1999 Volume 14 Issue 2 Pages 2_53-2_71
This paper explains simple mathematical models, all of which are devised by way of abstracting practical simulation models. First, following on Ackoff & Emery's discussion on ‘purposeful system’, the ‘conceptualization’ and ‘formalization’ of our ‘autonomy agent’ are presented. Each of the agent has an internal model, in order to deal with intellectual functions such as ‘cognition’, ‘learning’, ‘forecasting’, ‘planning’ and so on.
The first model is formulated as a decision model under a bounded rationality caused by his/her internal cognition model. Some mathematical concepts are also defined such as three kinds of ‘learning processes’, on which his/her internal model are transformed. ‘Model space’ and other concepts are also introduced.
The second model is formulated by introducing the first ones into a hierarchy system theory. This poly-agent system is designed as not a model of ‘incrementalism system’ but ‘hierarchical planning system’ for public administration. The hypergame theory is also referred as an example of game-theoretical situation consisted of the first ones. From the point of view of ‘problem solving- oriented’ modeling, a hybrid approach of such three kinds of model: mathematical model, computer multi-agent model, and gaming-simulation model, is presented. The mathematical models are expected to form a basis for designing the latter two operational simulation models; computer simulation and gaming simulation. Some potential implications on mathematical sociology are also suggested.
