Evolutionary dynamics with random payoff matrices

TL;DR

This paper surveys how randomness in payoff matrices affects evolutionary dynamics, emphasizing continuous models and highlighting open problems for future research in diverse fields like biology and economics.

Contribution

It provides a comprehensive review of existing literature on evolutionary dynamics with random payoffs and identifies key open challenges for future exploration.

Findings

Highlights the importance of uncertainty in evolutionary models

Summarizes key approaches to modeling random payoffs

Identifies open problems in the field

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.