Provided are an automatic driving control system and an automatic driving control method that are capable of clearing away suspicion of a foul by exchanging a “hand” for determining priority of passage by a fair method that allows no foul when automatically driven vehicles face each other on a road. When the automatically driven vehicles face each other on the road, the “hand” for determining the priority of passage is exchanged by performing transmission/reception two times by use of a composite number of prime numbers each having a large number of digits.