$(15$ points$)$ A solution in mixed strategies. There is yet another election. Two politicians, Jones and

Smith, will enter a debate. In this election there are three main issues $($issues A$,$ B$,$ and C$)$ to which

voters pay attention. There is no time to prepare for all three issues, so each politician must $($privately$)$

select one of these issues to emphasize during the debate. The estimated increase in the vote for Jones

$($expressed as a percentage of the total vote$)$ resulting from each combination of issues is given in the

table below. Note that this is a zero$-$sum game because one politician gains what the other loses $($in

votes$).$

Smith

$($a$)$ Determine the optimal strategies for Jones and Smith.

$($b$)$ If Jones plays her optimal strategy, what is the expected gain$/$loss in percentage votes?