An improved arbitration apparatus for a computer network of the type having a plurality of communicating nodes, the nodes communicating by a shared bus, wherein an arbitration apparatus located in each node, functions by assigning to each node an initial arbitration count number; the apparatus includes means, in each node, for testing for the presence of a carrier signal on the bus, indicative that another node is transmitting on the bus; and means, responsive to a number of counted quiet slots (when there is absence of carrier signed on the bus) equaling the arbitration count number, for beginning transmission of a message on the bus. Also, a means, responsive to a node winning an arbitration, changes the arbitration count number of each node. The apparatus reserves a specified quiet slot for a node having no knowledge of the history of arbitration to transmit it. Responsive to a node beginning communication during a deaf node quiet slot, the apparatus reassigns an initial set of arbitration count numbers to the nodes, for resetting a clock in each node.