<p>In the first chapter of this dissertation, I develop a new model of learning and level-k reasoning in games. My model frames attraction learning in the language of beliefs and extends it to include two important features. The first of these features is an implicit pattern recognition mechanism that learns the importance of contextual information, while the second is a nonlinear probability weighting function with an endogenous fixed point location. The resulting beliefs determine level-1 behavior in a larger level-k rule learning model. In keeping with the literature, I assume that rule learning occurs according to a reinforcement learning mechanism, but I improve the approximation of latent rule reinforcements to simulate the effect of rule exercise. A cognitive foundation for the full model is also provided by implementing it within the ACT-R cognitive architecture.</p> <p><br></p> <p>The second chapter investigates the extent to which human agents use level-k reasoning in repeated mixed strategy games. Towards this end, the Chapter 1 model is estimated using data from a novel experiment. The experiment consisted of two between-subject treatments: in one treatment, the information provided was sufficient to use any level of reasoning, while in the other treatment subjects were only provided with enough information to be level-1.  A random effects model is estimated using the data from both treatments to identify the model's belief learning parameters.  In the unrestricted treatment, I find that subjects learned to engage almost exclusively in level-1 reasoning. Simulations suggest that this result may be explained by the difficulty of exploiting a player who is level-1.</p>

Experimental tests of choice predictions in one-shot games show only little support for Nash equilibrium (NE). Poisson Cognitive Hierarchy (PCH) and level-k (LK) are behavioral models of the thinkingsteps variety where subjects differ in the number of levels of iterated reasoning they perform. Camerer et al. (2004) claim that substituting the Poisson parameter = 1:5 yields a parameter-free PCH model (pfPCH) which predicts experimental data considerably better than NE. We design a new multi-person game, the Minimizer Game, as a testbed to compare initial choice predictions of NE, pfPCH and LK. Data obtained from two large-scale online experiments strongly reject NE and LK, but are well in line with the point-prediction of pfPCH.

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&gt;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. / <p>Diss. Stockholm : Handelshögskolan, 2010. Sammanfattning jämte 4 uppsatser.</p>

Experimental tests of choice predictions in one-shot games show only little support for Nash equilibrium (NE). Poisson Cognitive Hierarchy (PCH) and level-k (LK) are behavioral models of the thinking-steps variety where subjects differ in the number of levels of iterated reasoning they perform. Camerer et al. (2004) claim that substituting the Poisson parameter tau = 1.5 yields a parameter-free PCH model (pfPCH) which predicts experimental data considerably better than NE. We design a new multi-person game, the Minimizer Game, as a testbed to compare initial choice predictions of NE, pfPCH and LK. Data obtained from two large-scale online experiments strongly reject NE and LK, but are well in line with the point prediction of pfPCH. / Series: Department of Economics Working Paper Series

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<div>This thesis consists of three chapters. In the first chapter, I investigate the effects of complexity in various voting systems on individual behavior in small group electoral competitions. Using a laboratory experiment, I observe individual behavior within one of three voting systems -- plurality, instant runoff voting (IRV), and score then automatic runoff (STAR). I then estimate subjects' behavior in three different models of bounded rationality. The estimated models are a model of Level-K thinking (Nagel, 1995), the Cognitive Hierarchy (CH) model (Camerer, et al. 2004), and a Quantal Response Equilibrium (QRE) (McKelvey and Palfrey 1995). I consistently find that more complex voting systems induce lower levels of strategic thinking. This implies that policy makers desiring more sincere voting behavior could potentially achieve this through voting systems with more complex strategy sets. Of the tested behavioral models, Level-K consistently fits observed data the best, implying subjects make decisions that combine of steps of thinking with random, utility maximizing, errors.</div><div><br></div><div>In the second chapter, I investigate the relationship between the mechanisms used to select leaders and both measures of group performance and leaders' ethical behavior. Using a laboratory experiment, we measure group performance in a group minimum effort task with a leader selected using one of three mechanisms: random, a competition task, and voting. After the group task, leaders must complete a task that asks them to behave honestly or dishonestly in questions related to the groups performance. We find that leaders have a large impact on group performance when compared to those groups without leaders. Evidence for which selection mechanism performs best in terms of group performance seems mixed. On measures of honesty, the strongest evidence seems to indicate that honesty is most positively impacted through a voting selection mechanism, which differences in ethical behavior between the random and competition selection treatments are negligible.</div><div><br></div><div><br></div><div>In the third chapter, I provide an investigation into the factors and conditions that drive "free riding" behavior in dynamic innovation contests. Starting from a dynamic innovation contest model from Halac, et al. (2017), I construct a two period dynamic innovation contest game. From there, I provide a theoretical background and derivation of mixed strategies that can be interpreted as an agent's degree to which they engage in free riding behavior, namely through allowing their opponent to exert effort in order to uncover information about an uncertain state of the world. I show certain conditions must be fulfilled in order to induce free riding in equilibrium, and also analytically show the impact of changing contest prize structures on the degree of free riding. I end this paper with an experimental design to test these various theoretical conclusions in a laboratory setting while also considering the behavioral observations recorded in studies investigating similar contest models and provide a plan to analyze the data collected by this laboratory experiment.</div><div><br></div><div>All data collected for this study consists of individual human subject data collected from laboratory experiments. Project procedures have been conducted in accordance with Purdue's internal review board approval and known consent from all participants was obtained.</div>

