A New Theory Of Nested Decision Processes With Memory

Choice problems are concerned with agents (such as individuals and firms) who have to select one alternative from a set of alternatives. Static models for such processes are well known, e.g., the multinomial logit model. However, such models are limited in their usefulness since the time factor is excluded. In addition, the introduction of social interaction among the individuals involved in the choice process is not allowed in most models. This paper aims to overcome these limitations. The choice process is treated in a stochastic framework, using a master equation approach. This means that uncertainties can be introduced in the perception of the relative advantages of the choice alternatives as seen by the agent. It is well known that synergy effects play a crucial role in most choice considerations. Those effects can be treated via the introduction of appropriate transition rates and yield the dynamics of the probability that a certain distribution of choices can be found, with the multinomial logit solution as a limiting case. Nested decision structures, i.e., decisions at a certain time that are influenced by all previous choices are of greater interest. The dynamic modeling of such a sequence of decisions requires new ideas and a detailed analysis of every single step. The possibility of both the arisal of new alternatives and of the disappearance of old ones must be taken into account. Small differences in subsequent utilities could lead to a dynamic selection process of a specific alternative. The stochastic choice model can be applied to problems of neural networks, to innovation theory and travel choice, among others.