Theory of multiplayer games; specific instances in the social and eco-evolutionary context

We shall extend the theory of multiplayer games [85,13] to include the recently developed theories of time delays and multiple evolutionary games [86] into a single coherent framework. The dynamic properties (fixation probabilities, fixation time and long-term abundances under mutation-selection balance) can be instructive to the mathematically keen whereas the static properties (number of equilibria, stability and equilibrium selection) can be useful in a social and biological context. Studying multiple games allows us to move a bit closer to reality where individuals not only employ multiple strategies and interact with multiple individuals but also take part in multiple interactions. The interactions could be instantaneous or time-delayed or possibly spatially constricted, which would provide a link with the other work packages in this application. We envision the applications of this theoretical development to span the fields of social evolution (cooperation, bargaining) to classical ecology (community dynamics, animal personalities) to evolutionary biology (polygenic trait evolution, interactions between life-history traits).