Marie-Pierre Quessada
email: marie-pierre.quessada@montpellier.iufm.fr

Pierre Clément
email: pierre.clement@univ-lyon1.fr

THE ORIGINS OF HUMANKIND: A SURVEY OF SCHOOL TEXTBOOKS AND TEACHERS' CONCEPTIONS IN 14 COUNTRIES

Keywords: human evolution, implicit values, science syllabuses, science textbooks, teachers' conceptions

To investigate the difficulty teaching human origins, and particularly the possible link between values and taught scientific knowledge, research was carried out in 14 countries, in the context of the project BIOHEAD-Citizen. In eight countries (Cyprus, Estonia, Finland, France, Hungary, Italy, Romania, Senegal), this topic is included in the biology syllabus; in the six other countries (Algeria, Burkina Faso, Lebanon, Morocco, Portugal and Tunisia), it is not. Analysis of the images of timelines or trees depicting evolution revealed that Homo sapiens is never represented by a woman alone, only twice by a couple, and never with ethnic diversity. Homo sapiens is generally at the top or end of the evolutionary schemas, indicating a goalended conception of evolution. Thus scientific knowledge related to human origins can be mixed with implicit values. In the 14 countries, 5,706 teachers (primary and secondary school teachers of biology or national language) completed a questionnaire. Conceptions differed greatly among countries. Creationist conceptions were correlated with level of belief in God, as well as with shorter training at university. In the countries where evolution is included in the students' curriculum, the biology teachers' conceptions were less radically creationist than when it was not included in the curriculum.

Introduction

On 21 June 2006, the InterAcademy Panel (IAP), representing 68 national science academies, published a joint statement on the teaching of evolution: "We, the undersigned Academies of Sciences, have learned that in various parts of the world, within science courses taught in certain public systems of education, scientific evidence, data, and testable theories about the origins and evolution of life on Earth are being concealed, denied, or confused with theories not testable by science" (IAP, 2006). This collective declaration reflects the difficulties involved in teaching evolution, due to the interactions between scientific knowledge and values concerning the teaching of this topic. In recent years, our knowledge of the evolution of mankind has been significantly modified, with each new discovery immediately popularised in the media. While many people are fascinated by our origin, paradoxically, this precise topic is not taught in some countries. For instance, in Lebanon, evolution was included in the new syllabus following the civil war [START_REF] Harfouch | Elaboration des programmes au Liban: La transposition didactique externe en oeuvre[END_REF], but today it is no longer compulsory and is taught in only some schools. In other cases, such as Greece [START_REF] Lakka | Greek students' alternative conception about evolution[END_REF], human evolution is in the syllabus but is not always taught. [START_REF] Prinou | The evolutionary theory in the Greek life sciences primary and secondary textbooks from the beginning of the 20 th century to date[END_REF] specified that, in Greece, from 1983 until 2000 "the evolution of humankind was only taught to a small percentage of pupils-those who were prospective candidates of medicine." Since 2000, human evolution has been included in a chapter on the theory of evolution which is "omitted from the subject matter of courses in the Upper Secondary School, a practice that reveals at least the underestimation of its importance" (Prinou et al., 2007, p. 1). School syllabuses, textbooks and teachers' conceptions can be analysed as one step in didactic transposition. Proposed by [START_REF] Verret | Le temps des études[END_REF] and then by [START_REF] Chevallard | La transposition didactique, du savoir savant au savoir enseigné[END_REF], the concept of didactic transposition is used to analyse the way in which some scientific knowledge is chosen and then transformed in order to be taught. Typically, it considers three levels of transposition: the reference knowledge, the knowledge to be taught and the taught knowledge. In fact, there are more than three steps, one of them being related to school textbooks. None of the steps are limited to scientific knowledge and they can be analysed as interactions between scientific knowledge (K), values (V) and social practices (P): the KVP model [START_REF] Clément | Didactic transposition and KVP model: Conceptions as interactions between scientific knowledge, values and social practices[END_REF][START_REF] Clément | Environmental education: Analysis of the didactic transposition and of the conceptions of teachers[END_REF]. Several scientists and philosophers have analysed the interactions between scientific content and socio-cultural context, particularly for the evolution of mankind [START_REF] Cohen | L'Homme des origines[END_REF][START_REF] Gould | The mismeasure of man[END_REF]. Quessada and Clément (2007) introduced the concept of didactic transposition delay (DTD). This is the delay between the date on which a scientific publication appears and the date on which its content is introduced into a syllabus or school textbook. Analysing the history of French science textbooks, [START_REF] Quessada | L'enseignement des origines d'Homo sapiens, hier et aujourd'hui, en France et ailleurs: Programmes, manuels scolaires, conceptions des enseignants[END_REF]Clément (2006a, 2006b) measured different DTDs. The DTD for syllabuses could be either shorter or longer than for textbooks. The lengths of these DTDs were correlated to different parameters of the socio-cultural context, such as the importance of the subject matter and the popularisation of the specific topic, as well as concurrent dominant values (ideologies, beliefs, etc.). Social pressure was particularly important with respect to teaching the origins of mankind. These results, related to current and past French socio-cultural context, led to the development of a larger comparative approach: the European project "BIOHEAD-Citizen" (Biology, Health and Environmental Education for better Citizenship). Participants from 19 countries worked on six topics, one being the origin of humankind (coordinated by M. P. Quessada and P. Clément). The 19 countries were chosen for their socio-cultural, geographical and historical differences in order to test specific hypotheses regarding comparisons among European and non-European countries, among religions (countries which are mostly Catholic, Protestant, Orthodox or Muslim, and having various levels of atheism or agnosticism) and, within Europe, among the North and South, East and West, etc. The conceptions related to this topic were analysed with the KVP model [START_REF] Clément | Didactic transposition and KVP model: Conceptions as interactions between scientific knowledge, values and social practices[END_REF], mainly as possible interactions between taught scientific knowledge (K) and values (V). The results presented here are restricted to the 14 countries for which the questionnaire administered to the teachers included a question about human origins: Algeria, Burkina Faso, Cyprus, Estonia, Finland, France, Hungary, Italy, Lebanon, Morocco, Portugal, Romania, Senegal and Tunisia. This research presents three complementary sets of data: the biology syllabuses of the different countries, the images of Homo sapiens in evolutionary trees of biology textbooks, and the teachers' answers on the questionnaire. What implicit values can be identified in the images of humans in school textbooks? Can we find the same images, the same implicit values, in textbooks from countries that contrast in their historical, geographical, economic, political, cultural or religious contexts? Which implicit values can be identified in the teachers' conceptions? What are the interactions between social practices, concurrent values, and scientific knowledge taught about human evolution in each country?

Methodology

The methodology used in the context of the BIOHEAD-Citizen project is presented in detail in [START_REF] Clément | Biology, health and environmental education for better citizenship: Teachers' conceptions and textbook analysis in 19 countries[END_REF] for the six topics of this project; for the topic "human origins", see [START_REF] Quessada | L'enseignement des origines d'Homo sapiens, hier et aujourd'hui, en France et ailleurs: Programmes, manuels scolaires, conceptions des enseignants[END_REF], [START_REF] Quessada | Human evolution in science textbooks: A survey in eighteen countries[END_REF], [START_REF] Quessada | L'homme dans les schémas d'évolution des manuels scolaires de 12 pays[END_REF], [START_REF] Clément | Didactic transposition and KVP model: Conceptions as interactions between scientific knowledge, values and social practices[END_REF]Quessada (2008, 2009). The information therein is summarized here.

Analysis of syllabuses in the 14 countries

One research team per country (except for France, with two teams) was involved in this work. We collectively defined the indicators to analyse the national syllabuses for all school levels (primary and secondary schools). The topic "human evolution" was generally taught in the biology course, but in some cases it was taught in the context of history (Cyprus), psychology (Portugal) or philosophy (Algeria, but just suppressed during the time of our research). Here, we only use the indicator "presence or absence" of the topics "evolution" and "human evolution" in the biology syllabuses. Analysed syllabuses were used in the 2004/5 school year. Since 2005, the syllabuses of some countries have changed. For example, biological evolution was introduced in Morocco in 2008.

Analysis of the textbooks containing information on human origins

In the BIOHEAD-Citizen Project, the textbooks were analysed using the same grid in each country. The data used in the current work come from only a small part of that grid. We analysed 50 schemas containing representations of Homo sapiens. These images were collected from 18 science textbooks, from nine different countries: Cyprus (1), Estonia (2), France (4), Italy (6), Lebanon (1), Portugal (1), Romania (1), Senegal (1), Tunisia (1). Burkina was not included in the project when this part of the work was being performed. In Finland and Hungary (countries which teach human evolution from its own chapter), there was no timeline or tree of evolution with a representation of Homo sapiens. In Portugal and Tunisia, we found such a timeline or tree of evolution with a representation of Homo sapiens in the chapter on evolution, although no specific part of the textbook dealt with human evolution.

The images of Homo sapiens were grouped into several specific categories: nude man without beard, nude man with beard, dressed man with suit, dressed man (other than suit), couple, small group of people, shadow of unidentifiable gender, brain, and skull. The position of Homo sapiens in the schema was analysed in relation to a finalistic or non-finalistic conception.

Analysis of teachers' conceptions

In the 14 countries, teachers filled out a long questionnaire, including 15 questions related to evolution and 17 questions related to their own characteristics (gender, age, level of training, socio-political or religious opinions). In each country, the sample was a balanced set of primary school teachers (P), secondary school teachers who taught biology (B) and secondary school teachers who taught the national language (L). In these three categories, half of the sample consisted of in-service teachers (In-P, In-B and in-L) and the other half of pre-service teachers (Pre-P, Pre-B and Pre-L). For each of these six sub-samples, about 50 teachers were interviewed: about 300 in each country (sometimes more when we tested complementary hypotheses, as in France, Lebanon and Tunisia; sometimes less when the country was small). In total (for the 14 countries), 5,706 teachers filled out the questionnaire. Some of the information gathered to characterize the interviewed teachers is presented in Table 1.

