dorsal/arxiv
View SchemaPromotion of cooperation induced by nonlinear attractive effect in spatial Prisoner's Dilemma game
| Authors | Jian-Yue Guan, Zhi-Xi Wu, Zi-Gang Huang, Xin-Jian Xu, Ying-Hai Wang |
|---|---|
| Categories | |
| ArXiv ID | physics/0701082 |
| URL | https://arxiv.org/abs/physics/0701082 |
| DOI | 10.1209/epl/i2006-10381-4 |
| Journal | EurophysLett_76_1214 (2006) |
Abstract
We introduce nonlinear attractive effects into a spatial Prisoner's Dilemma game where the players located on a square lattice can either cooperate with their nearest neighbors or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbors with a probability proportional to $\mathcal{A}^\alpha$ denoting the attractiveness of the neighbor, where $\mathcal{A}$ is the payoff collected by it and $\alpha$ ($\geq$0) is a free parameter characterizing the extent of the nonlinear effect; and then adopting its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density $\rho_C$ of cooperators in the stationary state for different values of $\alpha$. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect. In particular, for large values of $\alpha$, i.e., strong nonlinear attractive effects, the system exhibits two absorbing states (all cooperators or all defectors) separated by an active state (coexistence of cooperators and defectors) when varying the temptation to defect. In the critical region where $\rho_C$ goes to zero, the extinction behavior is power law-like $\rho_C$ $\sim$ $(b_c-b)^{\beta}$, where the exponent $\beta$ accords approximatively with the critical exponent ($\beta\approx0.584$) of the two-dimensional directed percolation and depends weakly on the value of $\alpha$.
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"abstract": "We introduce nonlinear attractive effects into a spatial Prisoner\u0027s Dilemma\ngame where the players located on a square lattice can either cooperate with\ntheir nearest neighbors or defect. In every generation, each player updates its\nstrategy by firstly choosing one of the neighbors with a probability\nproportional to $\\mathcal{A}^\\alpha$ denoting the attractiveness of the\nneighbor, where $\\mathcal{A}$ is the payoff collected by it and $\\alpha$\n($\\geq$0) is a free parameter characterizing the extent of the nonlinear\neffect; and then adopting its strategy with a probability dependent on their\npayoff difference. Using Monte Carlo simulations, we investigate the density\n$\\rho_C$ of cooperators in the stationary state for different values of\n$\\alpha$. It is shown that the introduction of such attractive effect\nremarkably promotes the emergence and persistence of cooperation over a wide\nrange of the temptation to defect. In particular, for large values of $\\alpha$,\ni.e., strong nonlinear attractive effects, the system exhibits two absorbing\nstates (all cooperators or all defectors) separated by an active state\n(coexistence of cooperators and defectors) when varying the temptation to\ndefect. In the critical region where $\\rho_C$ goes to zero, the extinction\nbehavior is power law-like $\\rho_C$ $\\sim$ $(b_c-b)^{\\beta}$, where the\nexponent $\\beta$ accords approximatively with the critical exponent\n($\\beta\\approx0.584$) of the two-dimensional directed percolation and depends\nweakly on the value of $\\alpha$.",
"arxiv_id": "physics/0701082",
"authors": [
"Jian-Yue Guan",
"Zhi-Xi Wu",
"Zi-Gang Huang",
"Xin-Jian Xu",
"Ying-Hai Wang"
],
"categories": [
"physics.soc-ph"
],
"doi": "10.1209/epl/i2006-10381-4",
"journal_ref": "EurophysLett_76_1214 (2006)",
"title": "Promotion of cooperation induced by nonlinear attractive effect in spatial Prisoner\u0027s Dilemma game",
"url": "https://arxiv.org/abs/physics/0701082"
},
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