Lucky numbers: Choice strategies in the Pennsylvania Daily Number game

Examined the amount of money bet during a week of Pennsylvania's Daily Number game. In this game, players receive a predetermined payoff for picking the 3-digit number (000 to 999) drawn on that day. The betting distribution was distinctly nonuniform. Several betting patterns were identified, such as picking triples and avoiding double 9s. In addition, 121 adults and 215 students were asked to rate selected numbers for randomness, luckiness, and perceived history of winning; to categorize numbers; and to free associate to numbers. It is proposed that people seem to choose highly patterned, available, and/or "lucky" numbers. People apparently do not bet numbers that reflect the random process of the game (do not utilize a representativeness heuristic).

Dynamics of Spatial Game Theory Networks with Novel Modifications

Introduction: Advances in biotechnology have shed light on many biological processes. In biological networks, nodes are used to represent the function of individual entities within a system and have historically been studied in isolation. Network structure adds edges that enable communication between nodes. An emerging fieldis to combine node function and network structure to yield network function. One of the most complex networks known in biology is the neural network within the brain. Modeling neural function will require an understanding of networks, dynamics, andneurophysiology. It is with this work that modeling techniques will be developed to work at this complex intersection. Methods: Spatial game theory was developed by Nowak in the context of modeling evolutionary dynamics, or the way in which species evolve over time. Spatial game theory offers a two dimensional view of analyzingthe state of neighbors and updating based on the surroundings. Our work builds upon this foundation by studying evolutionary game theory networks with respect to neural networks. This novel concept is that neurons may adopt a particular strategy that will allow propagation of information. The strategy may therefore act as the mechanism for gating. Furthermore, the strategy of a neuron, as in a real brain, isimpacted by the strategy of its neighbors. The techniques of spatial game theory already established by Nowak are repeated to explain two basic cases and validate the implementation of code. Two novel modifications are introduced in Chapters 3 and 4 that build on this network and may reflect neural networks. Results: The introduction of two novel modifications, mutation and rewiring, in large parametricstudies resulted in dynamics that had an intermediate amount of nodes firing at any given time. Further, even small mutation rates result in different dynamics more representative of the ideal state hypothesized. Conclusions: In both modificationsto Nowak's model, the results demonstrate the network does not become locked into a particular global state of passing all information or blocking all information. It is hypothesized that normal brain function occurs within this intermediate range and that a number of diseases are the result of moving outside of this range.

Capuchin Monkeys (Cebus apella) Fail to Be Equitable in an Ultimatum Game

The ultimatum game is a commonly used economics game testing humans' sense of fairness. In the game, a "proposer" is given a sum of money and is told they can split it however they want with another human partner. The partner can then either accept the division and both proposer and responder receive the proposed amounts, or the responder can reject the offer and neither player will get anything. Human subjects from most western cultures typically share almost half of an allotted amount, but it remains unknown whether our close primate relatives share this generosity. Recent attempts to present chimpanzees with the ultimatum game have provided inconclusive results, with some studies finding the animals share humans' disposition to behave 'fairly' and others concluding that chimpanzees act selfishly to maximize their own rewards. Capuchin monkeys are known to share many human and chimpanzee social and cooperative behaviors, and this study was the first to present capuchin monkeys with a version of the ultimatum game. Subjects were presented with two differently colored tokens representing different qualitative reward contingencies, one equitable and the other inequitable in favor of the subject proposer. Subjects could select and place one of the tokens in a transfer container. The capuchins were first tested with a "dictator game" where, after the subject monkey selected a token, the rewards (equitable or inequitable) were distributed to the subject and a nearby partner monkey that was not an active participant. The capuchins were then tested on an ultimatum game in which after the subject selected and placed a token in the container, the container was moved to the partner. The partner needed to remove the token and transfer it back to the experimenter for the rewards to be distributed. As such, the partner could reject the subject's offer by refusing to participate and neither would receive a reward. The experiment was conducted to determine if the subject monkey would select the equitable reward option rather than the selfish option in order to maintain the partner's cooperation in the task. Capuchin subjects behaved selfishly and selected the inequitable token significantly more often than the equitable token in both the dictator and ultimatum game with no significant difference in preference between the two games. Interestingly, despite the occasional occurrence of rejection by the partner monkeys (resulting in no reward for the subject), subjects never altered their strategy, continuing to prefer the selfish token. The study may indicate that capuchin monkeys have an inability to judge the effect of their behavior on a conspecific's reward outcome, or an indifference to the outcome if there is an individual cost associated with behaving prosocially.