EPSRC standard grant "Evolutionary Game Theory Under Uncertainty"

Evolutionary Game Theory (EGT) was introduced in 1973 by Maynard Smith and Price as an application of the mathematical theory of games to biological contexts. By incorporating game theory, developed earlier by John von Neumann, into Darwinian's natural evolution theory, they were able to explain many intriguing behaviours in animals such as altruism and collective behaviours. Over the last 50 years, EGT has become one of the most diverse and far-reaching theories in biology. It has also constituted a unified mathematical framework for studying many problems in a variety of other research fields such as ecology, physics, economics, and computer science, as well as for pressing application domains including climate change, pandemics, healthcare policy, and technology governance.

However, most existing works on EGT research assume the payoff entries of the underlying game, which are interpreted as biological fitness, to be deterministic. However, this assumption is not realistic and limits the applicability of EGT, since the payoff entries are calculated from the interactions between different individuals (players) within the population and are constantly subject to uncertainty such as from environmental noise, incomplete information, and estimation errors. Extending the existing theory to account for such uncertainty is thus crucial and will significantly advance our understanding of the emergence and evolution of collective behaviours and biological and social diversity.

In this project, we will develop novel mathematical methods and tools to study evolutionary games with noisy and incomplete information for both infinite and finite populations, with different strategic interactions. We will apply the methods and tools developed in this project to two major classes of strategic interactions: the social dilemmas and the bargaining games, in both pairwise and multi-player contexts. They systematically encapsulate a range of important social, biological, and economic interactions, capturing both symmetric and asymmetric collective decision-making regarding cooperation, coordination, trust, and fairness.

The key challenge in this project is due to the complexity of the underlying evolutionary processes, which are often in high dimensional spaces and involve many parameters that are biologically/physically relevant. From a mathematical point of view, one needs to deal with either systems of high-order multivariate random polynomial equations or huge Markov chains, let alone the randomness. To tackle these challenges, we bring together a diverse team from different areas of mathematics and applied sciences such as game theory, random polynomial theory, nonlinear dynamical systems, and probability theory. We also design and implement large scale simulations to guide theoretical analysis as well as to validate theoretical observations and predictions.