Dynamic instabilities induced by asymmetric influence: Prisoners’ dilemma game in small-world networks

Beom Jun Kim, Ala Trusina, Petter Holme, Petter Minnhagen, Jean S. Chung, and M. Y. Choi
Phys. Rev. E 66, 021907 – Published 26 August 2002
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Abstract

A two-dimensional small-world-type network, subject to spatial prisoners’ dilemma dynamics and containing an influential node defined as a special node, with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium-type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, its recovery requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long-range connections.

  • Received 12 March 2002

DOI:https://doi.org/10.1103/PhysRevE.66.021907

©2002 American Physical Society

Authors & Affiliations

Beom Jun Kim1,*, Ala Trusina2, Petter Holme2, Petter Minnhagen2, Jean S. Chung3, and M. Y. Choi4

  • 1Department of Molecular Science and Technology, Ajou University, Suwon 442-749, Korea
  • 2Department of Theoretical Physics, Umeå University, 901 87 Umeå, Sweden
  • 3Department of Physics, Chungbuk National University, Cheongju 361-763, Korea
  • 4Department of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea

  • *Electronic address: beomjun@ajou.ac.kr

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Vol. 66, Iss. 2 — August 2002

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