Essays on belief formation and pro-sociality

Abstract: This thesis consists of four independent papers. The first two papers use experimental methods to study pro-social behaviors. The other two use theoretical methods to investigate questions about belief formation. The first paper “Communication: Content or Relationship?” investigates the effect on communication on generosity in a dictator game. In the basic experiment (the control), subjects in one room are dictators and subjects in another room are recipients. The subjects are anonymous to each other throughout the whole experiment. Each dictator gets to allocate a sum of 100 SEK between herself and an unknown recipient in the other room. In the first treatment we allow each recipient to send a free-form message to his dictator counterpart, before the dictator makes her allocation decision. In order to separate the effect of the content of the communication, from the relationship-building effect of communication, we carry out a third treatment, where we take the messages from the previous treatment and give each of them to a dictator in this new treatment. The dictators are informed that the recipients who wrote the messages are not the recipients they will have the opportunity to send money to. We find that this still increases donation compared to the baseline but not as much as in the other treatment. This suggests that both the impersonal content of the communication and the relationship effect matters for donations. The second paper, “Limbic justice – Amygdala Drives Rejection in the Ultimatum Game”, is about the neurological basis for the tendency to punish norm violators in the Ultimatum Game. In the Ultimatum Game, a proposer proposes a way to divide a fixed sum of money. The responder accepts or rejects the proposal. If the proposal is accepted the proposed split is realized and if the proposal is rejected both subjects gets zero. Subjects were randomly allocated to receive either the benzodiazepine oxazepam or a placebo substance, and then played the Ultimatum Game in the responder role, while lying in and fMRI camera. Rejection rate is significantly lower in the treatment group than in the control group. Moreover a mygdala was relatively more activated in the placebo group than in the oxazepam group for unfair offers. This is mirrored by differences in activation in the medial prefrontal cortex (mPFC) and right ACC. Our findings suggest that the automatic and emotional response to unfairness, or norm violations, are driven by amygdala and that balancing of such automatic behavioral responses is associated with parts of the prefrontal cortex. The conflict of motives is monitored by the ACC. In order to decide what strategy to choose, a player needs to form beliefs about what other players will do. This requires the player to have a model of how other people form beliefs – what psychologists call a theory of mind. In the third paper “Evolution of Theories of Mind” I study the evolution of players’ models of how other players think. When people play a game for the first time, their behavior is often well predicted by the level-k, and related models. According to this model, people think in a limited number of steps, when they form beliefs about other peoples' behavior. Moreover, people differ with respect to how they form beliefs. The heterogeneity is represented by a set of cognitive types {0,1,2,...}, such that type 0 randomizes uniformly and type k>0 plays a k times iterated best response to this. Empirically one finds that most experimental subjects behave as if they are of type 1 or 2, and individuals of type 3 and above are very rare. When people play the same game more than once, they may use their experience to predict how others will behave. Fictitious play is a prominent model of learning, according to which all individuals believe that the future will be like the past, and best respond to the average of past play. I define a model of heterogeneous fictitious play, according to which there is a hierarchy of types {1,2,...}, such that type k plays a k time iterated best response to the average of past play. The level-k and fictitious play models, implicitly assume that players lack specific information about the cognitive types of their opponents. I extend these models to allow for the possibility that types are partially observed. I study evolution of types in a number of games separately. In contrast to most of the literature on evolution and learning, I also study the evolution of types across different games. I show that an evolutionary process, based on payoffs earned in different games, both with and without partial observability, can lead to a polymorphic population where relatively unsophisticated types survive, often resulting in initial behavior that does not correspond to a Nash equilibrium. Two important mechanisms behind these results are the following: (i) There are games, such as the Hawk-Dove game, where there is an advantage of not thinking and behaving like others, since choosing the same action as the opponent yields an inefficient outcome. This mechanism is at work even if types are not observed. (ii) If types are partially observed then there are Social dilemmas where lower types may have a commitment advantage; lower types may be able to commit to strategies that result in more efficient payoffs. The importance of categorical reasoning in human cognition is well-established in psychology and cognitive science, and one of the most important functions of categorization is to facilitate prediction. Prediction on the basis of categorical reasoning is relevant when one has to predict the value of a variable on the basis of one's previous experience with similar situations, but where the past experience does not include any situation that was identical to the present situation in all relevant aspects. In such situations one can classify the situation as belonging to some category, and use the past experiences in that category to make a prediction about the current situation. In the fourth paper, “Optimal Categorization”, I provide a model of categorizations that are optimal in the sense that they minimize prediction error. From an evolutionary perspective we would expect humans to have developed categories that generate predictions which induce behavior that maximize fitness, and it seems reasonable to assume that fitness is generally increasing in how accurate the predictions are. In the model a subject starts out with a categorization that she has learnt or inherited early in life. The categorization divides the space of objects into categories. In the beginning of each period, the subject observes a two-dimensional object in one dimension, and wants to predict the object’s value in the other dimension. She has a data base of objects that were observed in both dimensions in the past. The subject determines what category the new object belongs to on the basis of observation of its first dimension. She predicts that its value in the second dimension will be equal to the average value among the past observations in the corresponding category. At the end of each period the second dimension is observed, and the observation is stored in the data base. The main result is that the optimal number of categories is determined by a trade-off between (a) decreasing the size of categories in order to enhance category homogeneity, and (b) increasing the size of categories in order to enhance category sample size. In other words, the advantage of fine grained categorizations is that objects in a category are similar to each other. The advantage of coarse categorizations is that a prediction about a category is based on a large number of observations, thereby reducing the risk of over-fitting. Comparative statics reveal how the optimal categorization depends on the number of observations as well as on the frequency of objects with different properties. The set-up does not presume the existence of an objectively true categorization “out there”. The optimal categorization is a framework we impose on our environment in order to predict it.