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Adaptive cyclically dominating game on co-evolving networks: numerical and analytic results

Author

Listed:
  • Chi Wun Choi

    (The Chinese University of Hong Kong)

  • Chen Xu

    (College of Physics, Optoelectronics and Energy, Soochow University)

  • Pak Ming Hui

    (The Chinese University of Hong Kong)

Abstract

A co-evolving and adaptive Rock (R)–Paper (P)–Scissors (S) game (ARPS) in which an agent uses one of three cyclically dominating strategies is proposed and studied numerically and analytically. An agent takes adaptive actions to achieve a neighborhood to his advantage by rewiring a dissatisfying link with a probability p or switching strategy with a probability 1 - p. Numerical results revealed two phases in the steady state. An active phase for p p c has three separate clusters of agents using only R, P, and S, respectively with terminated adaptive actions. A mean-field theory based on the link densities in co-evolving network is formulated and the trinomial closure scheme is applied to obtain analytical solutions. The analytic results agree with simulation results on ARPS well. In addition, the different probabilities of winning, losing, and drawing a game among the agents are identified as the origin of the small discrepancy between analytic and simulation results. As a result of the adaptive actions, agents of higher degrees are often those being taken advantage of. Agents with a smaller (larger) degree than the mean degree have a higher (smaller) probability of winning than losing. The results are informative for future attempts on formulating more accurate theories.

Suggested Citation

  • Chi Wun Choi & Chen Xu & Pak Ming Hui, 2017. "Adaptive cyclically dominating game on co-evolving networks: numerical and analytic results," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(10), pages 1-9, October.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:10:d:10.1140_epjb_e2017-80203-8
    DOI: 10.1140/epjb/e2017-80203-8
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    Cited by:

    1. Park, Junpyo & Chen, Xiaojie & Szolnoki, Attila, 2023. "Competition of alliances in a cyclically dominant eight-species population," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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    Keywords

    Statistical and Nonlinear Physics;

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