On Learning How Players Learn: Estimation of Learning Dynamics in the Routing Game

The routing game models congestion in transportation networks, communication networks, and other cyber physical systems in which agents compete for shared resources. We consider an online learning model of player dynamics: at each iteration, every player chooses a route (or a probability distribution over routes, which corresponds to a flow allocation over the physical network), then the joint decision of all players determines the costs of each path, which are then revealed to the players. We pose the following estimation problem: given a sequence of player decisions and the corresponding costs, we would like to estimate the learning model parameters. We consider in particular entropic mirror descent dynamics, reduce the problem to estimating the learning rates of each player. We demonstrate this method using data collected from a routing game experiment, played by human participants: We develop a web application to implement the routing game. When players log in, they are assigned an origin and destination on the graph. They can choose, at each iteration, a distribution over their available routes, and each player seeks to minimize her own cost. We collect a data set using this interface, then apply the proposed method to estimate the learning model parameters. We observe in particular that after an exploration phase, the joint decision of the players remains within a small distance of the Nash equilibrium. We also use the estimated model parameters to predict the flow distribution over routes, and compare these predictions to the actual distribution. Finally, we discuss some of the qualitative implications of the experiments, and give directions for future research.