# Mixed Strategy subgame perfect equilibrium

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If player I can commit to a mixed strategy (1-p,p) for strategies (A,B) and player II knows the probability (1-p,p) applied to both strategies, what is the value of p in a subgame perfect equilibrium?

Hint: the probability must make player 2 indifferent between playing either strategies $$p$$ and $$q$$, or strategies $$p$$ and $$r$$.