Who receives more? Using cognitive development to understand economic reasoning during resource allocation.
By Carlos A. Ramirez Jr.
The economic field tends to assume rational agents for many mathematical models that explain strategic situations in our daily lives. The problem with these economic models is that they sometimes do not encapsulate the complexities of human behavior. In this review, I describe the results of the ultimatum game and the dictator game and provide alternative explanations based on psychological evidence for why the outcomes of these game theory games do not follow economic reasoning. To investigate why there is a discrepancy between the predicted and actual results of these games, we focus on developmental psychology and what research in the field can tell us about how cognitive processes, such as theory of mind, computing ratios, and determining reliability, develop. Theory of mind allows children to understand what other people are thinking and influences decisions regarding resource allocation. The ability to compute proportional ratios is advantageous for children when assessing equity among individuals. Determining reliability offers children a way to evaluate others during strategic tasks. By exploring human cognition’s effect on these specific strategic tasks in the context of development, we can better understand how competitive and cooperative decision making is not driven by achieving a mathematical equilibrium, but instead by developing cognitive processes that affect how choices are made.
In the field of economics, it is often assumed in many models that all agents are rational. In economics terms, this means that people will think logically about the situation at hand and mathematically discover a solution that will be the most rational choice in regards to their self-interest. For example, if there were two identical watches for two different prices, a person would always pick the watch with the lowest price. However, in many cases, agents are economically irrational; people make choices that may not be mathematically rational per se, but makes sense in the context of how they are feeling, the situation they are in, or how the specific circumstance is framed . To use the previous example, if a person’s mother owned a watch store and sold the watch they wanted at a higher price than another store, the person would be more likely to buy his or her mother’s watch instead of the cheaper watch due to feelings of attachment for his or her mother. The field of behavioral economics has thoroughly investigated irrational agents and researchers use a blend of economics and psychology to understand how people behave in competitive environments. In this review, I will be focusing on economically irrational agents as a basis for understanding how individuals interact in strategic situations through certain cognitive abilities.
Competition is a key aspect of human behavior and one of the main scenarios where people can behave irrationally. A common concept that researchers use to analyze competitive behavior is game theory. Game theory is a branch of mathematics that provides models for intelligent beings in strategic situations and has had a major impact on fields such as economics, biology, and psychology. There are many different takeaways from game theory, but the one that is important for this review are two games that are provided from the concept: the ultimatum game and the dictator game. These games provide a powerful tool for psychological research since they provide a quantitative way of testing social situations among people in controlled environments .
The ultimatum game is a task in which two people, the proposer and the responder, are asked to allocate resources. An example of a resource is money. Let us assume the proposer receives one hundred dollars and the responder receives nothing. The proposer is asked to give whatever amount they choose to the responder. The proposer has the knowledge that if the responder does not deem the portion fair, then they can decline the offer and neither one of them keeps any of the money. Therefore, the proposer should offer the responder as little money as they will accept so that the responder does not decline the offer and the proposer receives something. According to economic theory, the responder should take any offer of money that is greater than zero since having something is better than having nothing. However, it has been shown in experiments that the proposer typically offers around 40% of the total resource and the responder rejects offers below 25% [3, 4]. The experiments show that human behavior in this scenario does not follow economic theory because the results of this game are not predicted by the theories provided by economists.
The dictator game is similar to the ultimatum game, but it takes away the responder’s power to deny an offer and does not punish the proposer for their inequity. The proposer, therefore, acts as the “dictator” in this task. An economically rational decision for the proposer would be to keep all the money and not give any to the responder. Despite this notion, it has been shown that offers from the proposer are normally around 28% of the total resource in the dictator game .
It is clear that there is a discrepancy between what economists would expect to happen during these games and what is observed. What is causing this discrepancy and can it be modeled with an interdisciplinary approach by using already researched psychological variables? Do humans only act in mathematically self-interested ways or do cognitive processes make their behavior more complex and variable? Although there have been many proposals put forward that support both of these possibilities, I will discuss how research in cognitive development can aid in investigating the notion that cognitive processes make human behavior complex and variable, which can be observed from a young age [6, 1].
