| In this dissertation a variety of social interaction dynamics are studied concerning the question of how conventions come to be established. In chapter I, each person is characterized by his or her probability of adhering to the norm. At random, people observe the adherence behavior of others and, from period to period, adjust their own adherence probabilities in a corresponding direction. In a main case of the model, the distribution of adherence probabilities gradually evolves upward or downward, depending on initial conditions, until the population is in strong (possibly unanimous) conformity with the norm or in strong rejection of it. In other cases of the model, there is a single stable equilibrium (either adherence to or rejection of the norm). The population is infinite (a continuum) and the social network displays "uniform global interaction". In contrast, the other two chapters assume a finite population and a much more general social network.; In Chapter II, various existing models and new variants are discussed within a common mathematical framework. The emphasis is on highly general social networks and on various combinations of individual adjustment ingredients--imitation, purely random choice, thresholds, pure and mixed action rules, linear and nonlinear responses, and so on. The standard network assumptions in the literature are uniform global interaction and near neighbor lattices. A series of theorems demonstrates that results on evolution to unanimity are robust to much broader network specifications.; In Chapter III, we analyze deterministic and random versions of a threshold model. In the deterministic version, we identify a class of interaction structures--"radius uniform interaction"--which leads to unanimity. The radius uniform pattern is more general than uniform global interaction and uniform near neighbor interaction on a lattice. In the random version, we consider the two most common types of randomness--"log-linear" and "mistakes." In each case, we provide substantial generalizations of the interaction patterns under which unanimity results hold. |
