Kinetic models of immediate exchange

We propose a novel kinetic exchange model differing from previous ones in two main aspects. First, the basic dynamics is modified in order to represent economies where immediate wealth exchanges are carried out, instead of reshufflings or uni-directional movements of wealth. Such dynamics produces wealth distributions that describe more faithfully real data at small values of wealth. Secondly, a general probabilistic trading criterion is introduced, so that two economic units can decide independently whether to trade or not depending on their profit. It is found that the type of the equilibrium wealth distribution is the same for a large class of trading criteria formulated in a symmetrical way with respect to the two interacting units. This establishes unexpected links between and provides a microscopic foundations of various kinetic exchange models in which the existence of a saving propensity is postulated. We also study the generalized heterogeneous version of the model in which units use different trading criteria and show that suitable sets of diversified parameter values with a moderate level of heterogeneity can reproduce realistic wealth distributions with a Pareto power law