Does human imitate successful behaviors immediately?

The emergence and abundance of cooperation in animal and human societies is a challenging puzzle to evolutionary biology. Over the past decades, various mechanisms have been suggested which are capable of supporting cooperation. Imitation dynamics, however, are the most representative microscopic rules of human behaviors on studying these mechanisms. Their standard procedure is to choose the agent to imitate at random from the population. In the spatial version this means a random agent from the neighborhood. Hence, imitation rules do not include the possibility to explore the available strategies, and then they have the possibility to reach a homogeneous state rapidly when the population size is small. To prevent evolution stopping, theorists allow for random mutations in addition to the imitation dynamics. Consequently, if the microscopic rules involve both imitation and mutation, the frequency of agents switching to the more successful strategy must be higher than that of them transiting to the same target strategy via mutation dynamics. Here we show experimentally that the frequency of switching to successful strategy approximates to that of mutating to the same strategy. This suggests that imitation might play an insignificant role on the behaviors of human decision making. In addition, our experiments show that the probabilities of agents mutating to different target strategies are significantly distinct. The actual mutation theories cannot give us an appropriate explanation to the experimental results. Hence, we argue that the mutation dynamics might have evolved for other reasons

Gravitational Lensing Effects of Fermion-Fermion Stars: I. Strong Field Case

We investigate a two-component model for gravitational lenses, i.e., the fermion-fermion star as a dark matter self-gravitating system made from two kinds of fermions with different masses. We calculate the deflection angles varying from arcseconds to even degrees. There is one Einstein ring. In particular, we find three radial critical curves for radial magnifications and four or five images of a point source. These are different from the case of the one-component model such as the fermion stars and boson stars. This is due to the fermion-fermion star being a two-component concentric sphere. Our results suggest that any possible observations of the number of images more than 3 could imply a polytropic distribution of the mass inside the lens in the universe.Comment: 7 pages, LaTex and PostScript; 4 figures, PostScrip