Georgia Institute of Technology College of Sciences

In a recent series of papers a strong connection has been established between standard models of sexual evolution in mathematical biology and Multiplicative Weights Updates Algorithm, a ubiquitous model of online learning and optimization. These papers show that mathematical models of biological evolution are tantamount to applying discrete replicator dynamics, a close variant of MWUA on coordination games. We show that in the case of coordination games, under minimal genericity assumptions, discrete replicator dynamics converge to pure Nash equilibria for all but a zero measure of initial conditions. This result holds despite the fact that mixed Nash equilibria can be exponentially (or even uncountably) many, completely dominating in number the set of pure Nash equilibria. Thus, in haploid organisms the long term preservation of genetic diversity needs to be safeguarded by other evolutionary mechanisms, such as mutation and speciation. This is joint work with Ruta Mehta and Ioannis Panageas.