To investigate the rise of economic abilities during development we studied children aged between 3 and 10 in an exchange situation requiring them to calculate their investment based on different offers. One experimenter gave back a reward twice the amount given by the children, and a second always gave back the same quantity regardless of the amount received. To maximize pay-offs children had to invest a maximal amount with the first, and a minimal amount with the second. About one third of the 5-year-olds and most 7- and 10-year-olds were able to adjust their investment according to the partner, while all 3-year-olds failed. Such performances should be related to the rise of cognitive and social skills after 4 years.
Citation: Steelandt S, Dufour V, Broihanne M-H, Thierry B (2012) Children Base Their Investment on Calculated Pay-Off. PLoS ONE 7(3): e33239. https://doi.org/10.1371/journal.pone.0033239
Editor: Elsa Addessi, CNR, Italy
Received: December 2, 2011; Accepted: February 6, 2012; Published: March 8, 2012
Copyright: © 2012 Steelandt et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The research was supported by a grant from the Agence Nationale de la Recherche (ANR-08- BLAN-0042-01). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
How individuals make choices in the context of interactions with other people is a major topic within economics, and thinking from this discipline has strongly influenced research on decision-making. Trading with multiple partners following different exchange rules is commonplace in the dense social exchange networks developed within human societies. When facing partners offering different expected pay-offs, investors are expected to optimize their satisfaction by adjusting their decision to the most rational choice . Despite the increasing interest of economists in how adults and adolescents decide to invest according to the behavior of other persons , we still do not know how this ability appears and develops in an individual. No study to date has investigated the competence of children to calculate investment based on the offers made by partners.
Trust is known to represent a “social lubricant” in the economic world , and most models of economic interactions have demonstrated that decision-making is influenced by social preferences such as trust and reciprocity –. The experimental trust game, originally known as the investment game , has been used in numerous studies to model the economic behavior of people when trading. In this test, a player typically decides what proportion of an initial monetary endowment will be given to an anonymous player. This amount is then tripled and the recipient decides how much of the tripled amount will be kept and how much will be returned to the first player. Experimental results provide evidence that decision-making is affected by cultural origins –, and individual factors such as gender or age –. For instance, men from western societies invest the most , , and therefore appear to be the most trusting ,  and the most confident in their investment decisions , . Adult subjects were also more confident than teenagers . Several studies have shown that reciprocity, trust and fairness affect the decisions of children –, but the influence of age on investment decisions in an exchange situation remains little documented (see ).
In every transaction, partners not only decide how to trade with one another, but also choose with whom they trade. People may consider alternative, better partners if the current partners do not meet the expected cooperative conditions. In the context of public good provision games, for instance, adults usually adjust their investment following observation of contributions made by partners , . In the investment game, interacting several times with the same partner can create a context in which individuals develop trust in previously unknown persons. To explain how trust relationships can evolve over time, researchers have commonly used repeated games in which participants interact several times with the same partner . In studies where subjects can choose their partner, results show that people prefer partners who have already provided them with some form of benefit, and the choice made is based on the past result of their interaction , , . In contrast, imposing exchange partners on individuals may decrease the level of trust or result in more time being required before participants trust each other . As trusting behavior evolves with age, older children may accept to trade with unknown partners more easily than younger ones would, or they only may decide to take part in the transaction once they have estimated whether the partners were trustworthy.
When confronted by informants who differ by their level of reliability, children consistently prefer the one having given the more accurate information in the past –. Interestingly, an increasing number of works examine economic skills and the influence of partner's reliability in non-human primates –. One study in monkeys showed that a single individual out of twenty-one was able to adapt his investment according to the profitability of two different human partners . It appears that taking the quality of partners into account when trading requires complex cognitive skills. In humans, and especially in children, it is likely that this competence develops in relation with the development of the cognitive abilities needed in any transaction: giving to an unfamiliar person, judging the partner's reliability by reasoning about their mental state, and estimating the value of goods , .
Studies have shown that children can spontaneously give objects before the age of one –. By 14–18 months of age, they readily interact with unfamiliar people  and take part in exchanges with unknown experimenters , . Progressive development is also seen in attribution of mental states. At the beginning of the second year of life, children can share goals and read other people' intentions, i.e., the plan of action needed to reach goals , –. From 4–5 years of age, children start to understand the beliefs and thoughts of others, which may help them to recognize untrustworthy and dishonest partners –. Regarding numerical skills, children under the age of two can make value judgments by recognizing small discrete quantities –, and larger numerosities, albeit in an imprecise way –. At around the age of 2, they are able to count to about six and detect a violation of counting –, but children cannot master the same counting principles as adults before six years of age, i.e. the sequence of number words, the one-one correspondence between objects and words, and the cardinal principle , . By the age of 5 or 6, they solve verbal calculation problems requiring arithmetic skills –, although younger children can already predict the outcomes of simple additions and subtractions –.
We aimed to identify the developmental stage at which children adjust their investment in the context of an economic transaction. We tested children between the ages of 3 and 10 in an exchange task requiring them to calculate the amount of food items they gave initially, in order to maximize the food amount to be returned by two different experimenters. The experimental procedure was similar to that used with monkeys . One experimenter gave back a reward twice the amount of the child's initial investment, whereas the other always returned the same amount, whatever the child's initial investment. To maximize pay-offs, children had to respond in different ways to each experimenter, offering a maximal amount to the first one, and a minimal amount to the second.
The mean number of returned items varied according to individuals (F24,575 = 5.5, p<0.001; Figure 1), age and partner (3 years: mean number of sweets ± sd = 2.35±0.09, 5 years: m = 3.06±0.07, 7 years: m = 2.58±0.08, 10 years: m = 2.75±0.1, F1,575 = 9.4, p<0.001; doubling partner: m = 3.29±0.08; fixed partner = 2.08±0.09, F1,575 = 58.2, p<0.001). Given the interaction between the individuals and partners (F24,575 = 2.7, p<0.001), we compared the performances of each child according to the quality of partners.
