Suppose a network exchange theory experiment is run on the graph depicted in Fig$-$

ure $12\mathrm{.}14$ using the one$-$exchange rule with $$10$ placed on each edge.

Figure $12\mathrm{.}14$: A $4-$node path in a network exchange theory experiment.

$($a$)$ After running the experiment for a while, the experimenters vary the network:

they introduce two further nodes $e$ and $f,$ and bring in additional people to play the

roles of these nodes. Node $e$ is attached by a single edge to node $b,$ while node $f$ is

attached by a single edge to node $c.$

A new round of experiments is performed with this new six$-$node network. Explain

what you think will happen to the relative power of the participants, compared to the

situation in the original four$-$node network. Give a brief $(1-3$ sentence$)$ explanation for

your answer. You do not need to give actual numbers for the amounts of money the

nodes would receive.

$($b$)$ The experimenters now decide to vary the network again. They keep the same

set of nodes, but now they add an edge linking $e$ directly to $f.($The existing edges

continue to remain in place as well.$)$

A new round of experiments is performed with this modified six$-$node network. Explain

what you think will happen to the relative power of the participants, compared to the

situation on the previous six$-$node network in part $($a$).$ Give a brief $(1-3$ sentence$)$

explanation for your answer. You do not need to give actual numbers for the amounts

of money the nodes would receive.