Role of Neighbouring Wealth Preference in Kinetic Exchange model of market

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.