No 3-year-old children successfully adapted their strategy according to the quality of partners. At the age of 5, three subjects adapted their strategy according to the quality of partners. Seven subjects successfully adapted their strategy according to the quality of partners at the age of 7 and 10 respectively (Wilcoxon tests, n = 10). Each plot represents the mean number of sweets returned in one session of ten trials, along with standard errors.
Comparing the performances of 3-year-old children according to the quality of partners did not yield significant differences (Figure 1). Children seldom returned all initial items, often keeping at least one sweet (90.3% of returns).
Among 5-year-old children, five failed to adapt the amount of sweets given according to the quality of their partner (Figure 1). By contrast, three children showed significantly different behavior with each experimenter. One of them adapted his strategy from the first set of sessions; he quickly learned to give back a minimal number of sweets (one) to the fixed partner, and a maximal number (four) to the doubling partner. The other two children modified the amount of returned sweets in the course of experiments, learning to give one sweet to the first partner and four to the other from the 8th set of sessions onwards (Figure 1).
Among 7-year-old children, one boy did not display significant differences in his behavior according to partner's quality; he returned some sweets to both of them (Figure 1). All the other children were able to adjust their behavior according to the quality of partners, most of them learning in the first half of the study to give back a minimal amount to the fixed partner, and a maximal amount to the doubling one (Figure 1).
Among 10-year-old children, one failed to discriminate between experimenters; he repeatedly gave back around four sweets to both partners. All the others adapted their return from the first sets of sessions by giving back a minimal amount of sweets to the fixed partner, and a maximal amount to the doubling one (Figure 1).
By experimental design, a child's net income should differ according to the quality of partners. Only one boy of 5 years old did not experience a significant difference of total income between experimenters. For all the other children, income was higher with the fixed than with the doubling partner (Table 1). The difference between the numbers of sweets gained from each partner varied from 14 to 598 sweets (Table 1). It is worth noting that by the age of 5, children regularly counted the net income received during the exchange.
Because some children were from the same school, we could not control potential communication between them about experiments, especially in older children. When looking at the proportion of successful children tested at school versus those tested at home who did not know each other, we found similar proportions in decision patterns, both in 7-year-old children (83% of success at school vs. 100% of success at home), and 10-year-old children (80% vs. 100%).
No 3-year-olds were able to adjust their behavior according to the quality of partners. About one third of the 5-year-old children, and almost all children aged 7 and 10 succeeded in optimizing pay-offs by following different decision rules according to experimenters. The fact that the performances of the children tested at school were not better than those of subjects tested separately at home casts doubt on any possibility of information transmission between children belonging to the same school. It should be added that successful children did not adjust their investment according to the quality of partners from the first trial of a session; they learned to maximize their pay-off after several trials of the first or following sessions. Our results confirm that the ability to calculate investment based on partners' offers develops between 4 and 7 years of age.
It is unlikely that failures observed in 3-year-old children were due to their inability to differentiate between the food amounts returned by experimenters, since children are able to differentiate between discrete quantities from their first year of life –, , . In the present study, children sometimes returned a different number of sweets to experimenters, thus getting an opportunity to learn that partners did not respond in the same way. Despite having experienced a difference in net income of about three sweets between partners, younger children did not adjust their return according to experimenters' qualities.
In terms of calculation skills, children aged 3 to 4 are able to resolve basic subtractions that involve small number sets –, –. Similar abilities are observed in monkeys . Here, children aged 3 are comparable to most macaques and capuchin monkeys tested in the same task  as they could remove part of the items before investing, but failed to adapt their return to partners. A single monkey out of twenty one was able to adapt his strategy to both partners, which sets the performances of monkeys somewhere between those of 3- and 5-year-old children. This also suggests that calculation abilities may not be a limiting factor for succeeding in such tasks.
In our experiments, children did not merely have to choose between two options, but also had to draw different decision rules from the contrasting conduct of two partners, which was more demanding. The ability to follow multiple directions or to switch decision rules develops slowly during childhood , . When asked to sort objects according to color, 3-year-old children are still unable to inhibit this first representation when required to follow an alternative one based on the shape of objects –. Our study shows that adequate use of opposite decision rules is possible from the age of 5, and is fully mastered from the age of 7. Interestingly, 10-year-old children needed fewer testing sessions (i.e. less than three sessions) than younger ones (i.e. between one and five sessions) before succeeding. It cannot be excluded that it was enough for subjects to separately adjust to each of the partners they were faced with, without comparing their returns. However, younger children failed in the present task despite the fact that, at this age, they should be able to understand the intentions of each experimenter (see , ) as a partner requiring a certain amount of food to give rewards.
The development of a theory of mind and arithmetic skills may partly explain increasing performances in children. The success of several 5-year-old children is consistent with the fact that 4- and 5-year-old children understand that others may have thoughts and beliefs different from their own –, , and this ability can be used to detect the reliability of a partner. With regard to arithmetic, it is known that the first years of schooling markedly affect the cognitive skills of children regarding language, literacy and numeracy . Although it appears sufficient to recognize magnitude – even in an imprecise way – for children to adjust their return to partners, the task may ask for a more demanding ability when it comes to understanding the relation function between investing and the return of each partner (when children have to discriminate between ratio differences). School-related changes in counting and arithmetic abilities may lead children to be more efficient when calculating investment. We did not observe children using counting to remove items before exchanging, but most subjects over the age of 5 spontaneously counted the total number of received sweets at each trial. While Jordan, Huttenlocher and Levine (1994)  found that counting objects may not be necessary to solve non-verbal tasks, it could help children to differentiate the net incomes received according to the quality of partner and could improve decision-making. A marked increase of performance in arithmetic problem solving is reported from the age of 5 or 6 onwards , , . Given this long age-related development, it may not be surprising that children only solved the task from the age of 5 onwards. Thus, counting and understanding that people can think differently may improve performance on this task.
