, 192-214. https://doi.org/10.1016/j.geb.2013.05.006

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Brouhler, K., 2011. Exploring Strategic Behavior in an Oligopoly: Market Using Classroom Clickers. J. Econ. Educ. 42, 395-404. https://doi.org/10.1080/00220485.2011.606093

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Carter, L. K., and Emerson, T.L.N., 2012. In-class vs. online experiments: Is there a difference? J. Econ. Educ. 43(1), 4-18. https://doi.org/10.1080/00220485.2011.636699

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Correa, M., García-Quero, F., and Ortega-Ortega, M., 2016. A role-play to explain cartel behavior: Discussing the oligopolistic market. Int. Rev. Econ. Educ. 22, 8-15. https://doi.org/10.1016/j.iree.2016.03.001

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Davis, D., and Holt, C.A., 1993. Experimental economics. Princeton, NJ: Princeton University Press. De Gregorio, J., Lee, J. W., 2002. Education and Income Inequality: New Evidence from Cross-Country Data. Rev. Income. Wealth. 48, 395–416. https://doi.org/10.1111/1475-4991.00060

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DeYoung, R., 1993. Market Experiments: The Laboratory versus the Classroom. J. Econ. Educ. 24(4), 335-351. https://doi.org/10.1080/00220485.1993.10844804 Dickie, M., 2006. Do Classroom Experiments Increase Learning in Introductory Microeconomics. J. Econ. Educ. 37, 267-88. https://doi.org/10.3200/JECE.37.3.267-288

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Durham, Y., McKinnon, T., and Schulman, C., 2007. Classroom experiments: Not just fun and games. Econ. Inq. 45(1), 162–78. https://doi.org/10.1111/j.1465-7295.2006.00003.x Frank, B., 1997. The impact of classroom experiments on the learning of economics: An empirical investigation. Econ. Inq. 35(4), 763–69. https://doi.org/10.1111/j.1465-7295.1997.tb01962.x

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Gächter, S., Thöni, C., and Tyran, J-R., 2006. Cournot Competition and Hit-and-Run Entry and Exit in a Teaching Experiment. J. Econ. Educ. 37(4), 418-30. https://doi.org/10.3200/JECE.37.4.418-430 García-Martínez, J.A., Gutiérrez-Hita, C., and Sánchez-Soriano, J., 2012. Competitiveness, Cooperation, and Strategic Interaction. A Classroom Experiment on Oligopoly. Rev. Int. Sociol. 70, 167-187. https://doi.org/10.3989/ris.2011.07.1B Gorry, D., and Gilbert, J., 2015. Numerical simulations of competition in quantities. Int. Rev. Econ. Educ. 18, 49-61. https://doi.org/10.1016/j.iree.2015.01.003 Guest, J., 2015. Reflections on ten years of using economics games and experiments in teaching. Cogent Econ. Financ. 3,1-16. https://doi.org/10.1080/23322039.2015.1115619

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Huck, S., H.T. Normann, and J. Oechssler., 2004. Two are few and four are many: Number effects in experimental oligopoly. J. Econ. Educ. 53(4), 435-46. https://doi.org/10.1016/j.jebo.2002.10.002 Kaplan, T.R., and Balkenborg, D., 2010. Using Economic Classroom Experiments. Int. Rev. Econ. Educ. 9(2), 99-106. https://doi.org/10.1016/S1477-3880(15)30047-5 Martins, P. S., Pereira, P. T., 2004. Does education reduce wage inequality? Quantile regression evidence from 16 countries. Labour Econ. 11, 355–371. https://doi.org/10.1016/j.labeco.2003.05.003 Milgrom, P., Roberts, J. 1991., Adaptive and sophisticated learning in normal form games. Games Econ. Behav. 3(1), 82-100. https://doi.org/10.1016/0899-8256(91)90006-Z Offerman, T., Potters, J. and Sonnemans, J., 2002. Imitation and Belief Learning in an Oligopoly Experiment. Rev. Econ. Stud. 69(4), 973–997. https://doi.org/10.1111/1467-937X.00233

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O’Sullivan, A., and Sheffrin, S. M., 2003. Economics. Upper Saddle River, NJ: Prentice-Hall.

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Rassenti, S., Reynolds, S., Smith, V.L., 2000. Adaptation and convergence of behavior in repeated experimental Cournot games. J. Econ. Behav. Organ. 41, 117-146. https://doi.org/10.1016/S01672681(99)00090-6 Sjöström, T., Weitzman, M., 1995. Competition and the evolution of efficiency. J. Econ. Behav. Organ. 30, 25-43. https://doi.org/10.1016/S0167-2681(96)00840-2

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Watts, M., Guest, R., 2010. Experimental Economics and Economic Education. Int. Rev. Econ. Educ. 9(2), 6-9. https://doi.org/10.1016/S1477-3880(15)30045-1

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Wilson, D., 1983. The group selection controversy. https://doi.org/10.1146/annurev.es.14.110183.001111

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159-187.

APPENDIX: INSTRUCTIONS FOR STUDENTS7

𝑞22⁄ 2 + 100𝑞2 + 50.

Therefore, your profit function is at any round.

𝑗≠𝑖

𝑞𝑗 ) = 𝑃(𝑄𝑡 ) · 𝑞2 − 𝐶2 (𝑞2 ).