The main goal of this literature review is to lay the foundation for creating a logical model that both economists and psychologists can use to explain economically irrational behavior that will help in creating more accurate economic models and expand the definition of rationality. Economists typically call behavior that strays from economic models “irrational” because they do not have a consistent way to explain these types of actions and choices. Taking a developmental psychological approach to investigate the types of behaviors that cannot be explained by economic models can lead to more information about the type of cognitive tasks that occur during these behaviors . Furthermore, understanding how cognitive abilities develop can aid the research community in helping predict how humans will behave throughout their lives and will be a useful aid in developing a model for irrational behavior.
How is irrational behavior during resource allocation related to cognitive abilities? When deciding how to allocate resources, individuals are often engaged in the task with another partner, requiring not only an understanding of the social consequences of a decision, but also how that decision will be made based on a mathematical computation that divides the resource between the individuals participating. Given these requirements, this literature review focuses on three cognitive skills that develop during childhood that have implications for the social and mathematical aspects of resource allocation during the ultimatum and dictator games: theory of mind, computation of proportional ratios, and determining reliability.
Research on theory of mind, computation of proportional ratios, and reliability determination can provide information about the cognitive factors that go into making decisions during economic games. Theory of mind, the ability to recognize that somebody other than yourself has a mind and thoughts, has been shown to positively correlate with the fairness of children’s offers in the ultimatum game and the dictator game [7, 8]. The capability of children to compute proportional ratios may influence their inequity aversion, the distaste for unequal distributions, and could result in them making more even offers due to their inability to feel comfortable with unequal allocations of goods [9, 10]. Furthermore, the way children determine reliability is related to how they begin to trust other individuals and, therefore, may affect the way they behave in strategic situations. It is still not known how and when these cognitive abilities develop in children and what their implications towards economic theory can be. This review will analyze the ultimatum game and the dictator game and see how children interact with these game theory situations through focusing on specific cognitive factors (theory of mind, computation of proportional ratios, and determining reliability) to help investigate how previously thought irrational behaviors can be classified as rational.
THEORY OF MIND
Theory of mind is the ability to infer that other people have mental states apart from one’s own. This ability is often mastered when kids are between four and six years old and does not develop well in children with Autism Spectrum Disorder [11, 7]. Theory of mind is typically tested in children with a false belief task that requires them to think about different characters in a story . The researcher asks the children what the characters’ thoughts are after an action is finished. For example, a researcher shows the child a story about Bob and Sue. Bob and Sue are sitting on a couch with a ball between them. Bob leaves the room and Sue hides the ball underneath the couch. The researcher then asks the child where Bob will look for the ball when he reenters the room. Children with developed theory of mind answer that Bob will look on the couch for the ball because this is where he last saw it. However, children with undeveloped theory of mind answer that Bob will look for the ball under the couch because the child, not Bob, knows the true location. Children with undeveloped theory of mind lack the ability to see the situation as Bob sees it. Another test that can be used is a second-order false belief task, where the researcher asks the child where Sue thinks Bob believes the ball is. This type of task normally distinguishes those with strong theory of mind and weak theory of mind. Theory of mind can be very useful in situations where it can be beneficial to know what your counterpart is thinking.
Theory of mind can change the outcome of games such as the ultimatum game and the dictator game. It has been hypothesized that theory of mind is important because it can help the proposer avoid punishment . Haruto Takagishi and his colleagues displayed the usefulness of theory of mind when they tested children around the age of five with the ultimatum game using candy as the resource. In this task, a child would be given ten candies and then asked to distribute the candies between himself and another child. Takagishi and his colleagues found that children with theory of mind as tested by a false belief task, similar to the false belief task described earlier in this section, made fairer offers than those children who did not have theory of mind. The authors concluded that if the proposer can predict how the responder would react to various offers, the proposer can make an appropriate allocation that will not elicit a negative response from the responder .
