Problem
Colonel Blotto can send each of his five companies to one of ten locations whose importance is valued at $1, 2, 3, . . . , 10$, respectively. No more than one company can be sent to any one location. His opponent, Count Baloney, must simultaneously do the same with his four companies. A commander who
attacks an undefended location captures it. If both commanders attack the
same location, the result is a standoff at that location. A commander’s payoff
is the sum of the values of the locations he captures minus the sum of the
values of the locations captured by the enemy. Find all dominating strategies of each player.
My attempt
First of all, we need to decide how many strategies each player has. I think it's $10 \choose 5$ and $10 \choose 4$ for the first and second players respectively.
Next idea is that since player $1$ has more companies (5 vs 4), he should use location $5, 6, 7, 8, 9, 10$ as if player $2$ places his $4$ units to the $4$ locations within $5, 6, 7, 8, 9, 10$, player $1$ still receives more.