Game-Theoretic Context and Interpretation of Kerner’s Three-Phase Traffic Theory

We present four classical developments in traffic theory and Kerner’s (Phys A 392:5261–5282, 2013, [36]) critique that these are not consistent with fundamental empirical features of traffic breakdown at a highway bottleneck (transition from free flow (F) to congested traffic at the bottleneck) that is the basic empiric of traffic theory. Kerner argued that traffic breakdown is probabilistic, can be spontaneous (emerging internally at the bottleneck) or induced (emerging from a downstream bottleneck), and is a transition from free flow to synchronized flow (S) (synchronized flow is one of the two traffic phases of congested traffic) called as a F → S transition, after which wide moving jam (J) (J is another from two phases of congested traffic) may arise. Return to free flow occurs through hysteresis and usually at smaller flow rates. Common games in traffic theory are presented and exemplified, i.e. the chicken game, battle of the sexes, prisoner’s dilemma, and coordination game. The four developments and Kerner’s theory are linked to game theory, and especially to the chicken game. For the first F → S transition the density increases at a constant flow rate. Increasing density increases the prevalence of the chicken strategy due to drivers in a congested environment becoming apprehensive, fearful, and wary of accidents. For the second S → J the chicken strategy is equally likely while the flow rate decreases at constant density. For the third J → F transition the density decreases which decreases the prevalence of the chicken strategy. Finally, within free flow F where the flow rate and density again increase, the chicken strategy is played with higher probability.