Survival via cooperation in the prisoner's dilemma game

Abstract

By incorporating ecological dynamics into evolutionary games, we introduce natural and unnatural death to the spatial prisoner's dilemma game in which individuals can play mixed strategies. This introduction can give a simple explanation for the emergence and abundance of cooperation in animal and human societies. We found that individuals are more likely to cooperate in a highly competitive environment. In addition, our simulation results suggest that the individuals would tend to cooperate when the temptation to defect is small.

Effect of vaccination strategies on the dynamic behavior of epidemic spreading and vaccine coverage

“…For the pure-strategy case, there are two strategies, to vaccinate or not to vaccinate. For simplicity and efficiency but without loss of generality, we focus on the discretization of continuous strategies in the continuous-strategy case, that is, the individual i can choose a strategy x i from a strategy set 0 100 ; 1 100 ; Á Á Á ; 100 100 È É , where the value of x i denotes the vaccination probability of individual i [26] (we have checked that our results presented below remain the same when the vaccination probabilities of the individuals take continuous real values in the range ½0; 1). In the epidemic spreading-stage, the epidemic strain infects an initial number of individuals I 0 (1‰ of the population size) and then spreads in the population according to the classical susceptibleinfected-recovered (SIR) epidemiological model [27,28], with per-day transmission rate r for each pair of susceptible-infected (SI) contact and recovery rate g for each infected (I) individual getting immune to the disease.…”

Cooperation in spatial prisoner’s dilemma game with delayed decisions

“…Afterwards, Huberman and Glance made further study on this model with asynchronous updating method [30]. Expansive researches for the PDG on twodimensional lattice have been conducted to enhance the fraction of cooperators further, such as the introduction of heterogeneous activity [31][32][33], empty sites [34,35], mobile agents [36][37][38], mixed strategies [39,40]. In addition, some scholars have studied the effect of memory on the evolution of cooperation.…”

Nonlinear Mach-Zehnder-Fano interferometer

“…Recently, we have introduced the concept of Mach-Zehnder-Fano interferometer (MZFI) [5] providing with unique physical property that can not be found in a macroscopic resonator enhanced MZI [2][3][4]6]. The MZFI allows us to manipulate the interaction of different types of resonances which leads to the formation of a novel hybrid Fano-like resonant states [7]. Furthermore, the counterpart of the ring-resonator-coupled Mach-Zehnder interferometer in the microscopic scale, i.e.…”

“…At the same time, the nonliear response of the Fano defect would give a feedback to the scattering waves in the arms of MZFI (read as the nonlinear scattering potential ε) of which forms a complex nonlinear resonance system. Then, such nonlinear MZFI, whose nonlinear response can not be mapped from the standard nonlinear Fano resonant system [18], is sophisticated even in the linear region [7].…”

“…2. These two cases allow us to excite different sets of MZI loop's modes, which have nonzero overlap with the coupled site [7]. The scattering of the conventional Fano resonance geometry [see Fig.…”