In this talk, we will discuss evolutionary games on a binomial random graph G(n,p). These games are determined through a 2-player symmetric game with 2 strategies which are played between the adjacent members of the vertex set. Players/vertices update their strategies synchronously: at each round, each player selects the strategy that is the best response to the current set of strategies its neighbours play. We show that such a system reduces to generalised majority and minority dynamics. We show rapid convergence to unanimity for p in a range that depends on a certain characteristic of the payoff matrix. In the presence of a certain type of bias in the payoff matrix, we determine a sharp threshold on p above which the largest connected component reaches unanimity with high probability, and below which this does not happen.

This is joint work with Jordan Chellig and Calina Durbac.

**Date**: 16 January 2023, 14:00 (Monday, 1st week, Hilary 2023)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L3**Speaker**: Nikolaos Fountoulakis (University of Birmingham)**Organising department**: Department of Statistics**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt