In view of some persistent recent reports on a singular kind of growth of the
world wealth inequality, where a finite (often handful) number of people tend
to possess often more than the wealth of the planet's 50\% population, we
explore here if the kinetic exchange models of the market can ever capture such
features where a significant fraction of wealth can concentrate in the hands of
a countable few when the market size N tends to infinity. One already
existing example of such a kinetic exchange model is the Chakraborti or
Yard-Sale model, where (in absence of tax redistribution etc) the entire wealth
condenses in the hand of one (for any N), and the market dynamics stops. With
tax redistribution etc, its steady state dynamics have been shown to have
remarkable applicability in many cases of our extremely unequal world. We show
here, another kinetic exchange model (called here the Banerjee model) has
intriguing intrinsic dynamics, by which only ten rich traders or agents possess
about 99.98\% of the total wealth in the steady state (without any tax etc like
external manipulation) for any large value of N. We will discuss in some
detail the statistical features of this model using Monte Carlo simulations. We
will also show, if the traders each have a non-vanishing probability f of
following random exchanges, then these condensations of wealth (100\% in the
hand of one agent in the Chakraborti model, or about 99.98\% in the hands ten
agents in the Banerjee model) disappear in the large N limit. We will also
see that due to the built-in possibility of random exchange dynamics in the
earlier proposed Goswami-Sen model, where the exchange probability decreases
with an inverse power of the wealth difference of the pair of traders, one did
not see any wealth condensation phenomena.Comment: 10 pages and 9 figures; Invited paper in the Special Issue on
"Statistical Physics and Its Applications in Economics and Social Sciences",
in Entrop