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Stochastic Model of Network Formation with Asymmetric Players

  • MATHEMATICAL GAME THEORY AND APPLICATIONS
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Abstract

We propose a network formation model using the theory of stochastic games with random terminal time. Initially, the leader proposes a joint project in the form of a network to the players. Then the players have opportunities to form new links with each other to update the network proposed by the leader. Any player’s payoff is determined at any step by the network structure. It is also assumed that the formation of the links proposed by the players is random. The duration of the game is random as well. As a result of the players’ actions and the implementation of random steps of the Nature, a network is formed. We consider a cooperative approach to network formation and use the CIS-value as a cooperative solution. In this paper, we obtain a recursive formula to derive this value in any cooperative subgame. The paper also investigates the dynamic consistency of the CIS-value. The theoretical results are illustrated by a numerical example.

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Funding

The work was funded by Shandong Province “Double-Hundred Talent Plan” (No. WST2017009).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China

    E. M. Parilina

  2. Institute of Applied Mathematics of Shandong, Qingdao, 266071, China

    E. M. Parilina

  3. St. Petersburg State University, St. Petersburg, 199034, Russia

    Ping Sun & E. M. Parilina

Authors
  1. Ping Sun
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  2. E. M. Parilina
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Correspondence to Ping Sun or E. M. Parilina.

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Translated by V. Potapchouck

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Ping Sun, Parilina, E.M. Stochastic Model of Network Formation with Asymmetric Players. Autom Remote Control 82, 1065–1082 (2021). https://doi.org/10.1134/S0005117921060072

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