Related papers: Evolutionary Stability of Polymorphic Population S…
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a…
We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the…
Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from…
In evolutionary game theory an Evolutionarily Stable Strategy (ESS) is a refinement of the Nash equilibrium concept that is sometimes also recognized as evolutionary stability. It is a game-theoretic model, well known to mathematical…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…
We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…
To predict the behavior of a population game when time becomes very long, the process that characterizes the evolution of our game dynamics must be reversible. Known games satisfying this are 2 strategy games as well as potential games with…
Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
In this work, a theorem is first proved which presents a game theoretic formulation of a necessary and sufficient sustainizability over a set condition for a general system described by ordinary differential equations (ODEs). Then, two…
Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended…
Building upon the eco-evolutionary game dynamics framework established by Tilman et al., we investigate stochastic fluctuations in a two-strategy system incorporating environmental feedback mechanisms, where the payoff matrix exhibits…
We consider the dynamics, existence and stability of the equilibrium states for large populations of individuals who can play various types of non--cooperative games. The players imitate the most attractive strategies, and the choice is…
We examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time. The class of dynamics under consideration includes fictitious play and its regularized variants, the…
We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is…
In this paper, we consider both finite and infinite horizon discounted dynamic mean-field games where there is a large population of homogeneous players sequentially making strategic decisions and each player is affected by other players…
What does it mean to fully understand the behavior of a network of adaptive agents? The golden standard typically is the behavior of learning dynamics in potential games, where many evolutionary dynamics, e.g., replicator, are known to…
In this paper we show that the continuum time version of the Minority Game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with "sufficiently"…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…