Problem $2(2$ points$)$

Suppose a network exchange experiment is run on two different paths, one with three nodes and one with four, simultaneously, as shown in Figure $1.$ The experiment uses the one$-$exchange rule with $\backslash (\backslash$$ $1\backslash )$ placed on each edge. The graph used for the experiment has two different connected components, with seven participants in total.

$($a$)$ How much money will the Nash Bargaining Solution distribute to each node? $(0\mathrm{.}5$ point$)$

$($b$)$ Midway through the experiment, the experimenters vary the conditions by connecting nodes C and D$.$ Find a balanced configuration for how much money each node receives. $(0\mathrm{.}5$ point$)$

$($c$)$ List some applications of balanced outcomes and justify your answer. $(1$ point$)$