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

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Modeling and Simulation of Social-Behavioral Phenomena in Creative Societies (MSBC 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1717))

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Abstract

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.

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Notes

  1. 1.

    We write this equation in its traditional form, taking a notation \(P\) for transition probability matrix, but we have in mind that really it is matrix \(F(1)\) of transition probabilities for the counterfeit banknote.

  2. 2.

    Rossiyskaya Gazeta, 05.07.2022, https://rg.ru/2022/07/05/v-goznake-nazvali-naibolee-chasto-poddelyvaemye-kupiury.html, last accessed 2023/01/10.

  3. 3.

    We have also considered the initial distribution in another forms, like \(\vec{x}(0) = \left\{ {0.4,\;0.4,\;0.2,\;0,\;0} \right\}\), which approximately corresponds the situation in Russia at the turn of the century; at this time official salaries were paid to employees of state and employees of foreign firms only, pensions were negligibly small and so couldn’t motivate anybody, and lending to individuals was absent (there is no any exact statistical data about this distribution, there are only estimates obtained by research structures of commercial firms).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Financial University under the Government of Russian Federation, Moscow, Russia

    Olga Pyrkina

  2. Department of Economic Theory, Financial University under the Government of Russian Federation, Moscow, Russia

    Andrey Yudanov

Authors
  1. Olga Pyrkina
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  2. Andrey Yudanov
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Correspondence to Olga Pyrkina .

Editor information

Editors and Affiliations

  1. University of Arkansas at Little Rock, Little Rock, AR, USA

    Nitin Agarwal

  2. Central Economic Mathematical Institute of RAS, Moscow, Russia

    George B. Kleiner

  3. Vilnius Gediminas Technical University, Vilnius, Lithuania

    Leonidas Sakalauskas

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Pyrkina, O., Yudanov, A. (2023). Free-Rider Problem: Simulating of System Convergence to Stable Equilibrium State by Means of Finite Markov Chain Models. In: Agarwal, N., Kleiner, G.B., Sakalauskas, L. (eds) Modeling and Simulation of Social-Behavioral Phenomena in Creative Societies. MSBC 2022. Communications in Computer and Information Science, vol 1717. Springer, Cham. https://doi.org/10.1007/978-3-031-33728-4_6

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  • DOI: https://doi.org/10.1007/978-3-031-33728-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-33727-7

  • Online ISBN: 978-3-031-33728-4

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