Convergence in a Repeated Non-atomic Routing Game with Partial Signaling

TL;DR

This paper analyzes a repeated non-atomic routing game with partial signaling, showing that under certain conditions, link flows converge to a Bayes correlated equilibrium in parallel networks.

Contribution

It introduces a model of repeated routing with partial signaling and proves convergence to equilibrium under obedience conditions in parallel networks.

Findings

Link flows are asymptotically consistent with Bayes correlated equilibrium.

Obedience condition ensures convergence in parallel networks.

Participants' behavior aligns with equilibrium predictions over time.

Abstract

We study the following repeated non-atomic routing game. In every round, nature chooses a state in an i.i.d. manner according to a publicly known distribution, which influences link latency functions. The system planner makes private route recommendations to participating agents, which constitute a fixed fraction, according to a publicly known signaling strategy. The participating agents choose between obeying or not obeying the recommendation according to cumulative regret of the participating agent population in the previous round. The non-participating agents choose route according to myopic best response to a calibrated forecast of the routing decisions of the participating agents. We show that, for parallel networks, if the planner's signal strategy satisfies the obedience condition, then, almost surely, the link flows are asymptotically consistent with the Bayes correlated equilibrium induced by the signaling strategy.