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

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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 one connected network of agents using different strategies who are continually interacting and taking adaptive actions. A frozen 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.

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Authors and Affiliations

  1. Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, P.R. China

    Chi Wun Choi & Pak Ming Hui

  2. College of Physics, Optoelectronics and Energy, Soochow University, Suzhou, 215006, P.R. China

    Chen Xu

Authors
  1. Chi Wun Choi
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  2. Chen Xu
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  3. Pak Ming Hui
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Correspondence to Pak Ming Hui.

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Choi, C.W., Xu, C. & Hui, P.M. Adaptive cyclically dominating game on co-evolving networks: numerical and analytic results. Eur. Phys. J. B 90, 190 (2017). https://doi.org/10.1140/epjb/e2017-80203-8

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  • DOI: https://doi.org/10.1140/epjb/e2017-80203-8

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