Table 1. Samples from 14 countries (total = 5,706 teachers)

The questionnaire consisted of questions which had been validated by previous research, and submitted to the steps described in [START_REF] Clément | Biology, health and environmental education for better citizenship: Teachers' conceptions and textbook analysis in 19 countries[END_REF] and in [START_REF] Quessada | L'enseignement des origines d'Homo sapiens, hier et aujourd'hui, en France et ailleurs: Programmes, manuels scolaires, conceptions des enseignants[END_REF]: translation from the reference languages of the project (English and French) to the national language (using parallel independent translations, then a comparison with a back-translation); pilot interviews in most of the countries; the use of a longer pilot test in each country, then analysing the answers, their reliability after one month for the same pre-service teachers, multivariate analyses and finally a selection of the most discriminating questions.

Here we only present the answers from two questions (see below). They are significantly correlated to the data from the other questions related to evolution [START_REF] Quessada | L'enseignement des origines d'Homo sapiens, hier et aujourd'hui, en France et ailleurs: Programmes, manuels scolaires, conceptions des enseignants[END_REF]. Question B48 (God) was one of a list of factors to rate (natural selection, chance, environment, intelligent design, viruses, transposons).

B28. Which of the following four statements do you agree with most? Select ONLY one sentence:

1 It is certain that the origin of humankind results from evolutionary processes.

2 Human origin can be explained by evolutionary processes without considering the hypothesis that God created humankind.

3 Human origin can be explained by evolutionary processes that are governed by God. In four countries (Algeria, Burkina, Lebanon and Morocco), there was nothing related to biological evolution. This topic has been more recently included in the syllabuses in Morocco (2008) and Lebanon (2009). In Burkina, it is taught only in some schools using the French programme. In three countries (Romania, Senegal, Tunisia), evolution was taught in only one level, the last year of secondary school. In the seven other countries (Cyprus, Estonia, Finland, France, Hungary, Italy, Portugal), evolution was taught in three to six levels and was generally introduced in the primary schools (< 12-year-olds, Figure 1). In six countries (Algeria, Burkina, Lebanon, Morocco, Portugal and Tunisia), there was nothing on the topic of human evolution. However, in Portugal, human evolution was included in the psychology syllabus. In Tunisia, evolution was taught, but not human origins. In the eight other countries (Cyprus, Estonia, Finland, France, Hungary, Italy, Romania, Senegal), the origins of humankind were taught with evolution (Figure 2).

The images of human beings illustrating human evolution in school textbooks

In the 18 textbooks analysed, we found 50 images showing human evolutionary trees or timelines (sequences) containing at least one illustration of Homo sapiens. These images were classified into nine categories: nude man with beard (14), nude man without beard (9), man dressed in suit (9), skull (9), man dressed in other than suit (5), couple (2), shadow (1), brain (1). Homo sapiens was never represented in these textbooks solely by a woman. Only twice (in a French textbook and in an Italian one), was Homo sapiens represented by a couple. In the evolution schemas, all representations of humans had white skin; not one image illustrated ethnic diversity. Most of the textbooks illustrated human biological evolution as linear and finalistic, projecting an image of a white-skinned, male Homo sapiens. Figure 3 illustrates the most frequent type of drawing of this linear human evolution. Here, Homo sapiens appears as a naked, white-skinned man, resembling the prototypical image of Adam. Another frequent representation of Homo sapiens was as a male human, with characteristics of occidental society (white-skinned, occidental clothing and/or tools and accessories). The images below (Figure 4) show a man wearing modern blue dress in an Italian book, and even in the Senegalese textbook, a white man with a suit. [START_REF] Miller | Il Mondo della Natura. Il punto di vista della Biologia[END_REF], p.209 Désiré, 1983, p.314. Figure 4. Two representations of an occidental male Homo sapiens (modified: the originals are in colour)

Consequently, in the great majority of the textbooks analysed, biological evolution ends with an occidental white male Homo sapiens.

What are the teachers' conceptions related to human origins?

In answer to question B48 (Figure 5a), related to "the importance of God in species evolution", 8% of the teachers ticked "great importance" or "some importance" in France, while this percentage increased to 95 or more in Lebanon, Senegal, Tunisia, Morocco and Algeria. Nevertheless, some of these teachers were also evolutionists. In answer to question B28 (Figure 5b), 2% of the French teachers ticked the radical creationist item ("It is certain that God created humankind"), whereas 62 to 92% of the teachers ticked it in Tunisia, Lebanon, Senegal, Morocco and Algeria. Other teachers had conceptions that were both creationist and evolutionist, ticking the third item ("Human origin can be explained by evolutionary processes that are governed by God"): 6% of teachers in France and Algeria, to 32% or more in Tunisia, Burkina, Portugal, Finland, Romania and even 43% in Cyprus (Figure 5b). Further analysis of the answers to question B28 (Figure 6) revealed major differences among the 14 countries. Even when comparing only the Christian teachers' answers (Figure 6, B28 Chr), there were very significant differences among countries, showing a strong influence of national socio-cultural context. It is certain that the origin of the humankind results from evolutionary processes. Human origin can be explained by evolutionary processes without considering the hypothesis that God created humankind. Human origin can be explained by evolutionary processes that are governed by God.

It is certain that God created humankind. The answers of the "biologist" teachers (biology teachers in secondary schools + primary school teachers with a diploma in biology; their number is indicated for each country in Table 1) were not so different, within each country, from the answers of their non-biologist colleagues. The difference between biologist teachers and other teachers was nevertheless significant in nine countries (Chi2 with the Bonferroni correction): Cyprus, Estonia, Finland, France, Hungary, Italy, Lebanon, Portugal and Romania. In these countries, biologist teachers were more evolutionist than their colleagues, often with a more important amount of creationist + evolutionist conceptions (item 3 in question B28). In four of the five countries where there was no significant difference, Algeria, Burkina, Morocco and Tunisia, human evolution was not included in the syllabus (Figure 2). Another important result is shown in Figure 6, graph "B28 Level of training". There was a direct positive correlation between the time a teacher had trained at university and his/her acceptance of evolution: 19% radical creationist conceptions related to the origin of mankind when the level of teachers' training was >5 years at university; 36% with 3 or 4 years of university; 53% with 2 years or less at university.

B28 -B28. Which of the following four statements do you agree with most? Select ONLY one sentence:

It is certain that the origin of the humankind results from evolutionary processes. Human origin can be explained by evolutionary processes without considering the hypothesis that God created humankind. Human origin can be explained by evolutionary processes that are governed by God. It is certain that God created humankind.

Discussion and conclusions

Studies on Evolution teaching have been performed in various countries and often show the great importance of social context with respect to curriculum and textbook contents: [START_REF] Barberá | Biology curriculum in twentieth-century Spain[END_REF] on Spanish biology curricula; Jiménez Aleixandre (1994,1996) on Spanish textbooks; [START_REF] Swarts | Evolution in secondary high school biology textbooks of the People's Republic of China, United States of America and the latter stages of the Union of Soviet Socialist Republics[END_REF] on Chinese, American and Soviet secondary-school biology textbooks; [START_REF] Skoog | The coverage of evolution in high school biology textbooks published in the 1980s[END_REF] and [START_REF] Rosenthal | Social issues in high school biology textbooks: 1963-1983[END_REF] on US textbooks. We focused our study on human evolution, for which the obstacles and difficulties are exacerbated [START_REF] Quessada | L'enseignement des origines d'Homo sapiens, hier et aujourd'hui, en France et ailleurs: Programmes, manuels scolaires, conceptions des enseignants[END_REF]Quessada & Clément 2006a[START_REF] Quessada | La transposition didactique de l'évolution humaine dans les manuels au 19ème et 20ème siècles: Entre trahison épistémologique, traduction de valeurs et création didactique[END_REF], 2007). [START_REF] Skoog | The coverage of human evolution in high school biology textbooks in the 20th century and in current state science standards[END_REF] also studied the coverage of human evolution in 20th century in US high-school biology textbooks and in current science standards. He ascertained that before 1960, human evolution was given little attention in biology textbooks. In the following two decades, the situation with regard to human evolution worsened in that information was minimal. In 1990, human evolution was unrestricted. By 2004, three states included the teaching of human evolution in the state science standards. Our comparative study shows great differences between countries (with respect to syllabuses and teachers' conceptions): the social context strongly influences the way evolution is (or is not) taught, particularly human evolution. In other articles, we analysed the social factors which are correlated with the teachers' conceptions (Clément & Quessada, 2008, 2009;[START_REF] Quessada | L'enseignement des origines d'Homo sapiens, hier et aujourd'hui, en France et ailleurs: Programmes, manuels scolaires, conceptions des enseignants[END_REF][START_REF] Quessada | Conceptions sur l'évolution biologique d'enseignants du primaire et du secondaire de douze pays d'Afrique, d'Europe et du Moyen Orient[END_REF]: the degree of belief in God and in religious practice, the economic status of the country and the teachers' level of training. In the present paper, limited to the evolution of humankind, we also show that the longer the teachers trained at university, the greater is their acceptance of evolutionist ideas. Moreover, in most of the countries where human evolution is taught, the conceptions of teachers who had training in biology are less radically creationist, more creationist-evolutionist than those of their colleagues. This raises the problem of teachers' training: how can human evolution be introduced in syllabuses when teachers' conceptions are not evolutionist? What training can help effect this change? Our results encourage longer training periods for future teachers in every country, incorporating more biology. They also suggest incorporating an epistemological approach of science in their training, to help teachers differentiate belief from scientific knowledge, to consider religion and science as two non-overlapping domains, i.e. the non-overlapping magisterial (NOMA) proposed by [START_REF] Gould | Rocks for ages. Science and religion in the fullness of life[END_REF]. This could be a first step to introducing the topic "evolution of mankind" in schools of any country. The present work, along with previous articles [START_REF] Quessada | Human evolution in science textbooks: A survey in eighteen countries[END_REF]Quessada & Clément, 2009), also shows that social representations of human evolution coming from images in textbooks are more or less the same in all countries teaching evolution: Homo sapiens is nearly always an archetypal male with white skin, either naked or dressed in occidental clothing. The DTD is important, being more than 15 years: scientific representations with bush-like, non-linear evolution schemas were very rare in 2004 textbooks. These results show that scientific messages related to the origins of humankind are generally mixed with implicit values such as finalism (end-goaled evolution), sexism and occidentalism. Teachers have to identify these epistemological obstacles and try to explain the possible interaction between taught science and values to develop critical attitudes in pupils.