Social factors could also have affected the performances of children, and may explain better results found in 5-year-olds. In particular, trusting behavior is commonly believed to guide the choices of economic agents in investment situations , . Repeated experiences can establish a trust relationship between exchange partners  and this leads children to invest their attention towards how to gain more from the task rather than concentrating on the unknown partner. With increasing age, children could also prioritize the potential to gain more, even if they did not trust experimenters. On the other hand, it is possible that the capacity of younger children to focus on the task was impaired by failure to overcome their wariness of partners who were unknown and potentially untrustworthy. A recent study revealed that 3-year-olds evaluate trustworthiness of partners based on the inaccuracy of information, whereas 4-year-olds rely both on accuracy and inaccuracy . As partners were always trustworthy in our study, systematically giving children an accurate reward, it is quite possible that younger children may have experienced difficulty distinguishing between them. The number of sweets that they kept could also reflect their hesitation to put their trust in experimenters. Contrary to older children, 3-year-olds kept at least one sweet in almost all the trials, thus showing a preference to avoid losing their initial savings rather than acquire gains. Such loss aversion relates to the endowment effect, a cognitive bias commonly found in economics; it leads people to attribute a higher value to objects they own than to objects that they do not possess. A number of experimental studies have demonstrated that adult investors may behave in a way that may not be rational , –. Our results showed that children as young as 3 years old also violate the predictions of optimal decision-making models.
Although older children understood how to maximize their benefits, they did not appear perfectly rational since they did not follow an optimal rule on every trial. They often supported their decision verbally by asserting that they preferred to win less for a specific trial, or to set their sights on the contents of a cup that did not contain the maximal amount of sweets. It should be emphasized that children were rewarded regardless of the number of sweets invested; no exchange also rewarded them with the four sweets that they kept. The lack of negative reinforcement for giving one quantity or another can explain that successful children were not always optimizing investors. Such choices probably reveal the importance of play or exploration in their performances.
The present results show that children between the ages of 4 and 10 are in the process of learning how to behave in economic situations. Both cognitive and social factors are likely to be involved in their ability to calculate their investment according to the offers made by partners, and biases appear to influence their decision-making. More research will be necessary to confirm the present results in a larger sample of subjects, and further investigate the relationships between cognitive development and improving economic skills. In particular, it would be worthwhile to study children in an experimental situation that does not involve a social component, for instance, by testing them using two automated dispensers instead of experimenters.
The project was approved by both the Education Department of the Bas-Rhin (reference DIVEL1/09-670/IJ) and the district inspector for education. Parents were given a letter describing the general purpose of the study and written parental consent was required for children to participate in the tests. Participation was on an unpaid, voluntary basis, but children kept the sweets that they won during the sessions.
We studied 32 children (16 males and 16 females) aged 3 to 10. This sample was divided into four age groups of eight children: 3-year-old (mean age ± SEM = 41.4±4.0 months), 5-year-old (m = 66.5±0.9), 7-year-old (m = 88.0±3.6), and 10-year-old (m = 125.6±3.4). The sex ratio was balanced for representativeness; we tested equal numbers of girls and boys in each of the four age groups, i.e. four girls and four boys. An additional child was excluded from tests because he did not pay any attention to the experiments.
Participants were European, from middle-class backgrounds, with French as their first language. A majority of children belonged to the Robertsau preschool and elementary school in Strasbourg, France. We tested seven children separately (two 3-year-olds, two 7-year-olds and three 10-year-olds) at their home, i.e., outside the frame of the school.
We studied children in two conditions involving different experimenters. In the first case, the experimenter was a doubling partner, meaning that she always returned twice the number of rewards given by the subjects; potential rewards were presented in four cups containing either two, four, six or eight rewards. In the second condition, the experimenter was a fixed partner, meaning that she always returned eight rewards, regardless of the number of rewards given by subjects (one to four); potential rewards were presented in four cups, each containing eight sweets.
Each child took part in two sessions, one session of 10 trials each, with each of the experimenters. A session was composed of 10 trials separated by pauses of 5 sec. Children were given 5 min between the two sessions to fully understand the different conduct of the two experimenters. The net income, i.e. the amount of the rewards kept by the children plus those received, could vary within any one session from 24 to 48 sweets with the doubling partner, and from 24 to 66 sweets with the fixed partner (Table 2). We counterbalanced the role of experimenters, i.e. within each age-and-sex group, one experimenter was the doubling partner with two children, and was the fixed partner with the other two. We also alternated the intervention order of partners from one set to another. To help children learn to distinguish between both conditions, we associated them with different cues. We divided the table into two parts, each devoted to a different set of four cups, with a different color for each condition.
We recorded whether subjects had siblings or twins. We videotaped testing sessions whenever written consent was obtained. Children were tested individually in a quiet room (4 m×3 m) adjoining their classroom. The child was led to the testing room and introduced to the two experimenters. The child then sat on a chair opposite the experimenters at a rectangular table (0.8 m×0.5 m).
Before testing, the experimenter gave the child the possibility to exchange one reward for two. If they failed, the experimenter repeated the trial once. If the child failed again, the test was stopped. When the child was successful, the experimenter then offered her/him the possibility of exchanging two rewards for four. If s/he failed, we repeated the offer once. All subjects reached this stage, and were considered ready for testing.
The two sessions lasted approximately 15 min. The first trial began when the first experimenter (doubling or fixed partner) placed and filled the four plastic cups with the different rewards. The experimenter then gave the child four sweets by placing them on the surface of the table while saying, “Here are four sweets and here are more sweets”, showing the cups of sweets. After 3 sec, she pointed to the four sweets, held out her hand, palm up, in front of the child and asked, “How many of them do you want to exchange?” (Note that pilot trials run with children aged between 4 and 12 years revealed that the sentence “Do you want to exchange any of them?” implied that the transaction may be risky, leading children either to accept exchanging all the items or to refuse exchanging any of them. We opted for a more precise question that made clear that the children did not have to return all the items).
