Evolutionary game theoretical approach for equilibrium of cross-border traffic

Abstract

ABSTRACTThis paper offers a game-theoretical approach and analysis for the traffic assignment problem over a set of checkpoints. In the provided formulation, the vehicle drivers’ are considered to be the rational players of the game whereas the selection among the different available checkpoints are their strategies to choose from. The objective of the game is to find an equilibrium distribution of vehicles in order to moderate the delay time at cross borders. An ad-hoc discrete event simulation is developed to show the validity of the overall approach and the findings reached. The results of the conducted simulation runs reaffirm the conclusions made showing that the system reaches stability. A discussion of the practical considerations and implementation details of the changes advocated at border-crossing points is included.HighlightsA game-theoretical analysis is provided for the traffic assignment problem at border-crossings, where vehicle drivers’ are considered to be the rational players of the game and their strategies are the checkpoints they choose from. It is proven with the aid of Brouwer Fixed Point Theorem and Replicator Dynamics that should the vehicles be supplied with meaningful data about the quality of the different available checkpoints, equilibrium and evolutionary stable state (ESS) are reached.An ad-hoc algorithmic discrete event simulator is developed to demonstrate the validity of the game-theoretic analysis and the findings made.The developed approach can be easily put to practice should the proper sensory devices be installed at each checkpoint providing accurate meaningful indicators about their quality via radio frequencies or over cellular data infrastructures.This system could come to fruition if applied practically to a border-crossing point installing sensory devices and channeling input and feedback to vehicles across radio frequencies when the overall queuing system and vehicle distribution deviate from stability having a checkpoint shut down abruptly