4

  Figure 1. Number of grade levels in which evolution is included in the biology programmes of 14 countries (black = > 12 years old, white = < 12 years old)

Figure 2 .

 2 Figure 2. Number of grade levels in which human evolution is included in the biology programmes of 14 countries

Figure 3 .

 3 Figure 3. Linear conception of human evolution, ending with a white-skinned and bearded man. Modified from: Colombi, Negrino, & Rondano, 2001, p. 277 (the original is in colour)

  (a) B48. Indicate your evaluation of the importance of God in species evolution (tick only one of the B28. Which of the following four statements do you agree with most? Select ONLY one sentence:

Figure 5 .

 5 Figure 5. Teachers' answers to questions B48 and B28 (5,706 teachers in 14 countries)

B28

  Bio -Answers of the 2,205 biologist teachers, country by country B28 Non Bio -Answers of the 3,501 non-biologist teachers, country by country B28 Chr -Answers of the 2,449 Christian teachers, country by country B28 Level of training -Answers of the 5,706 teachers, for the following levels of training: I = < 2 years at university. II = 3 or 4 years. III = > 5 years.

Figure 6 .

 6 Figure 6. Teachers' answers to question B28 (5,706 teachers in 14 countries)

Acknowledgements

This work was supported by the European research project BIOHEAD-Citizen (Biology, Health and Environmental Education for better Citizenship), coordinated by G. Carvalho (Portugal), P. Clément (France) and F. Bogner (Germany). Thanks are due to the collective work performed by the teams from 19 countries. The data used for the present work come


Nicolas Jacquemet
email: nicolas.jacquemet@univ-lorraine.fr

Adam Zylbersztejn
email: zylbersztejn@gmail.com.

Juergen Bracht

Boǧaçhan Çelen

Pierre-André Chiappori

Tore Ellingsen

Nick Feltovich

Guillaume Fréchette

Jacob Goeree

Frédéric Koessler

Stéphane Luchini

Rosemarie Nagel

Andreas Ortmann

Jean-Marc Tallon

Antoine Terracol

Marie-Claire Villeval

What drives failure to maximize payoffs in the lab? A test of the inequality aversion hypothesis ⇤

Keywords: Coordination Failure, Subgame perfectness, Non-credible threats, Laboratory experiments, Social Preferences, Inequality Aversion. JEL Classification: C72, D83

Experiments based on the Beard and Beil (1994) two-player coordination game robustly show that coordination failures arise as a result of two puzzling behaviors: (i) subjects are not willing to rely on others' self-interested maximization, and (ii) self-interested maximization is not ubiquitous. Such behavior is often considered to challenge the relevance of subgame perfectness as an equilibrium selection criterion, since weakly dominated strategies are actually used. We report on new experiments investigating whether inequality in payoffs between players, maintained in most lab implementations of this game, drives such behavior. Our data clearly show that the failure to maximize personal payoffs, as well as the fear that others might act this way, do not stem from inequality aversion. This result is robust to varying the saliency of decisions, repetition-based learning and cultural differences between France and Poland.

(1.000.000; 1) r (0; 0) l R (X, Y ) L Note. 0 <X<1.000.000.T h ev a l u eo fY is irrelevant from the strategic perspective. We assume 0 <Y <1 so that the outcomes are Paretorankable.

Introduction

The game presented in Figure 1 illustrates the behavioral challenge posed by relying on the assumptions behind subgame perfectness. In this game, introduced by Rosenthal (1981), the first mover either decides alone on the outcome of the game (action R) or relies on the second mover (L). In the latter case, the second mover only has to decide whether to maximize both players' payoffs (r)o rn o t( l). Although the threat of non-maximization is non-credible and action l is ruled out by subgame perfectness, the first mover may still lose a substantial amount should the second mover fail to maximize payoffs. This makes the Pareto-dominated solution -in which the first mover plays L -a plausible case in real-life implementations. This puzzling behavioral outcome, originally introduced as a theoretical conjecture by Rosenthal, is robustly highlighted by all lab experiments using both sequential-move and simultaneous-move versions of the game. 1 Suboptimal outcomes arise due to two different driving forces: first, as expected by Rosenthal, subjects who play as first movers are very frequently reluctant to rely on second movers; second, surprisingly enough, an important share of second movers do indeed turn out to be unreliable and fail to maximize both players' payoffs.

Such evidence has long been seen as a pathological example of people's inability to use subgame perfectness. This interpretation however relies on the assumption of standard preferences that only include personal payoffs -so that the common knowledge of the payoff scheme provides complete information about all players' preferences. The aim of this paper is to investigate another possible explanation for these puzzling behaviors, namely inequality aversion (Fehr and Schmidt, 1999)which may rationalize suboptimal outcomes in all the payoff structures implemented to date in lab experiments. 2 Our investigation is based on two research questions: do unequal payoffs generated by the dominant outcome (i) make second movers unwilling to maximize both players' payoffs, and (ii) make first movers reluctant to rely on second movers that are actually reliable? We implement six variations of the payoff structure of the game, all sharing the main strategic dimensions of the original game. The Baseline treatments are compared to Egalitarian treatments which restore equality between players' payoffs in the Pareto-dominant outcome. We also assess the robustness of our results to enhanced saliency of the decisions in the game, and provide evidence on the cross-cultural robustness by collecting data in France and in Poland.

Our findings are threefold. First, our data unambiguously reject the inequality aversion hypothesis, since neither the behavior of the first movers nor the behavior of the second movers changes due to equalized payoffs. Second, we observe that payoff maximization among second movers is almost universal only once all the Nash equilibria in the game involve the same inequality of payoffs. This suggests that player Bs in other treatments -where player As' relative standing in the non-cooperative equilibrium is more favorable than in the cooperative one -might act inefficiently so as to penalize their partners for enjoying an undeserved procedural advantage. This points to a totally different kind of other-regarding preferences, related to procedural justice. 3 Our third finding is that first movers do not take into account this transition in second movers' behavior, as if they did not expect social preferences to have any effect on their partners' actions. We conclude the paper with a discussion of the avenues that remain open to explain such a robust inefficiency observed in the lab.

Two puzzling behaviors in existing laboratory experiments

Table 1 provides an overview of previous experimental implementations of the game studied in this paper. There are only three different outcomes in the game, detailed in the left-hand side of the 2 The extent to which this preference explains the divergence between human decisions and standard gametheoretical predictions is the subject of a lively debate in experimental economics. For instance, lab experiments by Charness and Grosskopf (2001), Kritikos and Bolle (2001), Charness and Rabin (2002) and Engelmann and Strobel (2004) provide evidence against the inequality aversion hypothesis, while subsequent experiments by Chmura, Kube, Pitz, and Puppe (2005), Fehr, Naef, and Schmidt (2006), Bolton and Ockenfels (2006), Blanco, Engelmann, and Normann (2011), as well as a neuroeconomic study by Tricomi, Rangel, Camerer, and O'Doherty (2010), report evidence in its favor.

3 Krawczyk (2011, p.112) defines procedural justice as "transparent and impartial rules ensuring that each of the agents involved in an interaction enjoys an equal opportunity to obtain a satisfactory outcome." In this approach to other-regarding preferences, the individual utility depends not only on the type of achieved outcomes, but also on the way in which they were generated. As discussed in the concluding section, there exists previous experimental evidence that people exhibit a taste for procedural justice and are even willing to sacrifice their own wealth for punishing those who enjoy an undeserved procedural advantage. table: either the first mover (henceforth player A) chooses to decide alone by picking L, or he relies on the second mover's (henceforth player B's) decision by choosing R. In this case, both players' payoffs are higher if r is chosen rather than l. The right-hand side of the table summarizes each outcome as a percentage of all observed decisions, as well as the frequency of action r conditional on reliance from player A.

The main focus of the original study by Beard and Beil (1994) is to test Rosenthal's conjecture that subjects may be unwilling to rely on the other players' ability to maximize payoffs -hence challenging subgame perfectness. [START_REF] Beard | Do People Rely on the Self-Interested Maximization of Others? An Experimental Test[END_REF] Their experimental evidence supports the Rosenthal conjecture: although the share of payoff-maximizing subjects is high in the sub-population of player Bs who are relied upon (from 83% in their treatment 1 to 100% in treatments 3 and 4, for instance), most player As decide not to rely on their partners. The comparison across treatments shows that behavior highly depends on the size of stakes: the lower the value of the secure option, the higher the reliance rate from player As; the higher the cost of being unreliable, the higher the reliability rate from player Bs. Beard, Beil, and Mataga (2001) replicate some of these treatments using Japanese subjects. While the results of their treatment 1 are in line with previous US evidence, behavior in treatment 2 is in a sense more striking. Because of the increase in the monetary incentives to reach (R, r) as compared with the secure outcome (L), a much higher share of player As rely on their partner -from 21% in treatment 1 to 50% in treatment 2. However, although the payoffs for player B remain unchanged between the two treatments, the share of payoff-maximizing decisions (conditional on having been relied upon in the first place) falls from 83% to 64%.