David Sally and Elisabeth Hill performed a similar test with the ultimatum game, but also included child participants with Autism Spectrum Disorder . Sally and Hill instructed children to play the ultimatum game on the computer with a point system instead of a candy system. The children would choose one of eleven cards on the screen with various options of how the points could be split. A child at another computer would then accept or reject the offer and the points would be split per the rules of the game. The children would play sixteen rounds of the game and their roles as proposer and responder would be switched twice. They concluded that younger children and children with ASD had a more difficult time making and accepting fairer offers . Furthermore, there seemed to be a discrepancy between those who passed the first-order false belief task and second-order false belief task. While the prior had the ability to make non-random decisions, the latter had a stronger tendency to be fair as seen in their offers. This trend demonstrates that the strength of a person’s theory of mind is positively correlated with his or her fairness.
Along with fairness, cooperation is an important aspect in the ultimatum and dictator games and having a theory of mind helps children cooperate more effectively. When children are playing the ultimatum game, there is a need to cooperate since the proposer and responder both have the same goal of getting the most amount of money as possible and not losing it all with an unfair allocation. The proposer needs to be more generous than they normally would be if they want to make sure that the responder accepts the offer. Meanwhile, the responder needs to make sure what they receive is fair and can therefore determine whether they can both keep their money. Research has shown that children will often work together in these types of situations to get fair amounts of the good . This can be hard to do without well-developed theory of mind skills since neither player would be able to determine what the other is thinking in this situation . The proposer must especially think about how the responder would respond because it is up to the responder to decide whether they keep their allocations of money.
Furthermore, the proposer’s theory of mind abilities influence the outcome of the dictator game as well. Instead of giving the responder nothing, children tend to be more generous with their offers . It goes against economic reasoning that children give any amount to the responder since the responder has no way of punishing the proposer if they view the allocation of money to be unfair. The proposer could be giving for external cooperation outside of the game to simply be more fair . Overall, theory of mind may help children behave in a more cooperative manner since it allows them to mentalize other people’s thoughts.
As shown in the research, theory of mind has a significant impact on how children behave during tasks such as the ultimatum game and the dictator game [7,8]. There are many different scenarios in the real world that replicate these games and theory of mind could lead people to be economically irrational during these situations. For example, individuals with ASD would find it incredibly difficult to reach the optimal outcome of the ultimatum game because it may be difficult for them to know what the other person is thinking. Lacking theory of mind could also prove difficult in situations where it might be beneficial to be cooperative and understand the perspectives of those around you. A focus on research of atypically developing children could be beneficial in further investigating economic choices as it is shown that certain mental abilities, notably theory of mind, are required for making economically rational decisions. Furthermore, additional research could help map out a trajectory of how atypically developing individuals behave during certain economic situations and broaden models to incorporate humans of varying abilities. Since there is evidence to suggest the strength of one’s theory of mind can have an effect on their strategy in game theory games, future experiments could alter how well children know each other before the tasks and maybe even train them on theory of mind [7,8]. By connecting strategic game theory games to theory of mind, there are many implications of how this can be researched in the future.
COMPUTING PROPORTIONAL RATIOS
Theory of mind is important when children need to evaluate what other children are thinking, such as when making decisions in game theory games. However, to make a proper decision, they also need to understand the basic element of what they are deciding: the fairness of the offer. Adams defined fairness as having the same proportion of reward as the work put into the task . Therefore, to understand what fairness is, a person must assess how much individuals have contributed and how to distribute a proportional reward based on that information. There are numerous theories that indicate that fairness is how people assess equity. For example, Adams suggests that people are uncomfortable with inequity and thus experience “inequity aversion”, which lead people to become more equitable as to avoid unpleasant feelings . It is important to see the origins of this behavior by investigating whether children have the mental capacity to process two different kinds of information and act equitable.
