Game Theory 101: Iterated Elimination of Strictly Dominated Strategies

http://gametheory101.com/Textbook.html

How can you reduce large matrices into simpler ones to solve? William Spaniel shows how iterated elimination of strictly dominated strategies (IESDS) can do just this for you.

For more, visit gametheory101.com.

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• How
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• Game
• Theory
• Explained
• Prisoner's
• Dilemma
• Dominance
• Lecture
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• Equilibrium
• Economics
• Iterated
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• Strictly
• Dominated
• Strategies
• IESDS

[xBustx]

Hi William, first off, your videos are awesome. Learned a lot. Thanks. Anyways I'm working on a problem that is asking if I can solve a problem with iterated strict dominance. I was doing fine until I got stuck. Am I allowed to eliminate a column if one of the payoffs are the same. For example, lets say its a 2 by 2 matrix.

(1,3) (4,4)

(5,3) (1,3)

Can you say that column 2 dominates column 1? Sorry can't find it in my textbook :/ Thanks in advance!

[JimBobJenkins]

@xBustx You should buy my textbook because it is cheap and I cover this. In the mean time, the answer is yes...and no. Search YouTube for "game theory 101 weak dominance" to get the explanation.

[MrMirKuja]

The last part where you were left with middle and top middle why did you say that 3 dominates 1 so you were left with the middle part that is {3,3} instead of 4 dominates 3 and be left with {1,4}?

[JimBobJenkins]

@MrMirKuja Because we were looking at player 1's moves and therefore have to look at player 1's payoffs.

[MrMirKuja]

@JimBobJenkins Yea but sometimes you eliminated columns by looking at player 2's moves. For instance why didn't you eliminate center first instead of right because player 1's outcome on right dominates player 1's outcome on center?

[JimBobJenkins]

@MrMirKuja You eliminate rows based off of player 1's payoffs and columns based off of player 2's payoffs.

[11cookeaw1]

If they know what the other person likes fully, and it's not a zero some game, then things can get interesting...

lets say up left gives 3.5 points for red instead of 3. Let's say their currently at centre middle, red could then change to left, knowing that blue will change to left, netting red 3.5 points instead of 3.

[Eehsun]

@chintanjadwani

It is Player 2 who determines what column is there to stay (since it is her who makes the choice among the options "left", "center" or "right"). Thus, only the possible interest of Player 2 is to be considered when comparing columns.

[killshitallday]

I understand it all perfectly the thing I don't get, is the outcome, who actually chooses what. You say they both know they both always defect, which means they narc on eachother, putting them both in jail for 5 years each. If the best outcome was both crooks not talking, and catching a year each, how can you prove who cracks first, or if they would crack at all? This game theory doesn't hold true, of course it's just a form of showing you all possible outcomes. I bet many crooks don't talk.

[chintanjadwani]

what if i compared the center and the right for player 1? Then 7 dominates 1, 6 dominates 3 and 8 dominates 2. Thus eliminating the center column, giving a completely different answer. Please clarify my mistake.