Importantly, both of these studies elicit decisions from player Bs conditional on the prior reliance of player As. Hence, this evidence does not suffice to infer the actual behavior in the entire population of player Bs, since the decisions of player Bs paired with unreliant player As cannot be observed. In contrast, Goeree and Holt (2001) and Cooper and Van Huyck (2003) use a simultaneous-move game of either normal or extensive form, and confirm the robustness of previous evidence. First, even when player Bs are actually reliable (such as in the Goeree and Holt treatment 1), a large share of player As are reluctant to rely on them. Second, in a large variety of treatments (treatments 2 and 3 in Goeree and Holt and both treatments of Cooper and Van Huyck) player Bs actually are often unreliable -decision r occurs from 15% to 25% of the time. Jacquemet and Zylbersztejn (2013) study the role of the amount of information about interaction partners acquired through three different channels: repetition-based learning, cheap talk communication from player B to player A and observation of player B's past actions by player A . To that end, the experiment implements the normal form of the game and thus elicit decisions in the whole population of player As and player Bs. In the initial round of their baseline treatment (last two rows of Table 1), 23% of player As prefer the secure choice and 100% of player Bs that are relied upon actually turn out to be reliable. This proportion is, however, much lower (80%) in the whole population of player Bs they could be matched with. Evidence from nine subsequent rounds of the same game (where repetition takes place under a perfect-stranger design with fixed roles and round-robin matching) suggests that learning is of very little help in disciplining that behaviorthe overall frequency of reliable decisions from player Bs amounts to 81%. More generally, this behavior on the part of player Bs is insensitive to any of the experimental treatments, as shown in the last two rows of the Table . This means that neither repetition-based learning, nor forwardlooking information through messages, nor even backward-looking information from observation of past decisions suffices to discipline player Bs' choices of weakly-dominated actions in this payoff configuration.

Empirical strategy

From existing experimental evidence, two puzzling behaviors arise: a large share of player As appear reluctant to rely on actually reliable player Bs; but at the same time the weakly-dominated strategy is often chosen by player Bs. The purpose of this paper is to test whether such behavior is related to the payoff structure of the game. [START_REF] Rosenthal | Games of perfect information, predatory pricing and the chain-store paradox[END_REF] To illustrate the point, the general structure of the game is presented in Table 2 -of which all the lab implementations presented in Table 1 above are particular cases. The crucial properties of the game hold if the parameters a, . . . , f take non-negative values and all payoffs are positive. Player B (weakly) maximizes both players' payoffs by selecting r, while player A prefers L to the outcome (R, l) that is attained when relying on an unreliable player B . As a result, the game has two Nash equilibria, (L, l) and (R, r). The first is imperfect (since it entails player B's weakly dominant strategy l), while the second is (trembling-hand) perfect and Pareto-superior. But in most experimental implementations of this game, the payoffs from the perfect Nash equilibrium are much higher for player A than for player B , i.e., a ≥ b, a

+ d ≥ b + f , b -e ≥ a -c.
Although this does not make B's unreliable decision l a rational answer to A's reliance, nonstandard preferences involving inequality aversion might explain why player Bs forgo efficiency at a personal monetary cost (Fehr and Schmidt, 1999). Moreover, if player As believe that this sort of preference exists among player Bs, they may prefer to choose the secure option instead of relying on their partner. In order to test this hypothesis, our empirical approach consists in complementing the original payoff structure with variations that maintain the strategic properties of the game, while equalizing the payoffs both players earn in the case of payoff-maximizing coordination, i.e., but to the best of our knowledge it has never been examined empirically. One exception is treatment 6 in Beard and Beil (1994), discussed in Section 3.1. Surprisingly, this treatment is not commented on in the original paper, neither it is discussed as a means to assess the sensitivity of behavior to more equalized payoffs. In any case, as stressed above, the original design of Beard and Beil (1994) is inappropriate for studying player Bs'be h a v i o r ,s i n c e their decisions are elicited only conditional on player A's choice. such that (a + d)=(b + f ).6

Overview of the experimental design

Table 3 summarizes our experimental design, which uses 6 payoff configurations (described in subsequent rows) and 2 different locations (described in the middle columns). They seek to address three empirical questions related to inequality aversion. First, we address the question of whether the equality-based preferences affect equilibrium selection by restoring payoff equality between players. Second, we investigate the interplay between saliency and equality concerns by increasing the opportunity cost of dominated actions. Third, following a related cross-cultural study by Beard, Beil, and Mataga (2001), we seek to identify potential cultural differences in model of inequality-aversion. Both subjects i, j 2{A, B} are assumed to choose their actions in the game presented in Table 2 according to the extended utility function defined on outcome O generating payoffs (Oi; Oj):

Ui(O|αi,βi)=Oi -αi ⇤ (Oj -Oi) ⇤ 1O i <O j -βi ⇤ (Oi -Oj) ⇤ 1O i >O j (1)
Parameters 0  βi  αi measure the sensitivity of player i to inequality (1O i <O j =1-1O i >O j =1if j earns more than i,0o t h e r w i s e ) . T h ep a y o ffs t r u c t u r e so fo u rB a s e l i n eT r e a t m e n t s( B T 1a n dB T 2i nT a b l e3 )a r e such that 9(αB,βB):UB((R, l) BT |αB,βB) >U B ((R, r) BT |αB,βB),s ot h a taplayer B whose utility is defined by (1) may prefer outcome (R, l) over (R, r).B yt h es a m et o k e n ,E g a l i t a r i a nT r e a t m e n t s( E T 1 -4i nT a b l e3 )a r e built in such a way that 8(αB,βB):UB((R, l) ET |αB,βB) <U B ((R, r) ET |αB,βB), so that for the same preference parameters, player B now prefers (R, r) over (R, l). As for player As,defineθT as the perceived likelihood that player Bs'r e a l i z a t i o no f(αB,βB) makes him prefer (R, l) over (R, r) in Treatment T .I fplayer A is an expected utility maximizer, then EUA(R T |αA,βA,θT )=θT UA((R, l) T |αA,βA)+(1-θT )UA((R, r) T |αA,βA). As a result, if the fear that player Bs are inequality-averse is high enough, player A may prefer the secure choice in the Baseline Treatment, since 9(αA,βA,θBT ):UA(L BT |αA,βA) ≥ EUA(R BT |αA,βA,θBT ).B y c o n t r a s t , t h e E g a l i t a r i a n T r e a t m e n t i s designed in such a way that θET =0.

preferences by comparing the behavior of French and Polish subjects. The differences from one treatment to the other are described in turn below.

Inequality aversion under weak saliency. Our starting point is Baseline Treatment 1which corresponds to the Beard and Beil (1994) treatment 1 and the Jacquemet and Zylbersztejn (2013) replication -which gives rise to the two puzzling behaviors we are interested in. To this treatment, we associate an egalitarian version, Egalitarian Treatment 1 that equalizes payoffs in the Pareto efficient outcome -also used as treatment 6 in Beard and Beil (1994). As shown in the last two columns of the table, presenting the observed proportions of reliant decisions (R) from player As and reliable decisions (r) from player Bs, equalizing payoffs in the Pareto-efficient outcome has virtually no effect on players' average behavior.

Behavioral effect of enhanced saliency. An important shortcoming of the first pair of treatments is that saliency may be violated, as reliance and reliability only induce a 0.25 euro variation in subjects' payoffs. Two additional treatments seek to assess the robustness of the results to this feature. In Egalitarian Treatment 3, built on ET1, we improve the saliency of reliable decisions for player B : the opportunity cost of playing r (instead of the weakly dominated decision l)a g a i n s t R is now 1.5 euros. 7 Similarly, in Egalitarian Treatment 4 based on ET3, we improve the saliency of being reliant for player A -the payoff difference between the two Nash equilibria amounts to 1.5 euros instead of 0.25 euros. In both of these treatments, we maintain equality in payoffs between players in the Pareto-efficient outcome. The comparison between ET3 and ET1 thus allows to identify the effect of saliency on player B's reliability in an equalized payoffs environment ; while the comparison between ET3 and ET4 similarly highlights the effect of saliency on player A's reliance. We derive mixed results from these two additional treatments: the behavior of player Bs is unaffected by both changes, while the share of reliant decisions from player As is significantly higher in ET4 than in ET1 and ET3.

Inequality aversion under enhanced saliency. In all treatments described up till now, a strong payoff inequality between players remains if player A chooses L. As a result, it could be that A's choice of being reliant is itself driven by the willingness to move away from outcomes with too much inequality in payoffs. In Egalitarian Treatment 2, built on ET4, we restore equality in the dominated equilibrium by raising player B's payoff. 8 The comparison between ET2 and ET4 thus seeks to identify the effect of player As' inequality aversion on the outcomes. Surprisingly enough, the main lesson drawn from this comparison is that ET2 strongly disciplines the behavior 7 In the course of trials leading to the current experimental treatments, we also slightly raised all payoffs from 5.0 in ET1 to 5.5 in ET3, to verify whether decimals have any effect on players' behavior. 8 By the same token as above, we slightly raise the payoff earned by player A in the event of unsuccessful attempts to rely on B, from 5.5 to 6.5.

of player Bs -the weakly dominated action is now almost never chosen. The behavior of player As, by contrast, is unaffected by this change. To assess whether such a high rate of secure choices -despite widespread reliability in the population of player Bs -is reinforced by payoff inequality, we complete our design with Baseline Treatment 2, built on ET2, in which the Pareto-dominant outcome gives rise to payoff inequality in favor of player A. 9 Again, we fail to find any effect of this dimension of the game, as both players behave in the same manner as in ET2.

Cross-cultural comparison. All our main treatments of interest were run in Paris (France).