Every time the child returned one or several sweets, the experimenter thanked them and presented the corresponding cup to the child saying “OK, here are the rewards. Do you want to try again?” before starting another trial. When the child kept or consumed all sweets, the experimenter said “OK, you can eat/keep the sweet(s). Do you want to try again?” After the session, the experimenter said “OK, that was great. Now you're going to play another game with my friend”. The second experimenter (doubling or fixed partner) drew attention to the change of condition by placing and filling four other plastic cups with a different amount of rewards, and then began the second testing session.
Control of Information Transfer
To avoid any exchange of information between children tested within the same school, the experimenter asked the child not to talk about testing with other children after the first two sessions were completed. It is also important to note that younger children were not verbally mature enough to have elaborate discussions with school friends  about how to gain more rewards during experiments.
We used a one-way repeated-measures ANOVA (Mauchly's test for sphericity = 0.74) to assess the effect of the individuals, age, sex and partner on the mean number of returned items. To test whether subjects responded differently to the fixed and doubling partners, we compared their performances at the individual level using the Wilcoxon matched-pairs test (exact procedure ) with SPSS software version 17 (SPSS Inc., Chicago IL, U.S.A.). The significance level was set as 0.05. Values are given as means and standard errors of the means.
The authors are grateful to Aline Ponzoni for support in data collection process, and to parents and children for their participation. We thank Mrs. Michelle Helmstetter and Annick Leclerc, headmistresses of the Robertsau preschool and elementary schools, and all the teachers for permitting us to conduct this study.
Conceived and designed the experiments: BT SS VD. Performed the experiments: SS. Analyzed the data: SS. Wrote the paper: SS BT VD MHB.
- 1. Nofsinger JR (2005) The psychology of investment (2nd ed). Upper Saddle, NJ: Prentice Hall. JR Nofsinger2005The psychology of investment (2nd ed)Upper Saddle, NJPrentice Hall
- 2. Hauk E, Nagel R (2001) Choice of partners in multiple two-person prisoner's dilemma games: an experimental study. J Conflict Resolut 45: 770–793.E. HaukR. Nagel2001Choice of partners in multiple two-person prisoner's dilemma games: an experimental study.J Conflict Resolut45770793
- 3. Arrow KJ (1974) The limits to organizations. New York: Norton. KJ Arrow1974The limits to organizationsNew YorkNorton
- 4. Bolton GE, Ockenfels A (2000) A theory of equity, reciprocity and competition. Am Econ Rev 90: 166–193.GE BoltonA. Ockenfels2000A theory of equity, reciprocity and competition.Am Econ Rev90166193
- 5. Charness G, Rabin M (2002) Understanding social preferences with simple tests. Q J Econ 117: 817–869.G. CharnessM. Rabin2002Understanding social preferences with simple tests.Q J Econ117817869
- 6. Falk A, Fischbacher U (2006) A theory of reciprocity. Game Econ Behav 54: 293–315.A. FalkU. Fischbacher2006A theory of reciprocity.Game Econ Behav54293315
- 7. Fehr E, Schmidt K (1999) A Theory of fairness, competition, and cooperation. Q J Econ 114: 817–868.E. FehrK. Schmidt1999A Theory of fairness, competition, and cooperation.Q J Econ114817868
- 8. Berg J, Dickhaut J, McCabe K (1995) Trust, reciprocity, and social history. Game Econ Behav 10: 122–142.J. BergJ. DickhautK. McCabe1995Trust, reciprocity, and social history.Game Econ Behav10122142
- 9. Bornhorst F, Ichino A, Kirchkamp O, Schlag KH, Winter E (2006) Similarities and differences when building trust: the role of cultures. Exp Econ 13: 260–283.F. BornhorstA. IchinoO. KirchkampKH SchlagE. Winter2006Similarities and differences when building trust: the role of cultures.Exp Econ13260283
- 10. Fershtman C, Gneezy U (2001) Discrimination in a segmented society: an experimental approach. Q J Econ 116: 351–377.C. FershtmanU. Gneezy2001Discrimination in a segmented society: an experimental approach.Q J Econ116351377
- 11. Willinger M, Keser C, Lohmann C, Usunier JC (2003) A comparison of trust and reciprocity between France and Germany: experimental investigation based on the investment game. J Econ Psychol 24: 447–466.M. WillingerC. KeserC. LohmannJC Usunier2003A comparison of trust and reciprocity between France and Germany: experimental investigation based on the investment game.J Econ Psychol24447466
- 12. Bellemare C, Kröger S (2006) On representative social capital. Eur Econ Rev 51: 183–202.C. BellemareS. Kröger2006On representative social capital.Eur Econ Rev51183202
- 13. Croson R, Buchan N (1999) Gender and culture: international experimental evidence from trust games. Am Econ Rev Pap Proc 89: 386–391.R. CrosonN. Buchan1999Gender and culture: international experimental evidence from trust games.Am Econ Rev Pap Proc89386391
