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Physics Conferences 7th KIAS Conference on Statistical Physics
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[Talk 18] Evolution of social behaviors in a growing habitat with vacancies
SPEAKER  |  Hyeong-Chai Jeong
INSTITUTE  |  Sejong University
DATE  |  July 6(Wed), 2016
TIME  |  09:40
PLACE  |  Korea Institute for Advanced Study (KIAS), Seoul, Korea
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ABSTRACT  |  We consider a stochastic evolutionary game in a growing habitat embedded in a regular lattice. Interactions between neighbors are mimicked by a prisoner¡¯s dilemma game. Fitness, $f$ of an individual is given by an increasing function of its payoff, $p$ in the form of $f = 1 + A\exp(wp)$. When a randomly chosen site is occupied, its inhabitant dies with probability of $d =1/f$. Otherwise, the chosen empty site is taken by an offspring of its neighbors. We study growth of population from a single seed and find that its dynamics critically depends on the parameter~$A$. As $A$ decreases, absorbing transitions from growing population phases to empty population phases occur for both types of seeds, cooperator and defector. The transition points, $A_{C}$ of the cooperators is smaller than that of the defectors, $A_{D}$ implying the existence of a parameter range $A_{C} < A < A_{D}$ in which only cooperative populations can exist. Our observation shows that vacancies, introduced by fitness dependent death processes, provide a natural way to develop cooperative communities in a growing population.
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