The Master Equation in Dynamic Decision Theory

Our interest in this chapter is confined to the observation of the time path of certain macro-states like the dynamics of the number of agents having decided for a specific alternative out of a set of alternatives and possible interactions between agents and different groups of agents. Since decisions have to be made under conditions of uncertainty, a stochastic description is adequate. Moreover, it is decisive to understand the matching or link between the micro level, characterized by decisions of single individuals and their driving forces, respectively, and the macro-level, describing the aggregate behaviour of the population of agents. Instead of the economics-dominated utility function concept, Akerlof and Kranton (Q J Econ 115(3): 715–753, 2000) introduced social identities into standard economics by expanding the utility concept. In other words, the individual benefit may depend on group processes and the behaviour of other decision makers. In so far, the social context becomes relevant. After introducing the discrete choice approach, especially the probit model and the multinomial logit model, the dynamic Master equation decision model will be discussed. This decision model incorporates interactions between individuals and social groups. Furthermore, the extension of the Master equation decision model to nested decision processes with memory is presented. As an example the emergence of conventions will be investigated.