Informal simulation of basic game
The graphics in links show progress of competing red and green agents using the NUV strategy
on a 100-vertex graph.
Figure 1
shows the trajectories starting at 0 until a later epoch 1: the trajectories remain
well separated.
Figure 2 continues until epoch 2 where they remain separated.
Figure 3 shows that at epoch 3,
each agent is blocked by the other; both have to move through several edges to reach their next
accessible unvisited vertex, epoch 4 in
Figure 4.
Green is now forced to move a long distance to the next accessible vertex at epoch 5, while
red is able to visit many new vertices during this time
Figure 5.
We see further progress in
Figure 6
and
Figure 7.
At this point we see that green is confined to the top right section of the graph
while red can explore all the remainder, so we must terminate
at with the partition shown in
Figure 8.
Red owns 59 vertices to green's 41.
Note: This small-n example seems atypical because green soon becomes trapped against a boundary.
Presumably this is unlikely for large n.
