Dynamic Evolutionary Game Theory

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The overall objective of my research program is to develop the theory of evolutionary games and its applications to biology and economics. The basic static concept of the evolutionarily stable strategy (ESS) has played a key role in the mathematical modeling of individual behaviour in conflict situations by also predicting the eventual behavioral distribution of standard single-species frequency-dependent evolutionary processes such as the replicator dynamics. Less well-understood are the dynamic consequences of the ESS concept (and its generalizations) for ecological systems when there are many species and/or population sizes evolve. The proposed research program will examine these consequences for predator-prey interactions and for more general coevolutionary models in ecology. I have recently shown that behavioral (i.e. frequency) effects and ecological (i.e. population size) effects decouple when analyzing the spatial distribution of a single-species among different habitats, providing a thorough understanding of these "habitat-selection" games. The proposed game-theoretic approach has the potential to provide a similar understanding of the much more complex biological systems involving more than one species. Predator foraging behaviour is of fundamental importance when modeling predator-prey systems. The proposed research seeks to predict sequential predator foraging decisions through the theory of extensive form games, a natural setting to model such ongoing interactions. This is a novel research direction and is an important initial stage connecting extensive form games to biology. The other objective is to investigate the evolution of cooperation in theoretical models and in corresponding game experiments, topics of much current interest for many prominent research groups. Explanations based on evolutionary game theory have typically assumed that players' payoffs depend only on their strategies and not on other factors such as their status. The proposal will incorporate asymmetries such as those between young and old, owner and non-owner of a resource into the model. Theoretical results will be compared to those from human game experiments to better understand mechanisms that generate cooperative behaviour.