Game Theory 101: Iterated Elimination of Strictly Dominated Strategies

[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.

[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.

[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.

[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.

[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.

[IcyHail]

hey william, im really interested in game theory and I find your videos very informative! im studying economics at the moment and hope to graduate next year. i was wondering do you know what jobs use game theory extensively? like the actual job title thanks!

[Son0fHobs]

Wait, why do you only compare rows/columns next to each other, as apposed to all three rows, or all three columns? As in an actual game, I can't see a player limited to certain options.

[JimBobJenkins]

@Son0fHobs Because of option A is better than option B in all cases, then you don't need to even consider option C to know that you should never play option B. Eventually, you have to consider option A versus option C (and that happens in this game), but you do not need to look at all three to see that option B is not a smart move.

[paxpakspax]

"Hi, I'm William Spaniel" HAHA the same accent every fckn time! haha good videos bro, Imma subscribe. 

[TheDrCN]

How would this work without perfect information? For example, if Blue didn't know that Right was a strictly dominated strategy for Red, then Down would still be an appropriate strategy for Blue.

[Xavygravy]

Game theory seems very interesting! A few of questions: 1. what is the reason for eliminating the rows/columns in turns? 2. why can't we eliminate middle/non-end rows/columns? 3. is it an error at 2:15 where it seems to read 1 > 3? Thanks in advance!

[JimBobJenkins]

@Xavygravy 1) Something strategies cannot be eliminated at the start. You have to go sequentially before you can. 2) You could, but not for this game. If you really wanted to, you could just swap the numbers in the right column with the center column. 3) This is indeed wrong.

[SonOfNye]

You sir have earned a subscriber.

[jacknicklaus99]

ohhh i get it now nvm

[jacknicklaus99]

i dont get it, right dominates middle for player one tho right?

[brunedeezy]

The terms "Cooperate" and "Defect" had me confused. To me, in this situation, to cooperate w/ police is to defect. Had some trouble following the example.

[bobbygnosis]

It took me two viewings to understand that you were looking at how player one was going to play. A minor defect. I have enoyed the first two videos and look forward to seeing the rest.

[thecapone45]

ok so i want to know if i can do this for things like,,, lets say.... a video game... land vs.air.vs. sea... and the three players are each good at three different things,,, (three strategies, three players) can i use game theory to see what the best strategy would be/ b/c mos tof this stuff is logical anways,,, so i kinda wanted to know when is the best time to use game theory.

[JimBobJenkins]

@thecapone45 Yes, and this is one of my research interests. There exist a few academic journals for game studies, but they currently lack this kind of structure.

[ithinkimemo04]

im kinda new to this game theory thing and im really not good in my vocabularies but im really good in math actually....so what does this game theory do..it leaves me interested....please help...

[JimBobJenkins]

@HomoForever This is a mechanical issue. The numbers represents the preferences over outcomes of the players, i.e. I prefer an outcome of 8 to an outcome of 6 to an outcome of 0, etc. So "8 is greater than 6" actually means "I prefer this '8' outcome to this '6' outcome." In turn, by definition, 8 is greater than 6.

[JimBobJenkins]

@JimBobJenkins Most professors will teach this sort of mechanical stuff from the start. I don't because it is uninteresting, and students cannot appreciate the mechanical details until they understand the basics of game theory (even if the game theory is built off of these mechanics).

[kissmyass112]

Thanks a lot man. i gotta write a 10 page research paper on this

[sanjog81]

Got it. Thanks so much. BIG help!!!

[sanjog81]

Hi...very interesting lectures. I've always had a fascination for the Game Theory but never came across such a comprehensive yet easy to understand representation.

Can you explain why you chose Center over Left for Player 2 rather than choosing Up over middle (which can also be the dominated strategy for Player 2) This would have left you with 13,3 as the unique equilibrium

[JimBobJenkins]

@sanjog81 When searching for dominated strategies, you only look at the payoffs for the player whose moves you are looking at. Up and middle are player 1's moves, so we only look at the blue payoffs for the outcomes that follow from it. Middle may be bad for player 2, but she has no control over player 1 if he wants to play it. So up does not dominate middle.

Also, [up, left] is clearly not an equilibrium because player 2 would want to deviate to middle and earn 4 points instead.

[saintdracula1]

Holy shit, thank you so much.

[silverspear08]

In you first iteration of elimination, center > right for player 2. So you eliminated right. However, if you look at it from player 1's side, right > center . Hence center should be eliminated.

The same conflict occurs in the 3rd elimination, left > center for player one. But here also you did the elimination after looking at it from player 2's perspective.

Can you explain ? thanks in advance

[JimBobJenkins]

@silverspear08 Think of it like this: Player 2 gets to decide whether she wants to move center or right. Even if player 1 really likes it when player 2 moves in a certain direction, he cannot actually force her to play one strategy over another. So we only look at player 2's payoffs when we are considering whether any of 2's strategies are strictly dominated.

[JimBobJenkins]

@silverspear08 You can also go back to the prisoner's dilemma video if another game with the same property might help.

[abdihassanawali]

@JimBobJenkins

I understand completely now. Thanks. As only a high school, I am attempting to understand game theory, and so far your videos are very easy to grasp. Thanks again, and I'll be sure to pass on your videos.

[abdihassanawali]

@JimBobJenkins

How do you determine which row/column to elimante first? Do you start from a cerain direction or from a certain variable or what?

[JimBobJenkins]

@abdihassanawali You to brute force the matrices until you find one that is strictly dominated. This can take a while. But once you find one, you can immediately eliminate it; if there are two or more that could be eliminated at the same time, there is no advantage or disadvantage to choosing one or the another first.

[JimBobJenkins]

Which square?

[lifesbrink]

I understand the idea that changing strategies changes the answers, but what does this square have to do with anything??

[csae2930]

Thanks...now i have to wonder again...

greets, an economic

[LukasSlothuus]

Is there anywhere online where I can find lots of game theory exercises?

[CAFowler2011]

really enjoying the lecture, but when eliminating strictly dominated strategies, wouldn't it all have to be from the perspective of one player? you eliminated the right row by means of player 2 while eliminated down by means of player 1

[JimBobJenkins]

@CAFowler2011 Nope. That's the great part about iterated elimination.

[Daggroth]

@JimBobJenkins But weren't we just talking about the perspective of one player? The same thing for player one isn't best choice for player 2...etc

[JimBobJenkins]

@Daggroth Hmm, it seems that there is some miscommunication here. When you are finding strictly dominated strategies, you can only look at the payoffs of the player whose strategy you are trying to eliminate. But once a strategy has been eliminated, you can ignore that part of the payoff matrix for BOTH players. That is what makes IESDS such a useful tool.

[Daggroth]

@JimBobJenkins

Yes, you eliminated the strategy for one person---but for the other player, what if that strategy is still valid? I see what you're saying, but I'm watching these after being up for some number of hours...so explain to me. I see that center dominates right---for player 2. But for player one right is much better than center, so why wouldn't player one use right?

[Daggroth]

@JimBobJenkins What I'm getting at, is even if you eliminate right for player 2, wouldn't it be a valid strategy for player 1? Seeing as how right is superior for player 1, but not player 2... or am I coming at this from the wrong way?