On the generalization of evolutionary continuous model in random markets

Authors
Elyas Shivanian 1
Mahdi Keshtkar 2
Hamid Reza Navidi 3
1 Imam Khomeini International University
2 Buein Zahra University
3 Shahed University
Abstract
A generalization of the continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way, in general, with possibly non- constant total amount of “money”. This model takes the form of an iterated nonlinear map of the distribution of wealth. We show the only way to reach equilibrium fixed point distribution is the agents to share their money without expansion or contraction factor. Furthermore, it is proved the higher momenta of the distribution exist and the iteration of higher momenta becomes stable under some specific conditions.
Keywords
equilibrium state
evolutionary model
nonlinear operator
Random markets
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