- 14. Croson R, Gneezy U (2009) Gender differences in preferences. J Econ Lit 47: 1–27.R. CrosonU. Gneezy2009Gender differences in preferences.J Econ Lit47127
- 15. Fehr E, Fischbacher U, von Rosenbladt B, Schupp J, Wagner GG (2002) A nationwide laboratory. Examining trust and trustworthiness by integrating behavioral experiments into representative surveys. Schmoller's Jahrbuch 122: 519–542.E. FehrU. FischbacherB. von RosenbladtJ. SchuppGG Wagner2002A nationwide laboratory. Examining trust and trustworthiness by integrating behavioral experiments into representative surveys.Schmoller's Jahrbuch122519542
- 16. Holm HJ, Nystedt P (2005) Intra-generational trust – a semi-experimental study of trust among different generations. J Econ Behav Organ 58: 403–419.HJ HolmP. Nystedt2005Intra-generational trust – a semi-experimental study of trust among different generations.J Econ Behav Organ58403419
- 17. Sutter M, Kocher MG (2007) Trust and trustworthiness across different age groups. Game Econ Behav 59: 364–382.M. SutterMG Kocher2007Trust and trustworthiness across different age groups.Game Econ Behav59364382
- 18. Finucane ML, Slovic P, Mertz CK, Flynn J, Satterfield TA (2000) Gender, race, and perceived risk: the ‘white male’ effect. Health Risk Soc 2: 159–172.ML FinucaneP. SlovicCK MertzJ. FlynnTA Satterfield2000Gender, race, and perceived risk: the ‘white male’ effect.Health Risk Soc2159172
- 19. Hinz RP, McCarthy DD, Turner JA (1997) Are women conservative investors? Gender differences in participant-directed pension investments. In: Gordon MS, Mitchell OS, Twinney MM, editors. Positioning Pensions for the Twenty-First Century. Philadelphia: University of Pennsylvania Press. pp. 91–103.RP HinzDD McCarthyJA Turner1997Are women conservative investors? Gender differences in participant-directed pension investments.MS GordonOS MitchellMM TwinneyPositioning Pensions for the Twenty-First CenturyPhiladelphiaUniversity of Pennsylvania Press91103
- 20. Buchan NR, Croson R, Solnick SJ (2008) Trust and gender: an examination of behavior and beliefs in the investment game. J Econ Behav Organ 68: 466–476.NR BuchanR. CrosonSJ Solnick2008Trust and gender: an examination of behavior and beliefs in the investment game.J Econ Behav Organ68466476
- 21. Eckel CC, Wilson RK (2004) Whom to trust? Choice of partner in a trust game. CC EckelRK Wilson2004Whom to trust? Choice of partner in a trust game.Unpublished. Unpublished.
- 22. Lundeberg MA, Fox PW, Punccohar J (1994) Highly confident but wrong: gender differences and similarities in confidence judgments. J Educ Psychol 86: 114–121.MA LundebergPW FoxJ. Punccohar1994Highly confident but wrong: gender differences and similarities in confidence judgments.J Educ Psychol86114121
- 23. Niederle M, Vesterlund L (2007) Do women shy away from competition? Do men compete too much? Q J Econ 122: 1067–1101.M. NiederleL. Vesterlund2007Do women shy away from competition? Do men compete too much?Q J Econ12210671101
- 24. Blake PR, Rand DG (2010) Currency value moderates equity preference among young children. Evol Hum Behav 31: 210–218.PR BlakeDG Rand2010Currency value moderates equity preference among young children.Evol Hum Behav31210218
- 25. Fan C-P (2000) Teaching children cooperation - an application of experimental game theory. J Econ Behav Organ 41: 191–209.C-P Fan2000Teaching children cooperation - an application of experimental game theory.J Econ Behav Organ41191209
- 26. Fehr E, Bernhard H, Rockenbach B (2008) Egalitarianism in young children. Nature 454: 1079–1083.E. FehrH. BernhardB. Rockenbach2008Egalitarianism in young children.Nature45410791083
- 27. Blake PR, McAuliffe K (2011) “I had so much it didn't seem fair”: eight- year-olds reject two forms of inequity. Cognition 120: 215–224.PR BlakeK. McAuliffe2011“I had so much it didn't seem fair”: eight- year-olds reject two forms of inequity.Cognition120215224
- 28. Janssen M, Ahn TK (2003) Adaptation vs. anticipation in public-good games. In: Rouchier J, Edmonds B, Hales D, editors. Mimeo. 36 p.M. JanssenTK Ahn2003Adaptation vs. anticipation in public-good games.J. RouchierB. EdmondsD. HalesMimeoModel to model workshop electronic proceedings. 36 Model to model workshop electronic proceedings.
- 29. Neugebauer T, Perote J, Schmidt U, Loos M (2009) Selfish biased conditional cooperation: On the decline of cooperation in repeated public goods experiments. J Econ Psychol 30: 52–60.T. NeugebauerJ. PeroteU. SchmidtM. Loos2009Selfish biased conditional cooperation: On the decline of cooperation in repeated public goods experiments.J Econ Psychol305260
- 30. Cochard F, Nguyen Van P, Willinger M (2004) Trusting behavior in a repeated investment game. J Econ Behav Organ 55: 31–44.F. CochardP. Nguyen VanM. Willinger2004Trusting behavior in a repeated investment game.J Econ Behav Organ553144
- 31. Bornhorst F, Ichino A, Kirchkamp O, Schlag K, Winter E (2004) How do people play a repeated trust game? F. BornhorstA. IchinoO. KirchkampK. SchlagE. Winter2004How do people play a repeated trust game?Experimental evidence. University of Mannheim, Mimeo. Experimental evidence. University of Mannheim, Mimeo.
- 32. Coricelli G, Fehr D, Fellner G (2004) Partner selection in public goods experiments. J Conflict Resolut 48: 356–378.G. CoricelliD. FehrG. Fellner2004Partner selection in public goods experiments.J Conflict Resolut48356378
- 33. Slonim R, Garbarino E (2008) Increases in trust and altruism from partner selection: experimental evidence. Exp Econ 11: 134–153.R. SlonimE. Garbarino2008Increases in trust and altruism from partner selection: experimental evidence.Exp Econ11134153
- 34. Birch SAJ, Vauthier SA, Bloom P (2008) Three- and four-year olds spontaneously use others' past performance to guide their learning. Cognition: Int J Cogn Sci 107: 1018–1034.SAJ BirchSA VauthierP. Bloom2008Three- and four-year olds spontaneously use others' past performance to guide their learning.Cognition: Int J Cogn Sci10710181034
- 35. Corriveau KH, Harris PL (2009) Choosing your informant: weighing familiarity and recent accuracy. Dev Sci 12: 426–437.KH CorriveauPL Harris2009Choosing your informant: weighing familiarity and recent accuracy.Dev Sci12426437
- 36. Scofield J, Behrend D (2008) Learning words from reliable and unreliable speakers. Cognitive Dev 23: 278–290.J. ScofieldD. Behrend2008Learning words from reliable and unreliable speakers.Cognitive Dev23278290
- 37. Gelman SA (2009) Learning from others: children's construction of concepts. Annual Review of Psychology 60: 115–140.SA Gelman2009Learning from others: children's construction of concepts.Annual Review of Psychology60115140
- 38. Brosnan SF, de Waal FBM (2009) Cebus apella tolerate intermittent unreliability in human experimenters. Int J Primatol 30: 663–674.SF BrosnanFBM de Waal2009Cebus apella tolerate intermittent unreliability in human experimenters.Int J Primatol30663674
- 39. Chen MK, Lakshminarayanan V, Santos LR (2006) How basic are behavioral biases? Evidence from capuchin monkey trading behavior. J Polit Econ 114: 517–537.MK ChenV. LakshminarayananLR Santos2006How basic are behavioral biases? Evidence from capuchin monkey trading behavior.J Polit Econ114517537
- 40. Mitchell RW, Anderson JR (1997) Pointing, withholding information, and deception in capuchin monkeys (Cebus apella). J Comp Psychol 111: 351–361.RW MitchellJR Anderson1997Pointing, withholding information, and deception in capuchin monkeys (Cebus apella).J Comp Psychol111351361
- 41. Steelandt S, Dufour V, Broihanne M-H, Thierry B (2011) Can monkeys make investments based on maximized pay-off? PLoS One 6: e17801.S. SteelandtV. DufourM-H BroihanneB. Thierry2011Can monkeys make investments based on maximized pay-off?PLoS One6e17801
- 42. Kahneman D, Tversky A (2000) Choices, values, and frames. Cambridge: Cambridge University Press. D. KahnemanA. Tversky2000Choices, values, and framesCambridgeCambridge University Press
- 43. Hay DF (1979) Cooperative interactions and sharing between very young children and their parents. Dev Psychol 15: 647–653.DF Hay1979Cooperative interactions and sharing between very young children and their parents.Dev Psychol15647653
- 44. Hay DF, Murray P (1982) Giving and requesting: social facilitation of infants' offers to adults. Infant Behav Dev 5: 301–310.DF HayP. Murray1982Giving and requesting: social facilitation of infants' offers to adults.Infant Behav Dev5301310
- 45. Rheingold HL, Hay DF, West MJ (1976) Sharing in the second year of life. Child Dev 47: 1148–1158.HL RheingoldDF HayMJ West1976Sharing in the second year of life.Child Dev4711481158
- 46. Steelandt S, Thierry B, Whiten A, Broihanne M-H, Dufour VThe early development of gifts and exchanges in children. S. SteelandtB. ThierryA. WhitenM-H BroihanneV. DufourThe early development of gifts and exchanges in children.Submitted. Submitted.
- 47. Steelandt S, Thierry B, Broihanne M-H, Dufour V (2012) Ability of children to delay gratification in an exchange task. Cognition 122: 416–425.S. SteelandtB. ThierryM-H BroihanneV. Dufour2012Ability of children to delay gratification in an exchange task.Cognition122416425
- 48. Eckerman C, Whatley J, Kutz S (1975) The growth of social play with peers during the second year of life. Dev Psychol 11: 42–49.C. EckermanJ. WhatleyS. Kutz1975The growth of social play with peers during the second year of life.Dev Psychol114249
- 49. Tomasello M (2007) Cooperation and communication in the 2nd year of life. Child Dev Perspect 1: 8–12.M. Tomasello2007Cooperation and communication in the 2nd year of life.Child Dev Perspect1812
- 50. Tomasello M, Carpenter M, Call J, Behne T, Moll H (2005) Understanding and sharing intentions: the origins of cultural cognition. Behav Brain Sci 28: 675–735.M. TomaselloM. CarpenterJ. CallT. BehneH. Moll2005Understanding and sharing intentions: the origins of cultural cognition.Behav Brain Sci28675735
- 51. Perner J (1991) Understanding the representational mind. Cambridge, MA: MIT Press. J. Perner1991Understanding the representational mindCambridge, MAMIT Press
- 52. Sullivan K, Winner E (1993) Three-year-olds' understanding of mental states: the influence of trickery. J Expl Child Psychol 56: 135–148.K. SullivanE. Winner1993Three-year-olds' understanding of mental states: the influence of trickery.J Expl Child Psychol56135148
- 53. Tomasello M, Rakoczy H (2003) What makes human cognition unique? From individual to shared to collective intentionality. Mind Lang 18: 121–147.M. TomaselloH. Rakoczy2003What makes human cognition unique? From individual to shared to collective intentionality.Mind Lang18121147
- 54. Wellman HM (1990) The child's theory of mind. Cambridge, MA: MIT Press. HM Wellman1990The child's theory of mindCambridge, MAMIT Press