To examine how the amount of work distributed between children affects how children allocate resources, Hook and Cook reviewed research measuring how children behaved in allocation tasks . Allocation tasks are situations where researchers describe how much work other children are doing while assigning work to the child they are conversing with. With this knowledge, children are asked to allocate the reward between themselves and another child. Hook and Cook suggest that children go through certain stages of equity as they develop and only reach proportionality with their fairness when they are older . The authors describe four types of allocation behavior: self-interest, equality, ordinal equity, and proportional equity. Self-interest is simply doing what is best for oneself by optimizing the amount that one receives in a situation where there is choice. Equality is defined as allocating resources equally among all participants. Ordinal equity is when someone is given a larger amount of reward for doing more work than someone else, but the reward is not necessarily proportional to the amount of work they did. For example, if Katie painted five birdhouses and Sam only two, then Katie might receive four of the seven candies. Proportional equity is when the ratio of the work one does equals the ratio of the reward they receive. Using our example from before, Katie would get five of the seven candies and Sam would get two candies since there is a one-to-one ratio between work and reward. Hook and Cook found that children under six years old acted either completely self-interested or equally when distributing resources; whereas children between six years old and thirteen years old understood ordinal equity and even displayed some inequity aversion when they are around nine years of age. When children are thirteen years or older, they understand inequity aversion and behave proportionally equitable. This type of understanding demonstrates that children understand what fair ratios are beginning at age six, but do not know exactly what is fair until the age of thirteen.
The developmental trajectory of understanding proportional equity mirrors the more general ability of understanding proportional relationships. Hook and Cook  also reviewed the literature that assesses how children compare dimensions or stimuli based on distance and time. In the Piaget study (as cited in ), Piaget moves two objects together, A and B, with one moving farther than the other and asked the children after the demonstration which object moved faster . Results indicated that seven to nine-year-olds could not solve the problem, ten to eleven-year-olds could solve the problem but did not understand the relationship between distance and time, and twelve to fourteen-year-olds could solve the problem, and understood that the object that moved farther in the same amount of time also moved faster. Hook and Cook found that the development of this ability mirrors the shift to proportional equity . They suggested that at the core of fairness is the ability to process multiple kinds of information. The fundamental ability here is being able to keep track of two different variables at once and then draw a conclusion by observing their relationship. Children have difficulty retaining this information, processing it, and formulating an answer. However, it is seen here that their cognitive abilities are not dependent on the situation one is in, but are truly applicable to many situations and inherently influence one’s thinking.
Using the ability to retain multiple pieces of information, children strategize differently during game theory games. Hook and Cook suggest that children at different ages can conserve varying amounts of information which influence their decisions when sharing with others . In the ultimatum game and the dictator game, both children have done the same amount of work and deserve the same amount of reward . Therefore, anything other than an equal split between the children would be deemed as unfair. Given the properties of these games, it is hard to test whether children consider the amount of work one is doing when allocating the rewards. A plausible experiment to test this would be to tell the children that one child is more deserving of the reward than the other. This could be done verbally (e.g. tell the child “she helped clean more today than you”) or as an action (e.g. have the kids perform a task in which one child does more work) before the game is played. Overall, these games help put these cognitive skills in action and reveal important findings in the fields of developmental psychology and economics.
When children grow older, their inequity aversion and ability to compute proportional ratios leads them to create allocations that are equitable and fair; however, people of different backgrounds and cultures could view fairness in different ways. Some cultures may view a larger reward to an elderly person as common sense even if they did less work than a younger person whom which they are sharing the reward. In fact, one study demonstrates that a child’s self-interest in fairness and distribution can vary depending on what type of culture they are from (e.g. those with traditional cultures in small urban areas are less self-interested) . Another study has shown that there are some similarities in the development of cognitive skills that have impacts on allocation and distribution . Whether the definition of equity is found consistent or inconsistent, it is clear that there are certain cognitive abilities that change the way people allocate resources. The ability to assess what people have contributed to an operation and dividing resources according to those contributions are the two variables that a child has to maintain in their mind. Furthermore, the relationships between these two variables must also be processed, which can be difficult for younger kids. Hook and Cook categorize these logical mathematical skills and what can be expected when kids obtain them . This is useful when trying to map a trajectory on how humans will behave in game theory game scenarios, especially the ultimatum game.
