ARTICLE IN PRESS JID: TRB [m3Gsc;December 23, 2015;21:9] Transportation Research Part B 000 (2015) 1–19 Contents lists available at ScienceDirect Transportation Research Part B journal homepage: www.elsevier.com/locate/trb A marginal utility day-to-day traffic evolution model based on one-step strategic thinking Xiaozheng He a , Srinivas Peeta b,∗ a NEXTRANS Center, Purdue University, 3000 Kent Avenue, West Lafayette, IN 47906, United States b School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907, United States article info Article history: Received 18 April 2014 Revised 20 October 2015 Accepted 4 December 2015 Available online xxx Keywords: Day-to-day traffic evolution Marginal decision rule Strategic thinking Behavioral game theory Rationality abstract 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 differ- ence 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 eval- uates 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 the- ory. 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. © 2015 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Motivation Over the past 3 decades, a large number of day-to-day (DTD) traffic evolution models have been developed to represent how traffic flow evolves under disequilibrium. These DTD models describe drivers’ individual route switching behavior, and the cor- responding traffic pattern changes at an aggregate level. The traffic evolution processes characterized by these DTD models allow transportation planners and operational managers to evaluate the transportation network performance under disequilibrium and help them develop reliable network design and traffic control plans to respond to expected and unexpected transportation network disruptions. Existing DTD models can be classified in terms of whether they are constructed in continuous or discrete ∗ Corresponding author. Tel.: +1 765-494-2209/765-496-9768; fax: +1 765 496 7996. E-mail addresses: seanhe@purdue.edu (X. He), peeta@purdue.edu (S. Peeta). http://dx.doi.org/10.1016/j.trb.2015.12.003 0191-2615/© 2015 Elsevier Ltd. All rights reserved. Please cite this article as: X. He, S. Peeta, A marginal utility day-to-day traffic evolution model based on one-step strategic thinking, Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.12.003