| Summary: | This paper presents a simple multi-agent model of group formation, while the behaviour is complicated. The statistical characteristics of the formation are suddenly changed at some states. Their agents are carrying characteristic vectors, meet each other in nondimensional free spaces without any restrictions randomly, and the agents make groups in the spaces if their characteristics are similar, that is, they have high similarities. Actually, for a given threshold on similarities, when the characteristic vectors between two agents are similar in the threshold, the agents join into one. They are not only for agents but also for groups, i.e. two groups can become into one if they are similar, and we repeat it. On the other hand, making groups decrease a satisfaction on groups. In this paper, we show, for a given threshold, there is not only an optimal threshold to maximize the satisfactions among groups which satisfy the threshold, but also the other one to minimize the satisfactions. The thresholds to maximize satisfactions are experimentally approximated by some function on the size of characteristic vectors rather than the number of agents.
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