Social networks and dynamic interaction among imperfectly rational agents

The first chapter models the dynamics of social norms. Each person in an infinite population decides in each period whether to adhere to a norm or not. The decision is stochastic. Each person is characterized by a probability of adherence. The adherence probabilities evolve over time through social interactions. Each person in each period observes one other person's norm adherence. The first person adjusts his or her probability of adherence up or down according to whether the second person is observed adhering to the norm or not. The network matrix is very simple. Each person observes another person determined solely at random from all other people in the population--uniform global matching. Under these strong assumptions, a full characterization of dynamic equilibria is possible.; The second chapter extends the model of the first chapter in several ways. The population is now finite instead of infinite; the number of actions is arbitrary instead of two; and, most importantly, the network matrix representing social interaction is general instead of restricted to uniform global random matching. Although results as detailed as those in the first chapter are no longer possible, a variety of useful results are found for a variety of specific models. A major theme of the chapter is that results often hold under much more general network assumptions than are typically used in the literature. In particular, such highly restrictive assumptions as uniform global networks or low dimensional lattices are often not needed.; The third chapter changes subjects relative to the first two, though still concerned with dynamic adaptive behavior and social interaction. The third chapter examines the dynamic justification for mixed-strategy Nash equilibria. Though Nash equilibrium is the central equilibrium concept of game theory, it has always been troublesome to justify how players find a Nash equilibrium. Various recent models of adaptation have had substantial success in showing how players might find pure strategy equilibria. However, adaptive models still have great difficulties showing how players might find a mixed strategy equilibrium. The third chapter is a critical survey and discussion of the difficulties.