Based on the asymmetric exclusion process, we propose a cellular automaton model to investigate traffic conflicts at the merging part of two roads, i.e., the main and its branch road, where vehicles from these roads play conflicts game. Traffic-rule abiders will adopt yield-at-entry rule while traffic-rule ignorers will adopt defective strategy at the holding area of the intersection. Simulation results of the evolution game indicate the daily experienced flow dilemma situation can be well-reproduced, i.e., the system efficiency will not be influenced by the traffic-rule ignorers when the system is in its low density phase, but become much more congested when the system is in the high density phase where traffic-rule ignorers benefits while abiders suffer. The gaming can well explain the reason why people choose to break traffic rule when conflicts emerge.
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