Game of collusions

A new model of collusions in an organization is proposed. Each actor ai=1,…,N disposes one unique good gi=1,…,N. Each actor ai has also a list of other goods which he/she needs, in order from desired most to those desired less. Finally, each actor ai has also a list of other actors, initially ordered at random. The order in the last list means the order of the access of the actors to the good gi. A pair after a pair of actors tries to make a transaction. This transaction is possible if each of two actors can be shifted upwards in the list of actors possessed by the partner. Our numerical results indicate, that the average time of evolution scales with the number N of actors approximately as N2.9. For each actor, we calculate the Kendall's rank correlation between the order of desired goods and actor's place at the lists of the good's possessors. We also calculate individual utility functions ηi, where goods are weighted according to how strongly they are desired by an actor ai, and how easily they can be accessed by ai. Although the individual utility functions can increase or decrease in the time course, its value averaged over actors and independent simulations does increase in time. This means that the system of collusions is profitable for the members of the organization.