We discuss various properties of a new ABM which is able to reproduce the most common stylized facts (arbitrage, fat tails, volatility clustering). In addition the model can be generalized to consider the problem of non-stationarity and the self-organization towards the quasi-critical state which shows the stylized facts. The phase space of the agents' strategies is divided in fundamentalists (stibilizing) and chartists (destibilizing). The key point has been to have the simplest possible model which is able to refroduce the stylized facts and their self-organization. This has the advantage that it is possible to identify the precise mathematical origin of the stylized facts. Of course this extreme semplification lucks many elements of realism. Howeveer these can be now added in a controlled way and analyzed in detail. We show the main properties of this model which was originally introduced with a liner dynamics for the price. We then consider a more realistic multiplicative dynamics and study the specific properties of each case. We also introduce the concept of entropy for the various properties and characterize the nature of  the self-organized state in this respect.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/15587 must be provided.

1. Agent Based models for Economics: Stylized Facts and their Self-organization