  The kinetic exchange model has gained popularity in the field of statistical
mechanics for investigating wealth interaction. Traditionally, kinetic exchange
models have been studied without considering preferential interactions.
However, in this study, we introduce two types of preferential interactions to
explore wealth dynamics and its associated distributions. In the first
preference, one agent is randomly selected, while the other agent is chosen
randomly with wealth just above or below the first agent. Through this
preference, we observe the emergence of a quasi-oligarchic society, where the
majority of the wealth cycles around the hand of very few agents. For the
second preference, we impose a constraint on the difference in pre-interaction
wealth between the two agents. This preference leads to the segregation of
society into two distinct economic classes. To investigate these phenomena, we
conducted extensive Monte Carlo simulations, enabling us to characterize the
behavior of wealth distributions in these two scenarios. Our findings shed
light on the dynamics of wealth accumulation and distribution within
preferential interactions in the context of the kinetic exchange model.
