System for preventing vehicle accidents at intersections includes a positioning system arranged in a vehicle for determining the absolute position thereof, a memory unit within the vehicle for storing data relating to edges of at least one lane of the roadway on which the vehicle may travel and the edges of at least one intersecting lane at an intersection, a receiver arranged in the vehicle for receiving position information about another vehicle in an intersecting lane, a processor coupled to the positioning system, the receiver and the memory unit for predicting a collision between the vehicles based on the position and optionally speed thereof and optionally map data, and a reactive component or system arranged in one or both vehicles and coupled to the processor. The component or system is arranged to initiate an action or change its operation if a collision is predicted.