Modeling bounded rationality in discretionary lane change with the quantal response equilibrium of game theory

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The primary purpose of discretionary lane change is to provide a speed advantage or a better driving environment. Game theory is one way to find each driver's most reasonable behavior plan by studying their competitive lane-changing behavior. Nash equilibrium provides an effective strategy to ensure the lane-changing vehicle can reach the maximum value of its expected returns. Other vehicles in the game also follow this strategy. However, due to the inadequate understanding of the driving environment and drivers’ physiological and psychological factors, it is difficult to have the entirely rational conditions required by Nash equilibrium, whose solution is usually quite different from the actual result. To quantify drivers’ rationality in lane-changing decisions, we established a model of bounded rationality based on the quantal response equilibrium (QRE), in which drivers are not perfect optimizers and face uncertainty in other drivers’ actions. The maximum likelihood estimation and data analysis from NGSIM confirm that drivers in discretionary lane-changing games exhibit bounded rationality. As the lane-changing decision continues, drivers become more aware of their surroundings to be more rational. More than 91.5% of our model predictions are in line, which means our QRE model can effectively describe discretionary lane-changing decision behavior. Compared to Talebpour's game model, our model has a stronger predictive ability and can more accurately describe discretionary lane-changing behavior.