Iterative Deletion of Dominated Strategies

economicsdetective.com/
As I mentioned before, not all games have a strictly dominant strategy. However, there's another way we can use the concept of strictly dominated strategies to find equilibria.
Let's say we have another two-player game. The players have choices A, B, C, and D. Player 1's payoff is negative one if players play B,D, zero if they play B,C, or A,D, and one if they play A,C. Player 2's payoffs are five if they play A,C, and two if they play A,D, and... actually there's no point in me saying what his payoffs are in the other two cases, because we already have enough information to find an equilibrium.
But how can that be? It's simple. Player 2 knows player 1's payoffs, and he knows that player 1 is rational. So he knows that player 1 will not play B, because player 1 is always better off playing A. B is strictly dominated by A, so player 2 can ignore the possibility that B will be played. So we can delete B as an option, and then we see that player 2 must choose C, as A,C gives him a larger payoff than does A,D.
This might be an dominant strategy equilibrium depending on player 2's payoffs, but it doesn't have to be.
Here's a more complicated example. There's no dominant strategy equilibrium here, but let's see if we can find an equilibrium by deleting the strictly dominated strategies.
We can see that player 1 will never pick C because he's always better off choosing B, so let's delete that. Now, given that C has been deleted, F can be deleted also. A,F and B,F both give player 2 a payoff of zero, and he could get a payoff of one by playing G, so he won't play F. With F deleted, player 1 won't ever play A, since he can always be better off playing B. That leaves player 1 playing B for sure, and player 2 can clearly see that he get his highest payoff in B,D, so he can eliminate E and G.
So there you have it, an equilibrium.

[@PunmasterSTP]

Very succinct and well-explained; thank you for sharing!

[@sreetamaray_]

GREAT GREAT WORK! Beautiful explanation!

[@Ineedhelpig1082]

I’m confused at the key he’s using. What do all those values indicate?

[@amoungstus]

Good video, using bigger matrix is a good visualization

[@MsEady123]

This was so helpful. Thank you

[@pontusliljeblad]

great videos, keep em coming!

[@manasichhabra6572]

I like this approach :)

[@joesr31]

Must the elimination always be alternating? like player 1 then player 2 then player 1....or can it be player 1 player1 player2 player 2?

[@GarrettPetersen]

joesr31 It doesn't have to be, but when you delete a strategy from player 1, it often creates a new dominated strategy for player 2.

[@CrazyLikeChris]

@@GarrettPetersen That makes things more confusing. so what is the best way to approach this? alternate or not?

[@caesertullo1824]

so is D the best choice for P2? I'm a bit confused.

[@bappibhai1]

Steps 1. P1 will never eliminate C as C is always < A & B 2. P2 will consider step 1 and eliminate F as F as F is always < D, E & G (considering P1 will not chose C) 3. P1 will consider both step 1 and step 2 and eliminate A as A is always < B (considering both players will not chose C and F) 4. P2 will now consider all the above steps and will only chose D as P1 (as being rational) will always chose B and for P2 D > all other options if P1 choose B

[@Meckka72]

Writing a paper in school about the Game Theory in general, would really like to get some explanation for the Bayesian Equilibrium and the Weak Perfect Bayesian Equilibrium. mind uploading a video for those?

[@PunmasterSTP]

I know it's been half a decade, but I just came across your comment and was curious. How'd the paper and the rest of your classes go?

[@shahreartowhid878]

Why F can be deleted? Please explain.

[@GarrettPetersen]

C is strictly dominated by B for player 1, so we delete it first. Then the remaining entries for F are strictly worse than E for player 2, so we can delete it.

[@Dururugi]

thanks!

[@sitrakamatthieu]

Thank you !!!! :')

[@RahulSinha15]

Nice :-) thank u.

[@jhewitt2008]

Sick

[@rtfherrd5658]

matematica di tipo elliederico

[@kyler3035]

I’m extremely interested in game theory but I have not conceptualized the fundamentals , (poor education ). With that said I can safely say I have no fucking idea what’s going on here. I need a elementary breakdown, (faraday’s elementary) what do these values in the matrix represent? Why is one favored??? What the hell is going on??

[@kyler3035]

It’s not your fault, but I’m seriously disappointed I don’t get the most rudimentary concepts of this field. Any recommendations that might help would be welcome.

[@augustocesarfg]

@@kyler3035 still need help?