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We present a detailed analysis of the self-organization phenomenon in whichthe stylized facts originate from finite size effects with respect to thenumber of agents considered and disappear in the limit of an infinitepopulation. By introducing the possibility that agents can enter or leave themarket depending on the behavior of the price, it is possible to show that thesystem self-organizes in a regime with a finite number of agents whichcorresponds to the stylized facts. The mechanism to enter or leave the marketis based on the idea that a too stable market is unappealing for traders whilethe presence of price movements attracts agents to enter and speculate on themarket. We show that this mechanism is also compatible with the idea thatagents are scared by a noisy and risky market at shorter time scales. We alsoshow that the mechanism for self-organization is robust with respect tovariations of the exit/entry rules and that the attempt to trigger the systemto self-organize in a region without stylized facts leads to an unrealisticdynamics. We study the self-organization in a specific agent based model but webelieve that the basic ideas should be of general validity.

Mechanisms of Self-Organization and Finite Size Effects in a Minimal Agent Based Model