Proposed safety applications for vehicle-to-vehicle (V2V) communication rely mostly on periodic broadcasting. In this work we analyze the performance and fairness aspects of such an one-hop periodic broadcast communication. We show that communication reliability is greatly dependent on the random relative phasing of the communicating vehicles and on the impact of hidden nodes. For a random initial phasing some vehicles suffer from consecutive packet losses thereby becoming invisible to neighboring vehicles for a long time, whereas some other vehicles have no packet loss at all. We propose a simple and effective approach to provide fair transmission opportunities and show the improvements through simulations