12,208 research outputs found
Perturbations of Functional Inequalities for L\'evy Type Dirichlet Forms
Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy
type Dirichlet forms are studied. When the range of jumps is finite our results
are natural extensions to the corresponding ones derived earlier for diffusion
processes; and we show that the study for the situation with infinite range of
jumps is essentially different. Some examples are presented to illustrate the
optimality of our results
Evolutionary dynamics of group cooperation with asymmetrical environmental feedback
In recent years, there has been growing interest in studying evolutionary
games with environmental feedback. Previous studies exclusively focus on
two-player games. However, extension to multi-player game is needed to study
problems such as microbial cooperation and crowdsourcing collaborations. Here,
we study coevolutionary public goods games where strategies coevolve with the
multiplication factors of group cooperation. Asymmetry can arise in such
environmental feedback, where games organized by focal cooperators may have a
different efficiency than the ones by defectors. Our analysis shows that
co-evolutionary dynamics with asymmetrical environmental feedback can yield
oscillatory convergence to persistent cooperation, if the relative changing
speed of cooperators' multiplication factor is above a certain threshold. Our
work provides useful insights into sustaining group cooperation in a changing
world
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