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Any Strategy Can Be Defeated
Consider the following example from the Page lecture:
Front 1 Front 2 Front 3
Player One 50 30
20
Player Two
0 31
21
Player Two wins with only 52 troops to player one's 100!
If given Player One's troop allocations, player two must simply set his troop allocation to zero on the front where
Player One has the most troops, then set the other fronts to have one more troop than Player One to minimize the amount of
troops necessary to win.
There is no Pure Strategy Equilibrium
Blotto relies on players to mix strategies, or to randomize over a set a strategies. If we do not mix our strategies,
we will lose.
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