ESR6 – The evolution of cooperation in populations involving multi-player games and time delays

ESR6: The evolution of cooperation in populations involving multi-player games and time delays

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.

During his first secondment with Prof. Mark Broom at City University London, they investigated time delay effects on mutant fixation in well-mixed populations using numerical Markov chain techniques. Currently, he is going to expand Prof. Miękisz’s model for analyzing time delay impacts on games with more strategies and players. Additionally, they will incorporate time delay into their pair approximation model to assess its influence on cooperation levels in structured populations. The overarching goal is to advance their theoretical understanding of how spatial structure and time delays affect the evolutionary game.