Game Theory 101: The Mixed Strategy Algorithm

http://gametheory101.com/Textbook.html

William Spaniel shows how to calculate mixed strategy Nash equilibria when they are not immediately apparent.

Category:

Education

Tags:

• game
• theory
• explained
• how
• to
• solve
• pure
• mixed
• strategy
• nash
• equilibrium

[swaine55]

what if you have 2 players which each have 3 options? such as up middle and down?

[JimBobJenkins]

@swaine55 You have to consider all combinations of mixed strategies, which is quite a headache.

[FilthParade]

These are great videos! I have a question for this game specifically though. Is the point to get the most points or just more points than the other player?

If the point is to just beat the other player than player two's strategy should be to get a point advantage and then always play right as she will always get either 2 points or zero. How would a strategy like that be represented?

[JimBobJenkins]

@FilthParade Players maximize their own payoffs. They are only concerned about their opponents' strategies insofar as it affects which strategies they play.

You are thinking of zero sum games, where the payoffs in every cell sum up to zero, i.e. if my payoff is X, yours is -X. This is a special class of games that I don't really focus on.

[JimBobJenkins]

@FilthParade Matching pennies is a zero-sum game, btw.

[corporalcharlie]

Again. Thanks a lot for this. I cant believe I'm learning more from a youtube video than from my ivy league classes with my lecturer from eastern europe..

Cheers mate!! Please keep it up.

[blanc11]

I just want to thank you for posting this amazing video! You have no idea how much you've helped me! Thanks again!

[daboiisgud]

God Bless you baba!

[rhyswaterfield]

thank you



[TheAnimefever]

This is awesome man

[irondia73]

saved my life.... thank you

[Nahelaa]

you're a life saver <3

[SamAt5am]

You are my own personal jesus christ. I missed a week of classes, and was so lost on my homework right now. Thank god for you. Thank you so much man.

[bigbrun13]

@corporalcharlie I'm at one of your fellow institutions with the same problem. Cheers indeed

[denilson12001]

@JimBobJenkins Great lecture!! But maybe I've got confused: why can't we jump the conclusion that the final trend would end up with Down-Right result, as DubaiGuy08 said below? Or, to more basic, what's the meaning of the calculated result? I mean, for Player 1: Down=5/6 it represents that Player 1 would like to chose more Downs than Ups, doesn't it?

And for Player 2: Right 2/3, that means Player 2 prefer to decide more Rights than Lefts, right? What's my misunderstanding? Thanks.

[northfromheree]

Thanks, pretty much useful! We'll see if it helps me get rid of my algorithmics assignment :)