A mathematical analysis on public goods games in the continuous space

被引:17
作者
Wakano, Joe Yuichiro [1 ]
机构
[1] Univ Tokyo, Dept Sci Biol, Bunkyo Ku, Tokyo 1130033, Japan
关键词
public goods game; reaction diffusion; traveling wave solution; altruism; continuous space; carrying capacity;
D O I
10.1016/j.mbs.2005.12.015
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
We consider the population dynamics of two competing species sharing the same resource, which is modeled by the carrying capacity term of logistic equation. One species (farmer) increases the carrying capacity in exchange for a decreased survival rate, while the other species (exploiter) does not. As the carrying capacity is shared by both species, farmer is altruistic. The effect of continuous spatial structure on the performance of such strategies is studied using the reaction diffusion equations. Mathematical analysis on the traveling wave solution of the system revealed; (1) Farmers can never expel exploiters in any traveling wave solution. (2) The expanding velocity of the exploiter population invading the farmer population can be analytically determined and it depends only on a cost of altruism and the diffusion coefficients while it is independent of the benefit of altruism. (3) When the effect of altruism is small, the dynamics of the invasion of exploiters obeys the Fisher-KPP equation. Numerical calculations confirm these results. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码:72 / 89
页数:18
相关论文
共 19 条
[1]  
[Anonymous], 1995, FORMA
[2]   Punishment and reputation in spatial public goods games [J].
Brandt, H ;
Hauert, C ;
Sigmund, K .
PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 2003, 270 (1519) :1099-1104
[3]  
DUNBAR SR, 1984, T AM MATH SOC, V268, P557
[4]   INVADING WAVE OF COOPERATION IN A SPATIAL ITERATED PRISONERS-DILEMMA [J].
FERRIERE, R ;
MICHOD, RE .
PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 1995, 259 (1354) :77-83
[5]  
HAMILTON WD, 1964, J THEOR BIOL, V7, P1, DOI [10.1016/0022-5193(64)90038-4, 10.1016/0022-5193(64)90039-6]
[6]   Spatial structure often inhibits the evolution of cooperation in the snowdrift game [J].
Hauert, C ;
Doebeli, M .
NATURE, 2004, 428 (6983) :643-646
[7]   Volunteering as Red Queen mechanism for cooperation in public goods games [J].
Hauert, C ;
De Monte, S ;
Hofbauer, J ;
Sigmund, K .
SCIENCE, 2002, 296 (5570) :1129-1132
[8]   Travelling waves for games in economics and biology [J].
Hofbauer, J ;
Hutson, V ;
Vickers, GT .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (02) :1235-1244
[9]   The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model [J].
Hosono, Y .
BULLETIN OF MATHEMATICAL BIOLOGY, 1998, 60 (03) :435-448
[10]   THE SPATIAL STRUGGLE OF TIT-FOR-TAT AND DEFECT [J].
HUTSON, VCL ;
VICKERS, GT .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES B-BIOLOGICAL SCIENCES, 1995, 348 (1326) :393-404