Game Theory 101: The Complete Textbook on Amazon:

The prisoner’s dilemma had an obvious solution because each player had one strategy that was always the best regardless of what the other players do. Most games don’t have solutions that are that simple, however. What if one player’s best strategy depends entirely on which strategy the other player chose?

This video covers iterated elimination of strictly dominated strategies. If one strategy is always worse than another for a player, that means the other player should infer that the first player would never choose that poor strategy. But this has interesting implications. It is possible to keep removing strategies from a game based on this information, until you eventually arrive at a single solution. We go over an example in this video.

As a general rule, if you ever see a strictly dominated strategy, you should always eliminate it immediately. Although there may be more strictly dominated strategies that you could eliminate first, those other strictly dominated strategies will still be strictly dominated in the reduced game. Therefore, you lose nothing by immediately eliminating a strategy.

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I am loving this thanks alot.

thank you thank you thank you

very clear 🙂

Tbh, IESDS is a fracking long ass word

for player 2 why do you eliminate the option of right? because i am o with its elimination when u compare it with center but if u compare it with left no strategy between left and right seems strictly dominated….

Does the elimination always follow a strict order? As in player 1 eliminates a strategy, then it's player 2's turn to eliminate a strategy, then it's back to player 1 to eliminate another ????

u r too fast sir yoh decrease your speed as you are teaching students, u sound as if u r in a hurry

You are the GOAT sir

Is there a jump in the video? How did we get from confess vs. keep quiet to up, middle, down vs. left, center, right? I don't understand what game this matrix is dealing with.

Thanks a lot

Why does (3,3) dominate (1,4)? doesn't Player 2 dominate by deviating?

This was a great explination, so much more clear then "choice theory a shrt introduktion" by Allingham, thasnks.

"right" is not actually STRICTLY dominated because it's better than "left" when player one does middle. I believe the correct terminology is "never a best response" so right is dominated by middle but not by left therefore it is not strictly dominated however it is never a best response because middle is always better than left.

Thank you for these videos. You are really helping me with my decision theory class as we are spending a lot of time on game theory.

Nice job explaining this but it would be helpful if you had labeled the players on the 3 by 3.

Why wouldn't (13,3) be the answer?

The way I rationalize it, is that; P1 will never choose middle because that's the action or move that will make him absolute worst off and P2 with also knowing the information P1 knows will never choose C because he know even though he has an highest return of 4 that P2 will always be unsatisfied because 13 is a larger lost to 3 for P1 than 4 is to 3 for P2. Thus, I will rather loose 4 to 3 as player two than to let player one loose 13 to 3 … which uses the exact same logic why neither P1 nor P2 will choose (4,1) nor (1,4) respectively. I personally and strongly believe choosing (3,3) goes against the logical or rational pattern initiated from the beginning of the game.

What's the application of this kind of knowledge? Can you give any historical or real world scenarios where knowing how this works has given someone an advantage or benefit?

the prisoners dilemma threw me off, I kept seeing the numbers as months in jail. So in this game the greater the number the better?

Heey Thank u for the videos.

A quick question.

How is the win defined?

is it :

1.) To get a maximum for myself or

2.) To be greater than the other.

Hi William… thanks for the video. i was trying out a different example.

(5,9) (6,3) (-1,8)

(8,-1) (3,6) (9,5)

(4,4) (2,7) (7,2)

i first compared C and R, and eliminated R since C dominated R by 2:1.

then I removed D as it has lesser payoff in comparison to U and M.

Now, I was left with –

(5,9) (6,3)

(8,-1) (3,6)

How to proceed from here?

HAHAHA, we all know that the assumption of intelligence doesn't always hold. :/

If we would say that the choice was between both of the players keeping quiet and both of them confessing then keeping quiet would be the dominant outcome. So could we not also, just as you did at the beginning of the video by comparing when one talked and the other stayed quiet the better outcome, compare the outcomes of both staying quiet or both confessing? If they were rational actors would they also not see that that was the best outcome?

This assumes that the players are aware of each other's payouts, correct? That seems odd to me.

Brilliant. This is helping me get the basics so well it makes me feel way smarter than I am. Thanks so much for this.

what happens if there is a 3 strategy game and one strategy is dominated by both of the other 2 strategies but not by any 1 single strategy ? thanks a lot

your logic is flawless! I am not convinced I have the aptitude for this.

What if the game is fixed though?.. ok, probably a dumb question. I sort of got where all the numbers come from in the prisoner's dilemma, maybe this would make more sense to me if these numbers fit into a particular situation. Does that make sense? Sorry if I'm just being thick though. Thanks for your time and for making all these videos!

You have great empathy with the learning audience, making it damn easy to understand what you're teaching. i.e. You understand what will confuse us or intimidate us and either acknowledge it or give an explanation for it.

Is there a physical copy of the textbook available, or is it just Kindle?

You talk really fast haha, even faster than I do.

Do you also sell your book in a paper version rather than the ebook format? I prefer paper books and would like to buy it!

Omg thank you so much. So helpful. It was driving me nuts.

Some of your simplified descriptions of probability theory have actually sparked me to review a topic outside my field of mathematical logic. When you mentioned negative probability it got me thinking about a paper Richard Feynman wrote long time ago, when I was math student minoring in physics. Something about that made me remember that somebody had proposed the idea of negative probability and lo and behold I searched for it and find it's there.There is negative probability in QM BTW William. It can apply to quantum states of small sub-atomic particles… the theory is so unrelated I won't delve into it here. Then you mentioned one that's bugged me for a long time x/0, the undefined operation in abstract algebra. I am starting to theorize how if this is allowed the profound implications of creating a new dimension to AA.

BTW, though your descriptions are sometimes painfully simple and directed at novices, I still enjoy them.

But what if they have no knowledge of their prison times? The payoff matrices should change drastically. If the only knowledge prisoner A and B are given is they can confess or not and that's all their accomplice can do is implicit. Here the minimization strategy should be to keep quiet with the rational assumption the other will too, because he doesn't know what will happen too. They do know that if they don't rat, the police can't do much to them. This is a permutation of PR. There are permutations to PT.

Basically this theory assumes that both players have some intelligence to figure out their best move right?

If the objective of either player is to gain the most amount of points relative to the other player, we are dealt with a different game meta with the same result. You would anticipate that either player would select centre/middle as it is statistically advantageous to do so (each outcome in that column or row is either a tie or point advantage).

This is more helpful than other vids I've watched. Inference over inference over inference though, wrinkles my brain.

Entirely different, yes.

Entirely different, yes.

oh okay, so that would mean the numerical values in the grid would be different then?

Then you'd have to change the payoffs entirely.

what is player one's strategic goal is to deny points to player two rather than earn maximum points?

The players move simultaneously. Player 2 has no choice in the matter because she has no ability to control player 1's move, and player 1 has no reason to play up when he could play middle instead.

great vid, thanks

Check out the next video on pure strategy Nash equilibrium!

what if for player 2 Center isn't a strictly dominating strategy? for example, in UP;CENTER if you have (1,2) instead of (1,4), then center isn't better than right