On the relationship between simulation logit dynamics in the population game theory and mirror descent method in the online optimization using the example of the Shortest Path Problem

This presentation describes a mirror descent method for the stochastic online optimization problems on the simplex. Based on this method the optimal strategies of the users of the transport network choosing a path are constructed. The behavior of all users following such strategies generates simulation logit dynamics in the population game corresponding to the Beckman model of the the equilibrium flow distribution over paths. Thus, a specific example (The Shortest Path Problem) is used to demonstrate a link between online optimization and population game theory.