C2=24 C7=56

C3=56 C8=90

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C1=50 C6=68

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𝜋2 (𝑞𝑖 , ∑

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𝐶2 (𝑞2 ) =

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This is a market decision-making experiment. There are 7 independent markets from A to G. In this experiment you will participate in the market labelled C. You are able to produce and sell units of fictitious goods. In this market there will be 10 producers and you will be known as producer C2. You are free to produce and sell as many units as you wish in the interval𝑞𝑖 ∈ (0,100), where 𝑞𝑖 is the level of output that you produce. All the output produced will be sold. This experiment is divided into two treatments of 10 rounds each. A round takes a week. You must select the quantity of the goods that you produce by sending an email from Monday 10a.m. to Friday 11.59 p.m. You are free to submit your quantity once each week. For example, if you choose to produce 50 units, you must send C2-50 any day from Monday to Friday (inclusive). Each other producer from market C will also make a quantity decision. 𝑄𝑡 is the sum of the quantities chosen by each producer (including you) in market C each round, therefore 10 𝑄𝑡 = ∑10 𝑖=1 𝑞𝑖 . The inverse demand function is at any round 𝑃(𝑄𝑡 ) = 1000 − 𝑞𝑖 − ∑𝑗≠𝑖 𝑞𝑗 . Hence, the more you produce the less will be paid per unit of output. Your cost function is at any round,

C4=67 C9=15

C5=34 C10=21

𝑄𝑡 = ∑10 𝑖=1 𝑞𝑡 = 481,

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Total quantity, price and profits are, respectively,

𝑃(𝑄𝑡 ) = 1000 − 481 = 519, 𝜋𝐶2 = 13618.

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All producers in all markets have the same costs and face the same market demand function, so the profit function is the same across players and markets. At the end of the week (after Friday), you will receive an email with the following information about market C in that week: The weekly outputs of each producer, the sum of all weekly outputs, the price of the good per unit in that week, the weekly profit made by each producer, and the accumulated profits that you and the others producers have earned up to this round. In each round you can choose either the same output as in the previous round or a different one.

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After 10 weeks, a ranking of your market will be drawn up, with the accumulated profits. Your reward for participating in this first stage will depend on that ranking. The seller from your market with the highest accumulated profit (𝜋 𝑇𝑂𝑃1 ) will obtain 0.5 extra points in the final mark. On the other hand, the seller from your market which has the lowest accumulated profit (𝜋𝐿𝑂𝑊1 ) will obtain zero extra points in the final mark. If you obtain an accumulated profit between them, your mark will depend linearly on the distance to both extremes according to the following function where 𝜋 is your accumulated profits: 1 𝜋 − 𝜋𝐿𝑂𝑊1 𝐹𝑖𝑛𝑎𝑙 𝑀𝑎𝑟𝑘(1) = ( 𝑇𝑂𝑃1 ). 2 𝜋 − 𝜋𝐿𝑂𝑊1 After 10 weeks a new stage will start. You will receive information about the functioning of the experimental game at the beginning of round 11. TREATMENT2 There is only one difference with Treatment 1. After 10 rounds (for rounds 11 to 20) just one ranking will be drawn up with the accumulated profits of all the producers from the seven

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markets. Your reward for participating in this treatment will depend on that ranking. The seller with the highest accumulated profit 𝜋 𝑇𝑂𝑃2 will obtain 0.5 extra points in the final mark. On the other hand, the seller which has the lowest accumulated profit (𝜋𝐿𝑂𝑊2 ) will obtain zero extra points in his/her final mark. If your accumulated profit is between the two, your mark will depend linearly on your distance from both extremes according to the following function, where 𝛱 is your accumulated profit, 1 𝜋 − 𝜋𝐿𝑂𝑊2 𝐹𝑖𝑛𝑎𝑙 𝑀𝑎𝑟𝑘(2) = ( 𝑇𝑂𝑃2 ). 2 𝜋 − 𝜋𝐿𝑂𝑊2 Good luck. 1

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We consider this level of precision to check whether or not this can play a role in the experiment. As expected, students play mostly with integers and no one with two. 2 Notice that linear-quadratic cost functions impose a huge penalization as long as output increases. Indeed, producing up to the maximum capacity does not only decrease the market price but also raises costs. However, when costs are linear there is no reason to produce a low quantity and strategic interaction is not enhanced. 3 Cumulative profits are found by adding ten times (each treatment is run ten times) the stage profits under each characterized equilibrium. 4The method currently being used to discriminate among the means is Fisher's least significant difference (LSD) procedure. Applying this method, there is a 5.0% risk of calling each pair of means significantly different when the actual difference equals 0. 5 The estimated additive GLM model without the variable Gender, 𝑪 ̂𝒊 = 𝜶 ̂+𝜸 ̂ 𝑳 · 𝑳𝒊 + 𝜸 ̂𝑻 · 𝑻𝒊 has an R-Square and adjusted R-Square of 56.91and 56.60, respectively, so the model maintains its prediction capacity. 6 We teach microeconomic education at different levels so we found interesting to design an experimental oligopoly to increase students’ comprehension of this subject. First, as strategic incentives are the hardest part to fully understand oligopoly theory by students, we found it interesting that students play under two different frameworks of incentives. Second, we also wanted to facilitate social interaction in order to make easier for students to know how their behaviors change under different scenarios (treatments) and also as time goes by. Finally, gender is a topic of great interest nowadays, and it is very easy to analyze in our experiment. Although we might take into account other factors such as friendship among the students, whether they share an apartment with other students or they live with their families, whether they live on campus or not, their marks in previous courses or studies, among others, we thought that the factors considered in this paper were relevant enough for our experiment. In future experiments, we will consider other factors. 7The instructions reproduced here are those given to the student labeled C2 in market C. Each student received the same instructions: only the market and the player number have been changed.

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