Free-Rider Problem: Simulating of System Convergence to Stable Equilibrium State by Means of Finite Markov Chain Models

The paper suggests a new approach to classic economic problem – “the problem of free-rider”. This well – known problem deals with a process of unrequited consumption of collective goods, and it can be considered as a problem of unfailing interest for economy of each frame of a society. The authors put forward and idea of spontaneous process self-regulation by means of economic instruments and give a description of possible problem solution. The approach suggested includes the control of “free-rider” activity by economic and social agents directly interacting with him. In spite of non-rivalry in consumption, the case when “free-rider” disserves the interests of his nearest surrounding, will results in increasing antagonism and suppression of “free-rider” activity spreading. A mathematical model reflecting authors view is based on Markov chains with absorbing states, created on the base of graph depicting an interaction of “free-rider” with his neighborhood. The simulation represents system convergence from arbitrary initial state to a stable final distribution for Markov chain, demonstrating an opportunity of system self-adjustment.