Evolutionary dynamics with random payoff matrices

Abstract Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources such as fluctuating environments, behavioural errors or incomplete information. Incorporating uncertainty into evolutionary models is essential for enhancing their relevance to real-world problems. In this perspective article, we survey the relevant literature on evolutionary dynamics with random payoff matrices, with an emphasis on continuous models. We also pose challenging open problems for future research in this important area.