The economic view of fairness is often static and focused on the individual’s needs. Normally this assumption leads researchers to believe that humans are inherently selfish and will not give unless their outcome is better if they did give. Through proportional reasoning and inequity aversion, we can see that this is not the case. Although one could argue that feeling uncomfortable with inequity is enough of an economic reason to give, it can also be argued that the underlying concept of fairness is key and leads humans to act economically irrationally. As illustrated in this review, it is clear that humans develop definitions of equity in stages and that acting completely selfishly is not the only outcome in sharing scenarios.
An additional factor to consider when investigating how children play game theory games is how they determine the reliability of the person they are interacting with. In this review, reliability will be defined as being able to trust that the other person will do what is predicted they will do. It is important to be reliable in situations of strategy and cooperation because being unreliable makes it hard to predict what will happen in the future. It is also a valuable skill to be able to know when someone is reliable so that the best possible strategy can be made for oneself.
Reliability affects how children play game theory games because being able to determine trustworthiness can change the outcome. Gummerum and colleagues discovered that pregame communication can positively affect cooperation between the players . Communication could lead to further understanding and trust in games such as the ultimatum game which could lead to more generous offers or more lenient acceptances of proposals. The literature on people communicating before they play the ultimatum game is not abundant. In one study, the researchers asked teachers to rate how well a child knew their partner with whom they played the ultimatum game . The researchers did not find a link between how well children knew their partner and how fair their offers were. However, it is not clear if teachers’ assessments of children’s relationships is a good indicator of how friendly and communicative children would be with their partners. In future work, it would be useful to directly manipulate children’s communication with and knowledge of their partner to identify developmental trends in how they trust in competitive situations.
In another study, Koenig and Harris tested the ability of children to determine trustworthiness of individuals in three experiments where a video clip of actors would point at objects and say what they were . In each experiment, a different introduction procedure would be used to frame the actors and objects in the video in a different way. The researchers found that there were certain tasks that children can and cannot do at certain ages. Specifically, it was found that three-year-olds cannot figure out who to trust in the future, while four-year-olds can. Furthermore, it was found that three and four-year-olds can both distinguish between knowledgeable informants and ignorant informants as well as detect verbal and nonverbal cues to determine trustworthiness. These results suggest that children can perceive others as trustworthy from around age four, which shows that there is potential that the perceived trustworthiness of an individual can affect the outcome of game theory games. For example, if one person deemed their counterpart untrustworthy in the prisoner’s dilemma game, a game where working together can lead to the best outcome for both players, they might choose to act selfishly rather than cooperate. Or, in the ultimatum game, if the proposer deems the responder unreliable, then they might pursue a bigger or smaller offer depending on how they are feeling.
Reliability and trustworthiness have been demonstrated to be influential factors in understanding how children interact during game theory games. Since people are constantly analyzing whether others can be trusted, an ability which children also have, one might wonder what the implications are during these tasks. Future studies could look into how economics can model reliability and trustworthiness as they affect how people behave in a strategic world.
The purpose of this review was to close the gap between what economists deem rational and irrational by reviewing the literature in developmental psychological research. By investigating children and how their cognitive abilities develop, both economists and psychologists can better predict how adults behave in strategic situations. Theory of mind is a key factor in how fair children will be when sharing resources because they understand what other children are thinking. The ability to compute proportional ratios give children the ability to decide equity when allocating reward between children who have done varying amounts of work. Determining reliability and trustworthiness have implications in how children behave during strategic tasks theoretically, although more research on this should be explored.
This review has implications in how rationality is formed in people from a young age. By exploring cognitive abilities and how these abilities develop, one can examine behavior during game theory games in a different light. Instead of viewing humans as completely self-interested beings looking for a mathematical equilibrium, one can describe them as complex entities who take into account multiple different variables before making a strategic decision. While many economic conclusions derived from game theory have powerful utility to many fields of study, one must consider cognitive abilities as well as human behavior is intricate. Overall, the literature suggests that cognitive behaviors influence economic decision making and taking developmental psychology research into consideration might be helpful when trying to understand irrational choices.
The author would like to thank Dr. Viridiana Benitez for mentorship and guidance and Prof. Jenny Saffran for continuous support and supervision.
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