  In this invited book chapter, we draw the reader to a brief review of the
different Kinetic Exchange Models (KEMs) that have gradually developed for
markets and how they can be employed to quantitatively study inequalities (the
Gini Index and the Kolkata Index) that pervade real economies. Since a
many-body economical market can be studied using tested laws of physics, these
models have the freedom to incorporate provisions like inclusion of individual
saving behaviors while trading and rendering these saving behaviors to be
time-independent and time-dependent respectively. This is to observe when and
how the well known exponential distribution for no-saving gives rise to a
distribution with a most probable income. A review of the earlier cases along
with their implementation with a bias, where the population in the low-income
bracket of the society is favored by selecting one of the traders in the
trading process to be the poorest of all, follows. The biased selection of
agents ultimately giving rise to self-organizing features in the money
distribution has also been reviewed in detail, using the behavior of the
Self-Organized Poverty Level. In the end, we elucidate the recent endeavors of
the KEMs in finding answers to the growing condensation of wealth in the hands
of a countable few rich people and providing probable solutions that can curb
further expansion of oligarchic societies.
