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In this note, we investigate the relationship between probabilistic updating mechanisms and discrete-time replicator-mutator dynamics. We consider the recently shown connection between Bayesian updating and replicator dynamics and extend it…
Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the…
We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent $a$, which describes the long-term growth rate, depends smoothly on the demographic parameters…
Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one \emph{fixed} rule, while in the real world,…
Configurational arrangement of network architecture and interaction character of individuals are two most influential factors on the mechanisms underlying the evolutionary outcome of cooperation, which is explained by the well-established…
The evolution of leadership in migratory populations depends not only on costs and benefits of leadership investments but also on the opportunities for individuals to rely on cues from others through social interactions. We derive an…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic…
Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might…
Fluctuating environments are situations where the spatio-temporal stochasticity plays a significant role in the evolutionary dynamics. The study of the evolution of cooperation in these environments typically assumes a homogeneous, well…
The replicator-mutator equation is a model for populations of individuals carrying different traits, with a fitness function mediating their ability to replicate, and a stochastic model for mutation. We derive analytical solutions for the…
Human-machine networks pervade much of contemporary life. Network change is the product of structural modifications along with differences in participant be-havior. If we assume that behavioural change in a human-machine network is the…
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…
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…
Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the system as a whole are phenomena that appear during…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
The dynamics of decisions in complex networks is studied within a Markov process framework using numerical simulations combined with mathematical insight into the process mechanisms. A mathematical discrete-time model is derived based on a…