Recruiting beneficiary: University of Warsaw, Poland
Internal supervisors: Prof. Jacek Miękisz, Prof. Marek Bodnar
Brief project description: Evolutionary games on graphs and those with time delays are difficult to analyse analytically. Usually one has to rely on numerical and stochastic simulations. The main objective of this project is to develop approximation techniques and tools which will make possible an analytical treatment of such evolutionary processes. We adopt mean-field type models and their generalizations in the form of systems of ordinary differential equations. Approximation of stochastic processes by deterministic evolution has been studied before. We will build on existing concepts and models having in mind specific applications to problems of sustained cooperation in evolutionary game models of social dilemmas. Moreover, we will explore joint effects of stochasticity and time delays on evolution of interacting populations in evolutionary and epidemiological models.
Updates: In the first project, Javad examined the effect of the initial placement of mutants in simple Birth-Death Moran processes using mean-field approximations on the fixation and extinction of mutants. He found that the degree of initial mutant can significantly affect the fixation probability and extinction time. For the second part, he extended an existing pair approximation model to study how the cost of maintaining links between interacting individuals impacts cooperative behavior in structured populations.