Evolutionary dynamics with game transitions

Abstract

The environment has a strong influence on a population’s evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals’ behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceedsk−k′, where k is the average number of neighbors of an individual andk′captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.

Asynchronous Decision-Making Dynamics Under Imitation Update Rule in Heterogeneous Populations

“…Note that the n C values of trajectories trapped in the fluctuation set(s) seem to be constrained in the interval [37,38] is because the probability of leaving the fluctuation at this interval is fairly small, although greater than zero. Similarly, the probability of leaving the fluctuation at [45,46] from the right end is much smaller than leaving from the left end, so we rarely see n C reaching 63, even though it does. More generally, we have the following cases regarding n C (0):…”

Structural Combinatorial of Network Information System of Systems based on Evolutionary Optimization Method.pdf

“…Based on the ideas of biological evolution, genetic algorithm is a self-adapted global optimization probability search algorithm formed by simulating the genetic mechanism and natural selection organisms [3,4,5]. The genetic algorithm regards the optimization problem as a "chromosome" and measures the pros and cons of the "chromosome" through the fitness function according to the "Survival of the Fittest".…”

“…Perform step 1 4. When = ∅ , save the chromosome directly to the next generation otherwise, perform the following steps.…”

Strategy equilibrium in dilemma games with off-diagonal payoff perturbations

“…Following this method, many authors have made important advances in the understanding of how a number of conditions can drive the system dynamics, such as resource heterogeneity [46], different behaviors [47,48], seasonal variations [33], diverse learning rates [49], different death rates [50], interaction topologies [51], and so on. However, another way to understand these phenomena is to study the behavior of a population whose evolution can be affected by a payoff matrix constantly perturbed by stochastic noise with zero mean value [52][53][54], regardless of its origin. In other words, as the environmental perturbations are very diverse and frequent, we can suppose that the sum of infinitely many small perturbations acts as a stochastic perturbation around an average value.…”