A marginal utility day-to-day traffic evolution model based on one-step strategic thinking

Most deterministic day-to-day traffic evolution models, either in continuous-time or discrete-time space, have been formulated based on a fundamental assumption on driver route choice rationality where a driver seeks to maximize her/his marginal benefit defined as the difference between the perceived route costs. The notion of rationality entails the exploration of the marginal decision rule from economic theory, which states that a rational individual evaluates his/her marginal utility, defined as the difference between the marginal benefit and the marginal cost, of each incremental decision. Seeking to analyze the marginal decision rule in the modeling of deterministic day-to-day traffic evolution, this paper proposes a modeling framework which introduces a term to capture the marginal cost to the driver induced by route switching. The proposed framework enables to capture both benefit and cost associated with route changes. The marginal cost is then formulated upon the assumption that drivers are able to predict other drivers’ responses to the current traffic conditions, which is adopted based on the notion of strategic thinking of rational players developed in behavior game theory. The marginal cost based on 1-step strategic thinking also describes the “shadow price” of shifting routes, which helps to explain the behavioral tendency of the driver perceiving the cost-sensitivity to link/route flows. After developing a formulation of the marginal utility day-to-day model, its theoretical properties are analyzed, including the invariance property, asymptotic stability, and relationship with the rational behavioral adjustment process.