The last concern our design addresses is the possibility that the treatment effects are driven by culture-specific motives. To assess the robustness of our results to this dimension, we run additional sessions in Warsaw (Poland). 10 We chose the three treatments in which observed behavior is in our view the most striking, i.e. ET2, ET3 and ET4. The number of sessions in each location is provided in Table 3.

Experimental procedures

Each payoff variation described above defines a treatment, and all treatments are implemented separately using a between-subject design. The design is kept the same for all treatments, based on the procedures of Jacquemet and Zylbersztejn (2013).

We introduce two important changes to Beard and Beil's original design. First, we study the effect of learning by repeating the one-shot game 10 times. 11 Each occurrence is one-shot in the sense that: roles are fixed; pairs are re-matched in each round using a perfect-stranger, round-robin procedure; we avoid the end-game effect by providing no information about the exact number of repetitions; and take-home earnings are derived from one round, randomly drawn out of the ten at the end of each experimental session. Second, we elicit both players' decisions in each occurrence of the game. In that respect, we break the original sequentiality of the game and ask each player 9 In designing this treatment, we seek to introduce payoff inequality between players, while holding constant the saliency of being reliable for player B .W et h u sc h oo s et or e d u c eplayer B's payoff in (R, l) to 7.00, instead of 8.50 in ET2, and accordingly adjust the payoff stemming from decision L.

10 As an Eastern European country, Poland seems to sufficiently differ in political and social history from France to serve the purpose of a robustness check of our results to a different cultural background. In particular, experimental evidence suggests that social preferences (like trust and reciprocity) may vary across European countries ( for unconditional choices in each round. Players are only informed about their own payoffs at the end of each round.

A typical session proceeds as follows. Upon arrival, subjects sign an individual consent form. They then enter the lab, where they are randomly assigned to their computers and asked to fill in a small personal questionnaire containing basic questions about their age, gender, education, etc. The written instructions are then read aloud. Players are informed that they will play some (unrevealed) number of rounds of the same game, each round with a different partner, and that their own role will not change during the experiment. Before starting, subjects are asked to fill in a quiz assessing their understanding of the game they are about to play. Once the quiz and all remaining questions have been answered, the experiment begins. Prior to the first round, players are randomly assigned to their roles -either A or B. They are then anonymously and randomly matched to a partner and asked for their choice: R or L for player As, r or l for player Bs. At the end of each round, each player is informed only about their own payoff. When all pairs have completed a round of the game, the subjects are informed whether or not a new round is starting. In the event of a new round, pairs are re-matched according to a perfect-stranger matching procedure (any pair meets only once in the session). At the end of the experiment, one round is randomly drawn and each player receives the amount corresponding to their gains in that round plus a show-up fee.

All in all, we ran a total of 21 experimental sessions: 16 in the Laboratoire d'Economie Experimentale de Paris (LEEP) at University Paris 1 Panthéon-Sorbonne, between June 2009 and January 2012, and 5 in the Experimental Economics Laboratory at Warsaw University in February 2012. 12 In both laboratories, subjects were recruited via an online registration interface adapted using Orsee (Greiner, 2004) and the experiment was computerized using software developed under Regate (Zeiliger, 2000). Each session lasted about 45 minutes, with an average payoff of 14 euros in Paris and 28 PLN (about 7 euros) in Warsaw. 13 No subject participated in more than one experimental session. Out of 420 participants, 206 were men and 214 were women. A vast majority of the population (332 subjects) were students in various disciplines, and 193 of them were likely to have some knowledge of game theory due to their field of study. 14 297 subjects had taken part in economic experiments before. The average age of the participants was 24.

12 Data from the sixth session run in Warsaw, implementing ET4, have been lost as a result of a software crash. 13 For French subjects, all the payoffs in experimental instructions were expressed in euros. For Polish subjects, we use the same payoff scheme, but expressed in Experimental Current Units (ECU). For the purposes of payment, ECU were converted to Polish Zloty (PLN) at the rate 1 ECU=2 PLN. The participation fee was 5 euros in Paris and 10 PLN (around 2.5 euros according to the current exchange rate in 2012) in Warsaw. Since a vast majority of our subjects are students, and petty student jobs usually pay about 8 euros per hour in Paris and 15 PLN per hour in Warsaw, we strongly believe that the participants' monetary incentives are comparable between countries.

14 Disciplines such as economics, engineering, management, political science, psychology, applied mathematics for the social sciences, mathematics, computer science, and sociology.

Results

In what follows, statistical inference is based on between-treatment tests for the significance of differences in the proportions of each outcome of interest. We use two kinds of statistical tests.

In round 1, where all observations are independent, we use two-sided Fisher's exact tests. In rounds 2-10, individual observations may be correlated within each session due to the re-matching of subjects from one round to the other. We take into account this data structure by using the following parametric procedure. First, we run an OLS regression of treatment dummies on a dummy dependent variable representing the outcome of interest. In this setup, coefficients correspond to the proportions of outcomes of interest in a given treatment, so that two-sided ttests and F -tests on coefficients allow us to test linear hypotheses about the equality of proportions between treatments. To take into account the within-session correlation, we cluster data at the session level, and use leave-one-out jackknife standard errors to deal with the issue of potential small-sample bias. This method is applied to data from rounds 1-10 and 2-10. 15 To ease the description of observed behavior, we use the following nomenclature. A cooperative decision means R (r) for player As (Bs). A cooperative outcome accordingly corresponds to the Pareto-Nash equilibrium (R, r), while a coordinated outcome describes a situation where either of the existing Nash equilibria -(L, l) or (R, r) -is attained. Last, we also consider two types of miscoordination (corresponding to different non-equilibrium outcomes): (L, r) and (R, l).

Replication of Beard and Beil's treatments

Our first comparison of interest is BT1 against ET1, two treatments previously studied by Beard and Beil (1994). In Table 4, we summarize the main outcomes from both their and our implementations of these two treatments. The data collected by Beard and Beil in the context of a one-shot sequential-move game seem to favor the inequality aversion hypothesis. The rate of reliance by player As doubles, from 34.3% (12 cases out of 35) in the Baseline Treatment 1 to 69.3% (18/26) in the Egalitarian Treatment 1 (p=0.010), and the rate of conditional reliability from player Bs increases from 83.3% (10/12) to 100% (18/18) (p=0.152). Therefore, player As do indeed act more cooperatively in an environment where bilateral cooperation gives equal profits to both partners, and player Bs actually seem to prefer an equal division of the gains for cooperation, although the magnitude of this preference is marginal. Our replication of both treatments in a repeated simultaneous-move game yields results that are more mixed and -most importantly -non-persistent. For inexperienced player As (actions observed in round 1), the likelihood of action R also doubles, as in Beard and Beil's study, increasing from 23.3% in BT1 to 46.7% in ET1 (p=0.103), but player Bs are at the same time marginally less reliable -the frequency of cooperative choices falls from 80% to 63.3% (p=0.252). Importantly, these differences completely disappear among experienced players (actions observed in rounds 2-10), where subjects' behavior is virtually identical under both conditions: the frequency of decisions R varies between 51.9% in BT1 and 45.6% in ET1 (p=0.574), while the frequencies of decisions r by player Bs 80.7% and 73.7% (p=0.602). 16

Inequality aversion under improved saliency

Table 5 summarizes the outcomes from our four companion treatments, along with a reminder of the main results from BT1 and ET1. For the three egalitarian treatments (ET2, ET3 and ET4), we split the results according to the location of the experiment. This allows us to assess the level of cultural specificity in the behavior observed in this game.

In the light of the data from these three treatments, it is difficult to argue that there is any systematic difference between the patterns of behavior in each country. Player As'b e h a v i o ri s only subject to minor discrepancies and seems quite similar in France and Poland. For treatments ET2 and ET4, players Bs' behavior in both countries is practically identical. The sole visible difference concerns player Bs' behavior in treatment ET3, where Polish subjects are slightly more likely to select action r than French subjects. However, statistical tests are unable to reject the 16 In line with individual behavior, outcomes do not react much to treatment. Overall, only 53% of outcomes in BT1, and 47.7% in ET1 (p=0.249), are coordinated. Cooperative outcomes account for 41.3% and 33% (p=0.497), respectively. Miscoordination (L, r) is extremely widespread, attaining 39.3% and 39.7% (p=0.955) of global outcomes. The most costly miscoordination (R, l) is also pronounced, reaching 7.7% and 12.7% (p=0.220) in BT1 and ET1, respectively. Note. For each treatment (in rows), the second column gives the number of observations -the number of individual subjects is N/10. For the first round of play, Rounds 2-10 and overall averages, the three sub-columns provide the average frequency of reliance from player A (decision R) and reliability from player B (decision r).

null of equal means in the two countries. 17 We therefore do not consider the cultural background as an influential factor in our experimental data, and accordingly pool both locations in the data analysis below.

In ET3 and ET4, we improve the saliency of the action leading to the Pareto-efficient outcome for each player in turn. As compared to ET1, ET3 increases player Bs' conditional surplus from playing r, while ET4 also increases player As' conditional surplus from playing R. Comparing these three experimental conditions, we observe very little variation in player Bs'actions: although reliable decisions are observed slightly more often when incentives become more salient -for instance, in 63% of round 1 decisions in ET1 compared with 80% in ET3 and 77% in ET4 -we cannot identify any statistically significant difference. 18 Setting ET1 as a benchmark, conditions ET3 and ET4 also allow us to investigate two important issues concerning player As' decision-making. First, do player As react to partners' enhanced incentives to act reliably in ET3 -notwithstanding player Bs' actual neutrality? Second, do player 17 The Kolmogorov-Smirnov test using all session averages does not detect differences between the two countries either in the population of player As (p =0 .980)o ri nt h ep o p u l a t i o no fplayer Bs (p=0.317). We can only test the nullity of the difference for each treatment separately in the first round, when individual decisions are not correlated. The p-values are p=0.569 in ET2, and p=1 in ET3 and ET4 for player As,a n dp=0.697, p=0.695, p=0.372 for player Bs. The results from parametric regressions (see Section 5) confirm this conclusion. 18 The p-values from mean differences between treatments ET1 and ET3/ET4 are p=0.175/p=0.399 in round 1, p=0.491/p =0.461 in rounds 2-10, and p=0.446/p=0.418 in rounds 1-10. The null hypothesis that behavior is the same in all three treatments cannot be rejected in round 1 (p=0.290), in rounds 2-10 (p=0.753), or in rounds 1-10 (p=0.710).

