We start this paper by proving that, if we fix the values of the source nodes (nodes with in-degree 0), the expected number of fixed points of any RBN is one (independently of the topology we choose).
These models relax the normal requirement of all nodes having the same update rule. Nodes within a block were updated synchronously, but blocks were updated asynchronously.
The statistical properties of this method are completely independent of the size of the grid.
Consecutive updating steps therefore show no correlation at all.
At the end of a round each vertex may change its strategy to that of its neighbour with the highest pay-off.
Here we study the spread of cooperative and selfish behaviours on a toroidal grid, where each vertex is initially a cooperator with probability $p$.
Cyclic dynamics occur only with synchronous updating.