Game Theory 101 (#13): Weak Dominance

Game Theory 101: The Complete Textbook on Amazon: www.amazon.com/Game-Theory-10...
gametheory101.com/courses/game...
A weakly dominated strategy is a strategy that is never better than another strategy and sometimes worse. Would a player ever want to play a weakly dominated strategy? That answer may not be so obvious. Sometimes, a player earns more in a Nash equilibrium by playing a weakly dominated strategy than he earns in any other Nash equilibria. As a result, we cannot easily dismiss weakly dominated strategies as inherently foolish.

[@toocolour_]

Bless your soul, this video is so much easier to understand than my professor's monotone 1 hour-long explanation of this topic. Thank you so much!

[@lenn6776]

Thank you so much for all the effort you're putting in these videos! You well-deserve the Game Theory monopoly on UA-cam!

[@swapnak9153]

What are these topics about actually?

[@guedes_133]

Isto é perfeito para trabalhadores-estudantes! Obrigado pelos vídeos.

[@Gametheory101]

No, that would still remove Nash equilibria. Look at the "odd rule" video later in this playlist.
It's weird, yes, but it's important if you want to carry out some sort of punishment to your opponent.

[@valentinagalindocabrera3939]

thanks for the video!

[@submarineofdoctors]

Amazing tutorials!!

[@FortuneLesi]

Thank you!

[@Skadongle]

Nice explanation

[@Yangyx891121]

Thanks! For the statement "it's important if you want to carry out some sort of punishment to your opponent", isn't the payoff function defined in the way that all players want it to be maximized? Anyway, I'll take a look at the later video.

[@mattmatty1234]

Thanks for replying by the way

[@mattmatty1234]

Thanks

[@omogay]

I've been watching your series in order so sorry if this is explained in a later vid, but the explanation doesn't seem consistent.
If we change the payouts a little to (UL4,1; UR0,0; DL3,3; DR2,2) then we can see that L strictly dominates R, which leaves P1 to choose U for the eventual 4,1 outcome. Following the logic presented in this video if P2 always picks R then P1 would always pick D for the 2,2 outcome which is better for P2. Does that mean all outcomes should be considered regardless of dominance?

[@googamanga]

Calculating the Mixed Strategy Nash Equilibrium here gives Player two an expected utility of 2, which is higher than 1 at the top left. Wouldn't that mean that top left is not the Nash Equilibrium? I get player two play Left 2/3 and Right 1/3. Shows that it's sometimes good to act like a wild card so that even when you are dominated you can still get your own :p

[@graphiaful]

At 5:00 you mean "weakly dominated" right? Great videos!

[@Gametheory101]

Yep, my mistake. Same problem around 4:50 as well.

[@mattmatty1234]

First moves, threats and promises? Techniques that improve your position in a game

[@Yangyx891121]

In this case, yes, we can't eliminate weakly dominated strategy. But what about a slight change? Suppose only (Up, Left) profile will yield positive results, while the other three profiles get (0,0) for both players. In this case, can we eliminate the weakly dominated strategy? I mean, in this case, for both players, choosing Left or Up is the only possible way of getting positive outcomes. Don't see why anyone would play weakly dominated strategy in this case. Lb hp 2 no ur view on this.

[@Gametheory101]

Interesting, I also just won $1 million playing golf.

[@ratul_org]

Really?

[@Gametheory101]

I don't know what that is.

[@bestbytest1974]

Isn't the best responses algorithm, described at #6, the first thing we must check? It gives us easily all Nash equilibriums if they are present. So why bother with IESDS in the first place?

[@Gametheory101]

That's chapter two.

[@mattmatty1234]

Can you do a video Strategic Moves?

[@Gametheory101]

Wait, did you mean someone other than the golfer?

[@marcopolo2395]

Is it possible to start with player 1?

[@niemand262]

In poker we use the terms hero and villain. I find it much more easily understood than player 1 vs 2. Great content, but man it can get tough hearing all the ones and twos. I'm starting to wonder if you're transmitting a super secret binary code.

[@alexting827]

wut

[@ricardocruz392]

Estricanimus Spertalipius Rex. Try. One. Last. Time.

[@BS33875]

why not take into consideration of the opponent's payoff?

[@Shaolinh808]

Vallah stabile Video

[@PunmasterSTP]

Weak dominance? More like “we’re going to ace our tests”, with all of the great information you’re teaching us!
(As an aside, I’m not actually in a game theory class nor do I have to take a test on it. My statement was purely doe the purpose of making a pun…)