Research Discussion: Memory Granularity effects on evolutionary binary games

Giacomo Baldo, University of Leeds. Part of the Leeds Applied Nonlinear Dynamics seminar series.

This is a research discussion in which students and members of staff present and discuss their current research.

Within a population, individual memory greatly influences individual and collective behaviour. Here, we consider a large well-mixed population of individuals faced by a general binary-choice problem, which is a choice between two available strategies. This applies to an array of social situations where interactions can be modelled, for example, by the Hawk-Dove and minority games.

Previous research has highlighted the emergence of fluctuations and limit cycles at the collective level around the mixed equilibrium of the underlying game due to the effect of memory. Here we focus on the properties of individual memory that trigger collective transitions. In particular, we develop a two-faceted description of memory, which includes length and granularity. We show that the precision of the individual's perception of the outside social environment is an important element determining the transition between synchronous and asynchronous collective states, and between periodic oscillations and random fluctuations of the group behaviour. Our results indicate that finely grained memories do not necessarily yield evolutionary advantages. We discuss why individuals may act differently from one another as they lose the ability to build a shared knowledge of the social environment.