As react to the enhancement of their own incentives to rely on their partners in ET4? Based on our data, the answer to the first question is clearly negative: the improvement of the saliency of player Bs' decisions between ET1 and ET3 only results in a marginal and statistically insignificant drop in the frequency of player As' secure choices. 19 The answer to the second question, on the contrary, appears to be positive. Although ET4 brings no significant improvement in term of player As' reliance in the initial round, the increase in the rate of reliability becomes highly significant in subsequent rounds. 20 Note that player Bs' behavior is similar in all three treatments (in particular in ET3 and ET4). The observed change in player As' behavior is thus mainly driven by the enhanced saliency of their personal payoffs ; rather than updated beliefs about the reliability of the partner. ET2 is designed to detect another potential motivation underlying reliance: as compared with ET4, payoffs generated by a secure choice are equalized, so that we should observe a fall in reliance if player As use decision R to move away from outcomes with highly unequal payoffs. We clearly reject this hypothesis both in the first round (p=0.487) and in subsequent repetitions (p=0.539). On the other hand, we find a strong effect on player Bs' behavior after the first round (where the rate of decisions r equals 84%). In this version of Egalitarian Treatment, subjects in the role of player B attain the highest proportion of decisions r, with almost 95% of actions r in rounds 2-10. 21 We complete our design by considering a variation of ET2, in which the payoffs associated with the Pareto-dominant outcome are unequal between players. The comparison between BT2 and ET2 thus complements BT1-ET1 in a context in which payoff differences are salient and the payoff differences are equalized between players in both Nash equilibria of the game. Once again, we find no important inter-treatment differences in either player As'orplayer Bs' actions. 22 Altogether, BT2 and ET2 provide the unique experimental environment where player Bs' reliable behavior is almost universal. Importantly, these games hold the payoff inequality constant across the Nash equilibria. This feature neutralizes the procedural advantage that player A holds over player B in the remaining games: ending the game with the safe action L rather than setting out to achieve (R, r) no longer generates disproportionately higher losses to player B than to player A. According to this interpretation, player Bs' inefficient behavior in our experiment is related to 19 p=0.469 in round 1, p=0.249 in rounds 2-10, p =0.193 in rounds 1-10. 20 In round 1: p=0.469 against ET1, p=0.809 against ET3; in rounds 2-10: p=0.013 against ET1, p=0.004 against ET3; for rounds 1-10: p=0.008 against ET1, p=0.007 against ET4. Although we cannot reject the null hypothesis that subjects' behavior in round 1 is the same in all three treatments (p=0.462), we can do so for rounds 2-10 (p=0.006) and rounds 1-10 (p=0.007).

21 Comparing ET2 against ET3: p=0.782 in round 1, p=0.081 in rounds 2-10, and p=0.104 in rounds 1-10.

Comparing ET2 against ET4: p=0.555 in round 1, p=0.006 in rounds 2-10, and p=0.001 in rounds 1-10. Although we cannot reject the null hypothesis that subjects' behavior in round 1 is the same in all three treatments (p=0.701), we can do so for rounds 2-10 (p=0.012) and rounds 1-10 (p=0.003).

22 For player As,w efi n dp=0.819 in round 1 and p=0.745 in rounds 2-10;, p=0.741 in rounds 1-10. For player Bs, p=0.306 in round 1 and p=0.858 in rounds 2-10; p=0.902 in rounds 1-10. procedural fairness and arises as a costly punishment of those who enjoy an undeserved strategic advantage. We further discuss this explanation in the concluding section.

To get further insight into individual behavior, we reorganize the data at the individual level by dividing player Bs (player As) in each treatment into categories according to the number of times they choose the weakly-dominated decision l (the secure and unreliant action L) over the 10 repetitions of the game. Figures 2a and2b provide the respective empirical densities of participants' types.

The general conclusion we can draw from this distribution is that aggregate decisions are not simply a matter of a few individual outliers. On the side of player Bs' behavior, the treatments can be split into two sub-groups. In BT2 and ET2, on the one hand, 75%-77% of subjects never use the weakly-dominated strategy l, and the individual frequencies of actions l amongst the remaining subjects never exceed 50%. In BT1, ET1, ET3 and ET4, on the other hand, the proportion of perfectly reliable player Bs varies between 37% and 57%, and the number of actions l among remaining subjects is much more dispersed, often exceeding 5/10. As for player As, we can also observe two distinct groups of treatments. The first sub-group, which comprises treatments BT2, ET2, and ET4, is characterized by a large proportion of subjects (between 37% and 57%) who always rely on their partners, and a relatively small proportion of those who never do so (between 7% and 13%). In BT1, ET1 and ET3, by contrast, most observations are dispersed far from the absolute reliance category, and this is coupled with a high share of absolutely unreliant subjects.

Robustness analysis

To assess the robustness of the conclusions drawn from the above two-by-two mean comparisons, we now turn to a parametric analysis on individual data pooled over all treatments. The two outcomes of interest are the two decisions leading to the Pareto-dominant outcome: R from player A and r from player B . Due to the nature of these two variables, we run probit regression models. In order to better identify the channels influencing behavior in each treatment, we include treatment variables measuring the specificity of the payoff structure. The indicator Egalitarian Treatment is set to 1 when payoffs generated by the dominant outcome are equalized between players (i.e., in all ET treatments; it is 0 for BT treatments). Two dummy variables are used to measure the improved saliency of each decision separately for player A -set to 1 when the gap in player As' payoff between (R, r) and (L) amounts to 1.50 euros (treatments BT2, ET2, and ET4) 0 if it equals only 0.25 euros (BT1, ET1, and ET3) -and for player B -set to 1 in treatments BT2, ET2, ET3 and ET4. The variable Player B disadvantaged is set to 1 for treatments BT1, ET1, ET3, and ET4 (to 0 otherwise). Last, we capture potential cultural differences by including an indicator of whether the session took place in Poland (Poland variable equal to 1) or France. Parametric models allow us to take into account both individual heterogeneity as well as learning over time in a more disaggregated way. Individual heterogeneity is measured by one's past willingness to choose the decision leading to the Pareto-dominant outcome. The individual taste for cooperation is revealed by the occurrence of action R at least once in the previous rounds for player As (1[Relied before]), and the occurrence of action r in the past for player Bs (1[Reliable before]). The two specifications in Table 6 consider two possible channels of time dependency. In the left-hand side specification, we assess the overall effect of the flow of information generated by the repetition of the game. To that end, we relate individual behavior to group-level behavior, measured as the frequency of reliant/reliable decisions taken in a given session in all rounds up to the current one -variables Population A t-1 and Population B t-1 . This information is never entirely known to individuals, but can be inferred in some instances from the personal earnings in a round of the game The right-hand side specification of Table 6 turns to individual measures of learning through personal experience with the past interaction partners. For player As,thev ariable Ratio of (R, r) among R represents the degree of player Bs' cooperative reciprocity observed by player A in the past (i.e. up to the current round), measured as the share of outcomes (R, r) among all the attempts to cooperate by playing R.A n a l o g o u s l y ,t h ev a r i a b l eRatio of (R, r) among r measures partners' cooperative reciprocity experienced by player Bs in their past interactions. All regressions also take simple time effects into account through round-specific dummies.

The results from separate estimations for each outcome variable are provided in Table 6. The estimates on treatment variables confirm that our conclusions are robust to this conditioning. We can observe no significant effect of whether the decisions are elicited in France or in Poland on either group of players. For player As, the only influential dimension of the payoff structure is the saliency of the opportunity cost of the secure choice (which is improved in treatments BT2 and ET2-ET4). For player Bs, saliency does not have any significant effect. The only significant change in behavior is obtained once the strategic disadvantage induced by low payoffs in the dominated outcome is eliminated, as in treatments BT2 and ET2. More importantly for our main purpose, equalizing payoffs in the Pareto-dominant outcome does not change either player Bs'o rplayer As' behavior.

The main additional insights from the regressions come from the individual taste and learning variables. In both specifications, subjects in both roles are conservative in their decision-making: both past reliance and reliability increase the odds of similar behavior in the future. As regards the time-dependent variables, we fail to observe any effect of past behavior in the general population of either player As or player Bs on their partners' actions: in the right hand side of Table 6, none of the Population variables appear to influence individual decisions. Subjects do not seem to update their decision-making according to the actual behavior in the population of their partners. As shown in the right-hand side of the Table, though, players' behavior dependents on their own experience in the past occurrences of the game: successful attempts to cooperate with partners in the past tend to foster cooperativeness in the future. This results show that one important reason for player As' mistrust is their disappointment from having relied on their past partners in vain.

Conclusion

Accumulated evidence on the experimental game introduced by Beard and Beil (1994) provides robust evidence on two puzzling behaviors. Experimental subjects (i) often fail to maximize their own payoff, and at the same time (ii) are reluctant to rely on the proven reliability of others. One common property of most experimental implementations of this game is the strong payoff inequality between players. This paper provides an experimental test of the hypothesis that both puzzles can be related to inequality aversion (as raised, e.g., by Goeree and Holt, 2001). Our design relies on two different pairs of payoff structures (one with equalized payoffs, one without), along with companion treatments strengthening the saliency of decisions and robustness sessions run in a different country.

