Game Theory 101: Battle of the Sexes in General Form

William Spaniel shows how to prove that mixed strategies are valid as he solves the general form of Battle of the Sexes.

Category:

Education

Tags:

• Game
• Theory
• Battle
• of
• the
• Sexes
• Pure
• Mixed
• Strategy
• Nash
• Equilibrium

[brandeisjks]

If yes, then wouldn't a required stipulation of the exogenous variables be A=a, B=b, C=c and D=d; or is the case of the letters just a convention used to distinguish between the Players, with letters of the alphabet assumed to be equal?

[JimBobJenkins]

@brandeisjks It would be the same expression with capital letters. The actual value of this fraction will differ, of course, according to what all of those variables equal.

[TamaThePeck]

at 1:33 you make a mistake, but then at 1:39 you make another mistake that evens the equation out again to being correct. On line 6 where it says: "Sf(a) + Sf(b) + c - 2Sf(c)"

the "+c" should be removed (or the "-c" on the end of the same line)

[JimBobJenkins]

Unfortunately, you are right. Perhaps I will look into redoing this one.

[LArgo5698]

I lost the game

[CogitoErgoCogitoSum]

If you know your opponents mixed strategy probability distribution, can you not adjust your own to ensure greater utility?

[brandeisjks]

Thanks for all the work you put into this. It's incredible that one can learn game theory from YouTube.

[brandeisjks]

Question:

In the video you work out the Man's mixed strategy and prove that it is valid.  Near the end you comment that each player will go to their preferred entertainment venue with the demonstrated mixed strategy probability, but don't explain why this probability is the same for the Woman. Is this because the game is symmetrical along noncooperative strategies?

[ForbiddianSC]

I would have to end up going to the ballet. :-(.