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# mixed/pure strategies? watch

1. Hi, i'm having trouble understanding exactly what pure/mixed strategies mean in game theory. google has been no help so far!

for instance:
I have a zero-sum game

Maximin = (-1, -2, -1) = -1
Minimax = (1, 1, 0) = 1

It says "As the maximin does not equal the minimax there are no dominant or duplicate strategies here. so we must solve over the mixed strategies.

in a game like this when one player has three pure strategies and the other two pure strategies, always start by examining the payoffs of he player with two pure strategies first."

I'm completely confused as to what they mean by mixed and pure strategies. could anyone please help as i'm wasting loads of time trying to figure it out

thank you!!!

p.s. this is another example http://i54.tinypic.com/119pe15.jpg
2. Wow, that looks interesting but got no clue either!
3. (Original post by michael_douglas)
Hi, i'm having trouble understanding exactly what pure/mixed strategies mean in game theory. google has been no help so far!

for instance:
I have a zero-sum game

Maximin = (-1, -2, -1) = -1
Minimax = (1, 1, 0) = 1

It says &quot;As the maximin does not equal the minimax there are no dominant or duplicate strategies here. so we must solve over the mixed strategies.

in a game like this when one player has three pure strategies and the other two pure strategies, always start by examining the payoffs of he player with two pure strategies first.&quot;

I'm completely confused as to what they mean by mixed and pure strategies. could anyone please help as i'm wasting loads of time trying to figure it out

thank you!!!

p.s. this is another example http://i54.tinypic.com/119pe15.jpg

A pure strategy is playing one particular strategy exclusively.
A mixed strategy is playing a random mixture of different strategies with various probabilities.

So, an example of a pure strategy would be when your opponent does this, you always do that. It results in a stable Nash equilibrium if you both play your dominant pure strategies.

A mixed strategy might be a penalty kick taker, who wants to mix up the direction of his penalties so that the goalie can't guess which way he will go.

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Updated: April 1, 2011
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