Atomic Dynamic Flow Games: Adaptive vs. Nonadaptive Agents

We propose a game model for selfish routing of atomic agents, who compete for use of a network to travel from their origins to a common destination as quickly as possible. We follow a frequently used rule that the latency an agent experiences on each edge is a constant transit time plus a variable waiting time in a queue. A key feature that differentiates our model from related ones is an edge-based tie-breaking rule for prioritizing agents in queueing when they reach an edge at the same time. We study both nonadaptive agents (each choosing a one-off origin–destination path simultaneously at the very beginning) and adaptive ones (each making an online decision at every nonterminal vertex they reach as to which next edge to take). On the one hand, we constructively prove that a (pure) Nash equilibrium (NE) always exists for nonadaptive agents and show that every NE is weakly Pareto optimal and globally first-in first-out. We present efficient algorithms for finding an NE and best responses of nonadaptive agents. On the other hand, we are among the first to consider adaptive atomic agents, for which we show that a subgame perfect equilibrium (SPE) always exists and that each NE outcome for nonadaptive agents is an SPE outcome for adaptive agents but not vice versa.