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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?

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

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  • $\begingroup$ Thanks, wouldn't that be a mixed NE? (not necessarily an SPNE). $\endgroup$ – Maths May 7 at 17:31
  • $\begingroup$ @Maths: You're showing a strategic form game, so it doesn't really make sense to talk about SPNE since there is no subgame there. $\endgroup$ – Herr K. May 7 at 17:36

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