Spatial evolutionary game with bond dilution

Min Lin; Nan Li; Liang Tian; Da Ning Shi

doi:10.1016/j.physa.2009.12.029

Spatial evolutionary game with bond dilution

Min Lin, Nan Li^*, Liang Tian, Da Ning Shi

^*Corresponding author for this work

Department of Physics

Research output: Contribution to journal › Journal article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we study numerically the prisoner's dilemma game (PDG) and snowdrift game (SG) on a two-dimensional square lattice with both quenched and annealed bond dilution. For quenched bond dilution, the system undergoes a dynamical transition at the critical occupation probability q^*, which is higher than the bond percolation transition point for a square lattice. In the critical region, the defined order parameter has a scaling form as P_e ∼ (q - q^*)^β for q < q^* with the critical exponents β = 1.42 for PDG and β = 1.52 for SG, which differ from those with quenched site dilution. For annealed bond dilution, the system exhibits a distinct cooperative behavior. We find that the cooperation is much enhanced in the range of small payoff parameters on a lattice with slightly annealed bond dilution.

Original language	English
Pages (from-to)	1753-1758
Number of pages	6
Journal	Physica A: Statistical Mechanics and its Applications
Volume	389
Issue number	8
DOIs	https://doi.org/10.1016/j.physa.2009.12.029
Publication status	Published - 15 Apr 2010

User-Defined Keywords

Bond dilution
Phase transition
Prisoner's dilemma game
Snowdrift game

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10.1016/j.physa.2009.12.029

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title = "Spatial evolutionary game with bond dilution",

abstract = "In this paper, we study numerically the prisoner's dilemma game (PDG) and snowdrift game (SG) on a two-dimensional square lattice with both quenched and annealed bond dilution. For quenched bond dilution, the system undergoes a dynamical transition at the critical occupation probability q*, which is higher than the bond percolation transition point for a square lattice. In the critical region, the defined order parameter has a scaling form as Pe ∼ (q - q*)β for q < q* with the critical exponents β = 1.42 for PDG and β = 1.52 for SG, which differ from those with quenched site dilution. For annealed bond dilution, the system exhibits a distinct cooperative behavior. We find that the cooperation is much enhanced in the range of small payoff parameters on a lattice with slightly annealed bond dilution.",

keywords = "Bond dilution, Phase transition, Prisoner's dilemma game, Snowdrift game",

author = "Min Lin and Nan Li and Liang Tian and Shi, {Da Ning}",

note = "Funding information (Section snippets): This work was supported by the China Aeronautic Science Foundation under Grant No. 2009ZG52066. L.T. gratefully acknowledges the financial support from CX07B-033z and BCXJ07-11. Publisher copyright: {\textcopyright} 2010 Elsevier B.V.",

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T1 - Spatial evolutionary game with bond dilution

AU - Lin, Min

AU - Li, Nan

AU - Tian, Liang

AU - Shi, Da Ning

N1 - Funding information (Section snippets): This work was supported by the China Aeronautic Science Foundation under Grant No. 2009ZG52066. L.T. gratefully acknowledges the financial support from CX07B-033z and BCXJ07-11. Publisher copyright: © 2010 Elsevier B.V.

PY - 2010/4/15

Y1 - 2010/4/15

N2 - In this paper, we study numerically the prisoner's dilemma game (PDG) and snowdrift game (SG) on a two-dimensional square lattice with both quenched and annealed bond dilution. For quenched bond dilution, the system undergoes a dynamical transition at the critical occupation probability q*, which is higher than the bond percolation transition point for a square lattice. In the critical region, the defined order parameter has a scaling form as Pe ∼ (q - q*)β for q < q* with the critical exponents β = 1.42 for PDG and β = 1.52 for SG, which differ from those with quenched site dilution. For annealed bond dilution, the system exhibits a distinct cooperative behavior. We find that the cooperation is much enhanced in the range of small payoff parameters on a lattice with slightly annealed bond dilution.

AB - In this paper, we study numerically the prisoner's dilemma game (PDG) and snowdrift game (SG) on a two-dimensional square lattice with both quenched and annealed bond dilution. For quenched bond dilution, the system undergoes a dynamical transition at the critical occupation probability q*, which is higher than the bond percolation transition point for a square lattice. In the critical region, the defined order parameter has a scaling form as Pe ∼ (q - q*)β for q < q* with the critical exponents β = 1.42 for PDG and β = 1.52 for SG, which differ from those with quenched site dilution. For annealed bond dilution, the system exhibits a distinct cooperative behavior. We find that the cooperation is much enhanced in the range of small payoff parameters on a lattice with slightly annealed bond dilution.

KW - Bond dilution

KW - Phase transition

KW - Prisoner's dilemma game

KW - Snowdrift game

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U2 - 10.1016/j.physa.2009.12.029

DO - 10.1016/j.physa.2009.12.029

M3 - Journal article

AN - SCOPUS:74849132977

SN - 0378-4371

VL - 389

SP - 1753

EP - 1758

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 8

ER -

Spatial evolutionary game with bond dilution

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