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

Fast and Accurate Computation of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first derive analytic expressions for the underlying convolution kernels, which allow for a rapid and accurate evaluation of the convolution with $O(N_t)$ operations over $N_t$ successive time steps. To handle the onlocality in space, we introduce the notion of boundary perturbation, which enables us to handle general bounded scatters by solving a sequence of wave equations in a regular domain. We propose an efficient spectral-Galerkin solver with Newmark's time integration for the truncated wave equation in the regular domain. We also provide ample numerical results to show high-order accuracy of NRBCs and efficiency of the proposed scheme.Comment: 22 pages with 9 figure