- 55. Cooper RG (1984) Early number development: discovering number space with addition and subtraction. In: Sophian C, editor. The origins of cognitive skills. Hillsdale, NJ: Erlbaum. RG Cooper1984Early number development: discovering number space with addition and subtraction.C. SophianThe origins of cognitive skillsHillsdale, NJErlbaum
- 56. Feigenson L, Carey S, Spelke ES (2002a) Infants' discrimination of number vs. continuous extent. Cognitive Psychol 44: 33–66.L. FeigensonS. CareyES Spelke2002aInfants' discrimination of number vs. continuous extent.Cognitive Psychol443366
- 57. Sophian C, Adams N (1987) Infants' understanding of numerical transformations. Brit J Dev Psychol 5: 257–264.C. SophianN. Adams1987Infants' understanding of numerical transformations.Brit J Dev Psychol5257264
- 58. Strauss MS, Curtis LE (1984) Development of numerical concepts in infancy. In: Sophian C, editor. Origins of cognitive skills. Hillsadle, NJ: Erlbaum. pp. 131–155.MS StraussLE Curtis1984Development of numerical concepts in infancy.C. SophianOrigins of cognitive skillsHillsadle, NJErlbaum131155
- 59. Brannon E (2002) The development of ordinal numerical knowledge in infancy. Cognition 83: 223–240.E. Brannon2002The development of ordinal numerical knowledge in infancy.Cognition83223240
- 60. Feigenson L, Dehaene S, Spelke ES (2004) Core systems of number. Trends Cogn Sci 8: 307–314.L. FeigensonS. DehaeneES Spelke2004Core systems of number.Trends Cogn Sci8307314
- 61. Lipton JS, Spelke ES (2003) Origins of number sense: large number discrimination in human infants. Psychol Sci 15: 396–401.JS LiptonES Spelke2003Origins of number sense: large number discrimination in human infants.Psychol Sci15396401
- 62. Xu F (2003) Numerosity discrimination in infants: evidence for two systems of representation. Cognition 89: B15–B25.F. Xu2003Numerosity discrimination in infants: evidence for two systems of representation.Cognition89B15B25
- 63. Xu F, Arriaga R (2007) Number discrimination in 10-month-old infants. Brit J Dev Psychol 25: 103–108.F. XuR. Arriaga2007Number discrimination in 10-month-old infants.Brit J Dev Psychol25103108
- 64. Gelman R, Meck E (1983) Preschoolers' counting: principles before skill. Cognition 13: 343–359.R. GelmanE. Meck1983Preschoolers' counting: principles before skill.Cognition13343359
- 65. Potter MC, Levy E (1968) Spatial enumeration without counting. Child Dev 39: 265–272.MC PotterE. Levy1968Spatial enumeration without counting.Child Dev39265272
- 66. Wynn K (1990) Children's understanding of counting. Cognition 36: 155–193.K. Wynn1990Children's understanding of counting.Cognition36155193
- 67. Wynn K (1992a) Children's acquisition of the number words and the counting system. Cognitive Psychol 24: 220–251.K. Wynn1992aChildren's acquisition of the number words and the counting system.Cognitive Psychol24220251
- 68. Butterworth B (2005) The development of arithmetical abilities. J Child Psychol Psych 46: 3–18.B. Butterworth2005The development of arithmetical abilities.J Child Psychol Psych46318
- 69. Starkey P, Gelman R (1982) The development of addition and subtraction abilities prior to formal schooling in arithmetic. In: Carpenter TP, Moser JM, Romberg TA, editors. Addition and subtraction: a cognitive perspective. Hilldale, NJ: Erlbaum. pp. 99–116.P. StarkeyR. Gelman1982The development of addition and subtraction abilities prior to formal schooling in arithmetic.TP CarpenterJM MoserTA RombergAddition and subtraction: a cognitive perspectiveHilldale, NJErlbaum99116
- 70. Barth H, La Mont K, Lipton J, Dehaene S, Kanwisher N, et al. (2006) Non-symbolic arithmetic in adults and young children. Cognition 98: 199–222.H. BarthK. La MontJ. LiptonS. DehaeneN. Kanwisher2006Non-symbolic arithmetic in adults and young children.Cognition98199222
- 71. Jordan NC, Huttenlocher J, Levine SC (1992) Differential calculation abilities in young children from middle- and low-income families. Dev Psychol 28: 644–653.NC JordanJ. HuttenlocherSC Levine1992Differential calculation abilities in young children from middle- and low-income families.Dev Psychol28644653
- 72. Levine SC, Jordan NC, Huttenlocher J (1992) Development of calculation abilities in young children. J Expl Child Psychol 53: 72–103.SC LevineNC JordanJ. Huttenlocher1992Development of calculation abilities in young children.J Expl Child Psychol5372103
- 73. Feigenson L, Carey S, Hauser MD (2002b) The representations underlying infants' choice of more: object files versus analog magnitudes. Psychol Sci 13: 150–156.L. FeigensonS. CareyMD Hauser2002bThe representations underlying infants' choice of more: object files versus analog magnitudes.Psychol Sci13150156
- 74. Starkey P (1992) The early development of numerical reasoning. Cognition 43: 93–126.P. Starkey1992The early development of numerical reasoning.Cognition4393126
- 75. Wynn K (1992b) Addition and subtraction by human infants. Nature 358: 749–750.K. Wynn1992bAddition and subtraction by human infants.Nature358749750
- 76. Wynn K (1995) Origins of numerical knowledge. Math Cog 1: 35–60.K. Wynn1995Origins of numerical knowledge.Math Cog13560
- 77. Xu F, Spelke ES, Goddard S (2005) Number sense in human infants. Dev Sci 8: 88–101.F. XuES SpelkeS. Goddard2005Number sense in human infants.Dev Sci888101
- 78. Carpenter TP, Moser JM (1984) The acquisition of addition and subtraction concepts in grades one through three. J Res Math Educ 15: 179–202.TP CarpenterJM Moser1984The acquisition of addition and subtraction concepts in grades one through three.J Res Math Educ15179202
