In this paper we discuss that monetary exchange emerges in a reciprocal system which consists of donations and returns. Agents reciprocate goods alternately without bilateral agreement in the system, that is constructed not from the viewpoint of the recipient, but from the one of the reciprocator. Moreover, reciprocity is regarded as interaction with incomplete identification consisting of the alternate procedure of constructing a map from coarse-grained data by a contraction mapping and of applying the map to fine-grained data. We show that reciprocity gives rise to the monetary exchange which implies globality without the concept of metric space or global semantics. It seems that interaction with incomplete identification does not carry the notion of globality. On the contrary, in our model globality paradoxically occurs from the accumulation of indefinite incomplete identification.
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