Colonel Blotto and Count Baloney are opposing commanders in a

battle. There are three locations valued $1,2,3,$ and each comman$-$

der has two military units to deploy $($both to the same location or

split to diferent locations$).$ If one commander sends more units to a

location than the other, that commander captures the location and

wins its value. If both commanders send the same number of units

to a location, it is not captured and nothing is won at this location.

$($a$)$ Model this conlict as a zero$-$sum matrix game. $($b$)$ Use the method of eliminating dominated $($not necessarily

strictly dominated!$)$ strategies to reduce this to a $1\backslash$times $1$ game. $($c$)$ What strategy would you recommend to these commanders and

why?