- 79. Huttenlocher J, Jordan N, Levine SC (1994) A mental model for early arithmetic. J Exp Psychol 123: 284–296.J. HuttenlocherN. JordanSC Levine1994A mental model for early arithmetic.J Exp Psychol123284296
- 80. Zur O, Gelman R (2004) Young children can add and subtract by predicting and checking. Early Child Res Q 19: 121–137.O. ZurR. Gelman2004Young children can add and subtract by predicting and checking.Early Child Res Q19121137
- 81. Beran MJ, Evans TA, Leighty KA, Harris EH, Rice D (2008) Summation and quantity judgments of sequentially sets by capuchin monkeys (Cebus apella). Am J Primatol 70: 191–194.MJ BeranTA EvansKA LeightyEH HarrisD. Rice2008Summation and quantity judgments of sequentially sets by capuchin monkeys (Cebus apella).Am J Primatol70191194
- 82. Blaye A, Bonthoux F (2001) Thematic and taxonomic relations in preschoolers: the development of flexibility in categorization choices. Brit J Dev Psychol 19: 395–412.A. BlayeF. Bonthoux2001Thematic and taxonomic relations in preschoolers: the development of flexibility in categorization choices.Brit J Dev Psychol19395412
- 83. Zelazo PD, Müller U, Frye D, Marcovitch S (2003) The development of executive function. Monogr Soc Res Child 68: PD ZelazoU. MüllerD. FryeS. Marcovitch2003The development of executive function.Monogr Soc Res Child68
- 84. Blaye A, Chevalier N, Paour J-L (2007) The development of intentional control of categorization behaviour: a study of children's relational flexibility. Cognition, Brain, Behav 11: 791–808.A. BlayeN. ChevalierJ-L Paour2007The development of intentional control of categorization behaviour: a study of children's relational flexibility.Cognition, Brain, Behav11791808
- 85. Cepeda NJ, Kramer AF, Gonzalez de Sather JC (2001) Changes in executive control across the life span: Examination of task-switching performance. Dev Psychol 37: 715–730.NJ CepedaAF KramerJC Gonzalez de Sather2001Changes in executive control across the life span: Examination of task-switching performance.Dev Psychol37715730
- 86. Crone EA, Ridderinkhof KR, Worm M, Somsen RJM, van der Molen MW (2004) Switching between spatial stimulus-response mappings: a developmental study of cognitive flexibility. Dev Sci 7: 443–455.EA CroneKR RidderinkhofM. WormRJM SomsenMW van der Molen2004Switching between spatial stimulus-response mappings: a developmental study of cognitive flexibility.Dev Sci7443455
- 87. Zelazo PD (2006) The Dimensional Change Card Sort (DCCS): a method of assessing executive function in children. Nat Protoc 1: 297–301.PD Zelazo2006The Dimensional Change Card Sort (DCCS): a method of assessing executive function in children.Nat Protoc1297301
- 88. Warneken F, Tomasello M (2007) Helping and cooperation at 14 months of age. Infancy 11: 271–294.F. WarnekenM. Tomasello2007Helping and cooperation at 14 months of age.Infancy11271294
- 89. Gopnik A, Astington JW (1988) Children's understanding of representational change and its relation to the understanding of false belief and appearance-reality distinction. Child Dev 59: 26–37.A. GopnikJW Astington1988Children's understanding of representational change and its relation to the understanding of false belief and appearance-reality distinction.Child Dev592637
- 90. Esquivel GB, Lopez EC, Nahari S (2007) Handbook of multicultural school psychology: an interdisciplinary perspective. Mahwah, NJ: Erlbaum. GB EsquivelEC LopezS. Nahari2007Handbook of multicultural school psychology: an interdisciplinary perspectiveMahwah, NJErlbaum
- 91. Jordan NC, Huttenlocher J, Levine SC (1994) Assessing early arithmetic abilities: effects of verbal and nonverbal response types on the calculation performance of middle- and low-income children. Learn Individ Differ 6: 413–432.NC JordanJ. HuttenlocherSC Levine1994Assessing early arithmetic abilities: effects of verbal and nonverbal response types on the calculation performance of middle- and low-income children.Learn Individ Differ6413432
- 92. Braynov S, Sandholm T (2002) Contracting with uncertain level of trust. Comput Intell 18: 501–514.S. BraynovT. Sandholm2002Contracting with uncertain level of trust.Comput Intell18501514
- 93. Corriveau KH, Meints K, Harris PL (2009) Early tracking of informant accuracy and inaccuracy by young children. Brit J Dev Psychol 27: 331–342.KH CorriveauK. MeintsPL Harris2009Early tracking of informant accuracy and inaccuracy by young children.Brit J Dev Psychol27331342
- 94. Camerer C, Colin F (1998) Bounded rationality in individual decision making. Exp Econ 1: 163–183.C. CamererF. Colin1998Bounded rationality in individual decision making.Exp Econ1163183
- 95. Kahneman D, Slovic P, Tversky A (1982) Judgment under uncertainty: heuristics and biases. Cambridge: Cambridge University Press. D. KahnemanP. SlovicA. Tversky1982Judgment under uncertainty: heuristics and biasesCambridgeCambridge University Press
- 96. Plott CR, Smith VL (2008) Handbook of experimental economics results. Amsterdam: North Holland Press. CR PlottVL Smith2008Handbook of experimental economics resultsAmsterdamNorth Holland Press
- 97. Tomasello M (2003) Constructing a language: a usage-based theory of language Acquisition. Cambridge, MA: Harvard University Press. M. Tomasello2003Constructing a language: a usage-based theory of language AcquisitionCambridge, MAHarvard University Press
- 98. Mundry R, Fischer J (1998) Use of statistical programs for nonparametric tests of small samples often leads to incorrect P values: examples from Animal Behaviour. Anim Behav 56: 256–259.R. MundryJ. Fischer1998Use of statistical programs for nonparametric tests of small samples often leads to incorrect P values: examples from Animal Behaviour.Anim Behav56256259