<p>Diss. Stockholm : Handelshögskolan, 2008 Sammanfattning jämte 5 uppsatser</p>

The general topic of our thesis is forward looking behavior in strategic situations. Mixing theoretical and experimental analysis, we document how strategic thinking is affected by the specific features of a dynamic interaction. The overarching result is that the information regarding decisions that are close to the current one, receive a qualitatively different consideration, with respect to distant ones. That is, the actual decisions are based on reasoning over a limited number of steps, close to actual decison node. We capture this feature of behavior both in a strategic (limited backward induction) and in a non-strategic (limited farsightedness) set up, and we identify relevant consequences on the outcome of the interaction, which powerfullly explain many observed experimental regularities.<p>In the first essay, we present a general out-of-equilibrium framework for strategic thinking in sequential games. It assumes the agents to take decisions on restricted game trees, according to their (limited) foresight level, following backward induction. Therefore we talk of limited backward induction (LBI). We test for LBI using a variant of the race game. Our design allows to identify restricted game trees and backward reasoning, thus properly disentangling LBI behavior. The results provide strong support in favor of LBI. Most players solve intermediate tasks - i.e. restricted games - without reasoning on the terminal histories. Only a small fraction of subjects play close to equilibrium, and (slow) convergence toward it appears, though only in the base game. An intermediate task keeps the subjects off the equilibrium path longer than in the base game. The results cannot be rationalized using the most popular models of strategic reasoning, let alone equilibrium analysis.<p>In the second essay, a subtle implication of the model is investigated: the sensitivity of the players’ foresight to the accessibility and completeness of the information they have, using a Centipede game. By manipulating the way in which information is provided to subjects, we show that reduced availability of information is sufficient to shift the distribution of take-nodes further from the equilibrium prediction. On the other hand, similar results are obtained in a treatment where reduced availability of information is combined with an attempt to elicit preferences for reciprocity, through the presentation of the centipede as a repeated trust game. Our results could be interpreted as cognitive limitations being more effective than preferences in determining (shifts in) behavior in our experimental centipede. Furthermore our results are at odds with the recent ones in Cox [2012], suggesting caution in generalizing their results. Reducing the availability of information may hamper backward induction or induce myopic behavior, depending on the strategic environment.<p>The third essay consists of an experimental investigation of farsighted versus myopic behavior in network formation. Pairwise stability Jackson and Wolinsky [1996] is the standard stability concept in network formation. It assumes myopic behavior of the agents in the sense that they do not forecast how others might react to their actions. Assuming that agents are perfectly farsighted, related stability concepts have been proposed. We design a simple network formation experiment to test these extreme theories, but find evidence against both of them: the subjects are consistent with an intermediate rule of behavior, which we interpret as a form of limited farsightedness. On aggregate, the selection among multiple pairwise stable networks (and the performance of farsighted stability) crucially depends on the level of farsightedness needed to sustain them, and not on efficiency or cooperative considerations. Individual behavior analysis corroborates this interpretation, and suggests, in general, a low level of farsightedness (around two steps) on the part of the agents. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished