Some adaptive economic processes in social interactions ∗

On the human brain activities in social interaction, there may be associated with some kind of reinforcement mechanism like crowd psychology or mimicking drive, or sometimes, creating a social mechanism like punishments. Some of such reinforcement mechanisms can be interpreted with a nonlinear Polya urn process of which W. Brian Arthur(1994) is fond. He called structure as emergence of a new combination of proportion generated by the stochastic process. In the case of unknown parameters on the distribution of a new emergent agent (mutant), as Masanao Aoki(1996) formulated, we can derive emergence of an unknown structure a new structure. In these dynamics, it is important to group by heterogeneous types in a social interaction. We have several subgroup dynamics given by either Dirk Helbing(1995,2003) or Steven Durlauf(1997,2000). On the other hand, when analyzing adaptive behaviors, replicator dynamics directly works well as an intriguing compromise device for many applications. Focusing a side of learning by adaptive agents under the flavor of the Santa Fe institute, economists began to be involved into treating multi-armed bandit problem, in the event, adopting loss minimizations in the face of uncertainty. The rigid worlds of optimization characterized by the duality notions shall be replaced in economics soon. Leaving from the rigid world of optimization, we will perform some appropriate models of path-independent process as well as path-dependent process on adaptive economic processes in social interactions of heterogeneous agents. By the use of them, microscopic orders of the society can be discussed properly under a certain macroscopic order. A prominent of model on path-independent process will appear from Aoki(1996, 2001), and a prominent one on path-dependent from Arthur(1994). ∗The first draft of this paper was presented at International Nonlinear Sciences Conference, February 7–9, 2003, Vienna, Austria. IBRCU Working Paper No.9,Arpil 2003 2