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The idea of evolutionarily stable state (ESS) of a population is a cornerstone of evolutionary game theory; moreover, it coincides with the game-theoretic concept of Nash equilibrium. Such a state corresponds to a strategy adopted by the…
Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on…
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…
The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally…
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…
One of the most challenging issues of evolutionary biology concerns speciation, the emergence of new species from an initial one. The huge amount of species found in nature demands a simple and robust mechanism. Yet, no consensus has been…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
Given a large population of players, each player has three possible choices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a…
We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective…
In a recent series of papers a surprisingly strong connection was discovered between standard models of evolution in mathematical biology and Multiplicative Weights Updates Algorithm, a ubiquitous model of online learning and optimization.…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…
Evolutionary game theory offers a general framework to study how behaviors evolve by social learning in a population. This body of theory can accommodate a range of social dilemmas, or games, as well as real-world complexities such as…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
A population of heterogenous agents compeeting through a minority rule is investigated. Agents which frequently loose are selected for evolution by changing their strategies. The stationary composition of the population resulting for this…
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation…
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 environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Existing theories for the evolution of aging and death treat senescence as a side-effect of strong selection for fertility. These theories are well-developed mathematically, but fit poorly with emerging experimental data. The data suggest…
We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing…