Routing Games in the Wild: Efficiency, Equilibration, Regret, and a Price of Anarchy Bound via Long Division

Abstract

Routing games are amongst the most well studied domains of game theory. How relevant are these pen-and-paper calculations to understanding the reality of everyday traffic routing? We focus on a semantically rich dataset that captures detailed information about the daily behavior of thousands of Singaporean commuters and examine the following basic questions: - Does the traffic stabilize? - Is the system behavior consistent with latency-minimizing agents? - Is the resulting system efficient? In order to capture the efficiency of the traffic network in a way that agrees with our everyday intuition we introduce a new metric, the Free-flow Index (FFI) , which reflects the inefficiency resulting from system congestion. Along the way, we provide the first model-free computation of an upper bound to the price of anarchy utilizing only real world measurements of traffic data.

Counter-Intuitive Effects of Q-Learning Exploration in a Congestion Dilemma

“…A popular metric, which assumes that players are rational, is the Price of Anarchy, which is designed to reflect the loss of efficiency due to selfish non-cooperative behaviour [4] [41] [42] [43]. Specifically it is the ratio of the social welfare (the average reward of all players) between the best coordinated solution and the worst Nash equilibrium.…”

“…There may be many reasons not least of which that it is practically challenging to evaluate whether or not drivers behave optimally, and it is not known what the optimal decisions are. A relevant study conducted in Singapore with extensive driver routing data attempted to determine whether the traffic system operated at an equilibrium [43], but demonstration of the occurrence of Braess's like selfish routing would require in the least a counterfactual case where road network capacity is altered.…”