To sum up, the empirical answers to our main research questions are clearly negative: our data unambiguously reject the inequality aversion hypothesis, previously proposed as a potential driving force behind the two puzzling behaviors we study -inequality aversion does not cause either the actual failure to maximize own payoffs or the fear that others might fail to do so. Through the replication of some of our treatments in an East European country, we also confirm that cultural differences -due, for example, to the focus on WEIRD (Western, Educated, Industrialized, Rich, and Democratic) people, as defined by Henrich, Heine, and Norenzayan (2010) -do not drive the observed behavior. This result is in line with the robustness experiments performed by Beard, Beil, and Mataga (2001) on Japanese subjects. Again in accordance with previous evidence (as summarized in Section 2), we also find that the saliency of reliance is an important driving force of the willingness to rely on partners. Last, all these results are robust to repetition-based learning through several periods of play of the one-shot game.

The only instance in which we observe a strong effect of the treatment on behavior is when we impose that the difference in payoffs between players is the same in both Nash equilibria. This also affects the default earning of player Bs when player As decide alone on the final outcome (by selecting the secure choice) -which can be seen as a natural reference point for player Bs.O bserved behavior in these last two treatments thus echoes the literature on money-burning behavior, showing that people sacrifice their own wealth to reduce the wealth of others who have benefited from an exogenous procedural advantage (see, e.g., Zizzo and Oswald, 2001). 23 According to this interpretation, what we observe could thus be the result of player Bs' willingness to punish player As for procedural injustice. Whether the behavior of player Bs in this class of games can be explained by such preferences certainly deserves a more systematic investigation, which remains open for future research.

Still, we find that the rate of secure choices by player As does not vary as a function of player Bs' behavior, and remains high even in settings where player Bs commonly use the payoffmaximizing strategy. This means that the fear that player Bs' behavior is driven by social preferences (taking the form of either the inequality aversion or the propensity to burn other's money) is definitely not the reason why suboptimal outcomes are observed in this class of games. Our data thus restrict the set of possible explanations to only a few candidates, which either point to other sources of strategic uncertainty, or challenge the assumption that players behave strategically in this class of games. More precisely, the first explanation is that the behavior of player As is induced by strategic uncertainty, but the source of strategic uncertainty (i.e. the reason why player As' beliefs are misaligned with player Bs' actual behavior) still has to be elicited. One clue on that point from our results is that this source of strategic uncertainty survives repetition-based learning over ten rounds of play. The second avenue is that player As react non-strategically to the decision problem, so that their choices are unaffected by player Bs' behavior. Such non-strategic play may occur due to, among others, the failure of game form recognition (Chou, McConnell, Nagel, and Plott, 2009); misconceptions (Plott and Zeiler, 2005); subjects' confusion about the strategic context (Ferraro and Vossler, 2010); or, last, by a lack of commitment from subjects towards the experiment they are involved in and their unwillingness to take the decision problem seriously enough (see, e.g., Jacquemet, Joule, Luchini, and Shogren, 2009, 2013). The two groups of explanations lead to very different conclusions: the first one raises a caveat of game theory's ability to describe behavior, while the other challenges the internal validity of experiments applied to this class of games. Exploring these questions is next on our agenda.

independent between clusters, Cov(✏ ig ,✏ jh )=08g 6 = h, but allow for any type of dependence within a cluster, Cov(✏ ig ,✏ jg )=σ 2 ijg 8i, j, g. To that end, we correct the estimated covariance matrix at the cluster level using the following procedure, in which the model is written at the cluster level, Y s = X s β + ✏ s , where Y s and ✏ s are [N s ⇥ 1] vectors, X s is a [N s ⇥ (K+1)] matrix, β is a [(K+1) ⇥ 1] vector:

1. Using the parameters estimated on pooled data, βOLS =( X 0 X) -1 (X 0 Y ), we calculate the vector of error terms in each cluster: ✏s = Y s -X s βOLS 2. We then estimate the cluster robust covariance matrix (CRCME):

VCRCME = X 0 X -1 S X s=1 X 0 s ✏s ✏0 s X s ! X 0 X -1 (2)
A.1.2 Correction for small sample bias in standard errors

The procedure described above provides a consistent estimator of the covariance matrix which can typically be biased in small samples. What is more, the bias is generally found to be negative, so that significance tests reject the null hypothesis too often. A first way to deal with this issue is to correct for the degrees of freedom by substituting ✏s = p C df ✏s , with C df = S(N -1) (S-1)(N -K) ,i n( 2 )a procedure known in the literature as HC1. Bell and McCaffrey (2002); Cameron, Gelbach, and Miller (2008) propose a more accurate correction, called HC3, which estimates the residuals as ✏s = q S-1 S [I Ns -H ss ] -1 ✏s , where I Ns is a [N s ⇥ N s ] identity matrix, and H ss = X s (X 0 X) -1 X 0 s . For an OLS regression, this corrected variance-covariance matrix amounts to implement a deleteone jackknife procedure:

Ṽjackknife = S -1 S S X s=1 ⇣ β-s - β⌘⇣ β-s - β⌘ 0 (3)
where β-s is the vector of coefficients estimated after leaving out the sth cluster. 25

25 Reported p-values are associated to statistics computed according to this HC3 procedure. We also ran robustness checks by implementing the HC1 correction, which generally leads to lower estimated standard errors. Our choice is thus conservative as regards our ability to find significant differences in behavior. Based on a correction closely related to the HC3 procedure, Angrist and Lavy (2009) find an inflation of the cluster-robust standard errors by 10% up to 50%.

Figure 1 :

 1 Figure 1: The Rosenthal (1981) game

Figure 2 :

 2 Figure 2: Empirical distribution of players according to their actions

Table 1 :

 1 Summary of experimental evidence on Rosenthal's game

	Experiment	Form		Payoff			Outcomes (%)		Nb.
			(L)( R, r)( R, l)	LR , rR , l	r	obs.
	Beard, Beil-Tr.1	Seq	(9.75; 3)	(10; 5)	(3; 4.75)	66	29	6	83	35
	Beard, Beil-Tr.3	Seq	(7.00; 3)	(10; 5)	(3; 4.75)	20	80	0	100	25
	Beard, Beil-Tr.4	Seq	(9.75; 3)	(10; 5)	(3; 3.00)	47	53	0	100	32
	Beard et al.-Tr.1	Seq	(1450; 450) (1500; 750) (450; 700) 79	18	3	83	34
	Beard et al.-Tr.2	Seq	(1050; 450) (1500; 750) (450; 700) 50	32	18	64	28
	Goeree, Holt-Tr.1	Ext	(80; 50)	(90; 70)	(20; 10)	16	84	0	100	25
	Goeree, Holt-Tr.2	Ext	(80; 50)	(90; 70)	(20; 68)	52	36	12	75	25
	Goeree, Holt-Tr.3	Ext	(400; 250)	(450; 350)	(100; 348) 80	16	4	80	25
	Cooper, Van Huyck-Tr.9	Str	(4.00; 1)	(6; 5)	(2; 4.00)	27	-	-	86	187
	Cooper, Van Huyck-Tr.9	Ext	(4.00; 1)	(6; 5)	(2; 4.00)	21	-	-	84	187
	JZ-Baseline 1, round 1	Str	(9.75; 3)	(10; 5)	(3; 4.75)	77	23	0	80	30
	JZ-Baseline 1, rounds 2-10	Str	(9.75; 3)	(10; 5)	(3; 4.75)	48	43	9	81	270
	JZ-Communication (2-10)	Str	(9.75; 3)	(10; 5)	(3; 4.75)	41	53	7	80	300
	JZ-Observation (2-10)	Str	(9.75; 3)	(10; 5)	(3; 4.75)	47	47	6	82	300

Note. Several representations of the game have been applied so far, as stated in column 1: simultaneous-move strategic-form game (Str), simultaneous-move extensive-form game (Ext), sequential-move game (Seq). Player Bs'a c t i o n sr in the first three studies are only reported conditional on player As'a c t i o nR. The monetary payoffs displayed in columns 2-4 are in USD in

Beard & Beil (1994)

and Cooper & Van Huyck (2003), in US cents in Goeree & Holt (2001), in yens in Beard et al. (2001) and in euros in Jacquemet & Zylbersztejn (2013, JZ) treatments.

Table 2 :

 2 Generic game

		player B
	player A	lr
	L	(a;b)	(a;b)
	R	(a-c;b-e) (a+d;b+f)

Table 3 :

 3 Overview of experimental treatmentsNote. For each treatment, the first three columns provide the payoffs of each player, in euros. The next two columns give the number of 20 subjects-sessions run in each location. The last two columns summarize the average behavior observed in each treatment over all subjects and repetitions.

			player A	player A chooses R	Nb. of	Likelihood
	Treatments	chooses	player B	player B	Sessions	of decisions
			L	chooses l	chooses r	Paris Warsaw	Rr
	Baseline 1	(BT1)	(9.75 ; 3.00) (3.00 ; 4.75) (10.0 ; 5.0)	3-	0.490 0.807
	Egalitarian 1 (ET1)	(9.75 ; 5.00) (5.00 ; 9.75) (10.0 ; 10.0)	3-	0.457 0.727
	Egalitarian 3 (ET3)	(9.75 ; 5.50) (5.50 ; 8.50) (10.0 ; 10.0)	22	0.575 0.828
	Egalitarian 4 (ET4)	(8.50 ; 5.50) (5.50 ; 8.50) (10.0 ; 10.0)	21	0.730 0.823
	Egalitarian 2 (ET2)	(8.50 ; 8.50) (6.50 ; 8.50) (10.0 ; 10.0)	32	0.776 0.936
	Baseline 2	(BT2)	(8.50 ; 7.00) (6.50 ; 7.00) (10.0 ; 8.5)	3-	0.743 0.940

  Willinger, Keser, Lohmann, and Usunier, 2003). This robustness treatment complements the contribution ofBeard, Beil, and Mataga (2001), who use the data from USA and Japan to show that inefficient behavior in Rosenthal's game persists across cultures. It should be stressed, however, that this treatment does not aim to provide a thorough cross-cultural comparison, but rather to rule out the possibility that our main treatment effects of interest are specific to the location of our experiments.11 Although Rosenthal made his conjecture for a one-shot game, Beard and Beil note in their paper (pp. 261-262) that it seems equally valid for repeated play. The authors furthermore state that learning through experience may affect people's behavior independently of payoff-related factors.

