Rationality Model and Choice Optimization: One Answer to Aumann\´s "Open Problem" and One Introduction to a New Mathematical Tool

The dynamical process of choice optimization is the realistic starting point of constructing dynamical economics or evolutionary economics. Rationality model is the logical basis for choice optimization. But in fact, as the common theoretical base in modern economics, rationality modeling is a complex problem unsolved. In this paper, a model of natural rationality (R) is introduced, and R is defined as nonlinear function of agent\´s output benefits (OBS) and input costs (ICS). This mathematical model of natural rationality can be considered as one answer to Aumann\´s "open problem". On the basis of the rationality model, mathematical model of natural rationality is compared with model of bounded (or incomplete) rationality and unbounded (or complete) rationality, and their relations are analyzed according to the completeness degree of information. At last, the dynamic optimization process of rational choice on the basis of mathematical model of natural rationality is introduced.