Table 4 :

 4 Observed behavior in Treatments 1

			Nb.	Decisions	Coordination Miscoordination
		Game	Obs.	Rr	(R, r)( L, l) (L, r)( R, l)
	Beard and Beil (1994, Tr.1)	35	0.343 0.833 0.286	-	-0 . 0 5 7
	Baseline Treatment 1	Round 1 Rounds 2-10 Overall	30 270 300	0.233 0.800 0.233 0.200 0.567 0.519 0.807 0.433 0.107 0.374 0.490 0.807 0.413 0.117 0.393	0.000 0.085 0.077
	Beard and Beil (1994, Tr. 6)	26	0.692 1.000 0.692	-	-0 . 0 0 0
	Egalitarian Treatment 1	Round 1 Rounds 2-10 Overall	30 270 300	0.467 0.633 0.300 0.200 0.333 0.456 0.737 0.333 0.141 0.404 0.457 0.727 0.330 0.147 0.400	0.167 0.122 0.127

Note. For each treatment (in rows), the first column gives the total number of observations -the number of subjects is equal to N in Beard and Beil's experiment, and N/10 in ours. The two subsequent columns present the individual decisions observed in each treatment (the rate of reliability is conditional on reliance from player A in Beard and Beil's data and unconditional in ours). The last four columns present the empirical frequencies of the four possible outcomes (two of which -(L, l) and (L, r) -are not observable in Beard and Beil's data).

Table 5 :

 5 Observed decisions

				Round 1	Rounds 2-10	Overall
			N	Rr	Rr	Rr
	Baseline Treatment 1	300	0.233 0.800	0.519 0.807	0.490 0.807
	Egalitarian Treatment 1	300	0.467 0.633	0.456 0.737	0.457 0.727
	Egalitarian Treatment 3	France Poland Overall	200 200 400	0.600 0.550 0.575 0.800 0.750 0.850	0.611 0.539 0.575 0.831 0.761 0.900	0.610 0.540 0.575 0.828 0.760 0.895
	Egalitarian Treatment 4	France Poland Overall	200 100	0.650 0.600 0.633 0.767 0.700 0.900	0.756 0.711 0.741 0.830 0.833 0.822	0.745 0.700 0.730 0.823 0.820 0.830
	Egalitarian Treatment 2	France Poland Overall	300 200 500	0.500 0.600 0.540 0.840 0.867 0.800	0.766 0.856 0.802 0.947 0.952 0.939	0.740 0.830 0.776 0.936 0.943 0.925
	Baseline Treatment 2	300	0.500 0.933	0.770 0.941	0.743 0.940

Table 6 :

 6 Parametric regressions on the determinants of cooperative behavior Relied before] and 1[Reliable before] are dummy variables, =1 if player A (B) played R (r) at least once prior to the current period. The variables Ratio of (R, r) among R (Ratio of (R, r) among r) measure the share of outcomes (R, r) among all the attempts to cooperate by playing R (r). The variable Population A t-1 (B t-1 ) measures the average rate of reliance (reliability) in all rounds of a given session up to the current one. The number of observations is N =1 8 9 0in both models.

		(1)		(2)
		Pr(R)	Pr(r)	Pr(R)	Pr(r)
	Egalitarian Treatment	-0.012	-0.004	0.041	-0.002
		(0.051)	(0.061)	(0.027)	(0.047)
	Improved saliency for player A	0.092*	-0.013	0.134***	-0.014
		(0.048)	(0.068)	(0.046)	(0.063)
	for player B	0.025	0.028	-0.022	-0.011
		(0.053)	(0.066)	(0.036)	(0.065)
	Poland	0.063	0.035	0.042	0.051
		(0.050)	(0.051)	(0.038)	(0.051)
	Player B Disadvantaged	-0.003	-0.126**	0.014	-0.119**
		(0.058)	(0.064)	(0.050)	(0.056)
	Learning: player A
	1[Relied before]	0.502***	-	0.147***	-
		(0.024)	-	(0.038)	-
	Population B t-1	0.247	-	--
		(0.205)	-	--
	Ratio of (R, r) among R	--0.391***	-
		--	(0.044)	-
	Learning: player B
	1[Reliable before]	-0 . 3 0 2 * * *	-0 . 1 9 6 * * *
		-( 0 . 0 4 0 )	-( 0 . 0 4 4 )
	Population A t-1	-0 . 0 3 1	--
		-( 0 . 2 1 8 )	--
	Ratio of (R, r) among r	---0 . 2 0 8 * * *
		---( 0 . 0 5 9 )
	Round Dummies:
	t =3	-0.038	-0.026	-0.036	-0.028
		(0.037)	(0.021)	(0.037)	(0.019)
	t =4	-0.091**	-0.037	-0.091**	-0.047**
		(0.039)	(0.025)	(0.041)	(0.019)
	t =5	-0.103***	-0.060*	-0.101***	-0.074***
		(0.028)	(0.031)	(0.029)	(0.025)
	t =6	-0.111***	-0.064**	-0.108***	-0.083***
		(0.036)	(0.029)	(0.036)	(0.023)
	t =7	-0.122***	-0.041	-0.120***	-0.065*
		(0.026)	(0.047)	(0.026)	(0.036)
	t =8	-0.151***	-0.012	-0.149***	-0.037
		(0.028)	(0.041)	(0.025)	(0.028)
	t =9	-0.137***	-0.056	-0.134***	-0.086***
		(0.027)	(0.039)	(0.025)	(0.028)
	t =10	-0.154***	-0.037	-0.149***	-0.067**
		(0.030)	(0.037)	(0.028)	(0.027)
	Note. Significance levels: * 10% ; **5%; ***1%. Average marginal effects (standard errors in parantheses) from Probit
	regressions on individual decisions. The four models are estimated separately on observations from rounds 2-10 with session-
	level clustered data and delete-one jackknife standard errors. Treatment dummy variables are: Poland (=1 for sessions run
	in Warsaw), Player B disadvantaged (=1 for BT2 and ET2), Improved saliency for player A (=1 for BT2, ET2, and ET4),
	Improved saliency for player B (=1 for BT2, ET2, ET3, and ET4), Egalitarian Treatment (=1 for ET1, ET2, ET3, and
	ET4). 1[

The experimental literature on this game has been initiated by the seminal study by[START_REF] Beard | Do People Rely on the Self-Interested Maximization of Others? An Experimental Test[END_REF] and is reviewed in details below. An advantage of the simultaneous-move implementation used in this paper is that both players make decisions independently, so that their behavior is always observable to the experimenter.

Subgame perfectness refines the Nash equilibrium through the iterative elimination of weakly dominated strategy -which are non-credible threats in the sequential game. The failure to maximize payoff in the game we study precisely amounts to using weakly-dominated strategies. See Jacquemet and Zylbersztejn (2013) for a more detailed analysis of the theoretical properties of the game.

This hypothesis has been already raised in the literature -see for instance (Goeree and Holt, 2001, p.1416) -

The treatment effects we seek to identify are best illustrated in the framework of the[START_REF] Fehr | A Theory of Fairness, Competition, and Cooperation[END_REF]

The procedure is described in more detail in Appendix A.1.

In accordance with our results on the effect of saliency, Zizzo and Oswald (2001) also show that the price elasticity of the demand for such punishment is very low.

Heteroscedasticity is due to the linear probability specification. Even if the data generating process was i.i.d (i.e. V (uis)=σ 2 ,a n dE(uisujt)=08i 6 = j and 8t)t h em o d e li m p l i e st h a t : V (y|X)=Pr(y =1 |X)[1 -Pr(y = 1|X)] = Xβ(1 -Xβ).

A Appendix

A.1 Parametric test for equality of proportions

The experimental design raises the issue of two kinds of correlation in the data. First, since players make a sequence of decisions, each subject's choices might be serially correlated. Second, interaction partners change after each round of the experiment, which might result in an intersubject correlation. To account for this structure of the data, we perform statistical tests for the comparisons of means through parametric regressions that assume clustered standard errors at the session level. This specification is asymptotically robust to any misspecification of the OLS residuals Williams (2000); Wooldridge (2003). We moreover apply a delete-one jackknife correction to take into account a potential small sample bias.

A.1.1 Standard errors estimation

The data are split into clusters (at the session level) and we denote i each observation in each cluster s, with i={1,...,N s } and s={1,...,S} so that the total number of observations is N = P S s=1 N s . We perform statistical tests for differences between means through linear probability models of the form:

in which y is is a dummy dependent variable, X is = {1,x is1 ,...,x isK } is the set of explanatory variables including the intercept, {β 0 ,...,β K } is the set of unknown parameters, and ✏ is is the error term. We consider regressions on dummy variables reflecting changes in the environment (for instance, experimental treatments). Because the endogenous variable is itself binary, we also have that: E(y|X)=P (y =1 |X). In this specification, the parameters thus reflect the mean change in the probability of the outcome induced by the change in the environment. In the case of one explanatory variable,

so that the parameter measures the mean variation in the probability of y. The t-tests on each parameter thus provide significance levels on the differences.

To compute the standard errors, we allow for dependence inside clusters as well as unspecified heteroscedasticity across observations, 24 i.e. we assume that any two error terms i and j are