Game Theory 101 (#6): Best Responses

[@Gametheory101]

Check the payoff matrix again. There are no strictly dominated strategies here. Recall that a strictly dominated strategy must always be WORSE than another strategy. If it is sometimes equally as good, then it is not strictly dominated. We cover this type of "weak dominance" later.

[@uselesvideo]

Hey, I have exam day after tomorrow on a little bit of game theory that's the reason I started watching this playlist but now I am hooked. Thanks a lot for this AWESOMETICULAR playlist. Cheers.

[@Gametheory101]

Weak dominance is very tricky. The videos at the end of this chapter get to it. Remember, though, that Nash equilibrium requires a player to not have any profitable deviations; indifference is okay. That's why there are four pure strategy Nash equilibria here and not just one.

[@TheAmazingShindig]

There seems to be some confusion about this table and what this strategy means. Let me try to clear some things up. 1) The first thing to say is that, of course, this table does not represent all of the intricacies of commanding troops in an actual battle. The theme of generals and soldiers is just a skin draped over the abstract game to lend motivation to the outcomes. 2) The values of each choice are not meant to represent the mathematically expected outcome for each strategy if your opponent plays randomly. We assume here that your opponent is smart enough to not send 1 or 2 units. Beyond that, it makes no difference if they send 0 or 3. In either case, you both do as well as one could expect to do against a skilled opponent. 3) To elaborate on the last point, consider the game of tic-tac-toe. Some moves will set you up to trap your opponent. These moves are similar to sending 3 units to the battle. Yes, you could win, but like tic-tac-toe, this is irrelevant if your opponent knows the best strategy. You are essentially just choosing your favorite flavor of draw. 4) The thing that really makes this table strange is the fact that you can draw by not sending troops when your opponent does. If we were to change the table so that not defending against an attack is considered a loss (which is more realistic anyway) then indeed, sending 3 units would be the only good choice. I hope this helps.

[@davidchl7]

hi, i dont usually leave comments. actually, i dnt even sign in, but i just signed in to say Thank you so much and I love you.

[@KitanaSamoa]

Extremely helpful video. Helped me figure out how to calculate best response(s) with considerable ease.

[@alvaropapic1099]

ARGHSTERIZCKS awesome series by the way!

[@eltepusunny]

I came to the comments to see this comment LOL

[@danayakhartchenko7366]

I thoroughly enjoy the struggle to pronounce asterisk with much dilemma every time it is said, :)

[@Michmanjuga]

is that the best you've heard here?

[@Gametheory101]

I call unequivocally state that I do not enjoy reaching that dilemma on a regular basis.

[@danayakhartchenko7366]

William Spaniel Its one of those simple things in life that brought me joy.

[@Archangel10123]

+WilliamSpaniel FYI: "Star" is a suitable synonym. :-)

[@thaer12345]

Why don't we just solve this with the strictly dominated strategy technique we employed in one of the earlier videos? The one where you simplify a matrix by erasing columns and rows. It's a much simpler way to solve this game.

[@jasondean88888]

Those asking: At the beginning he states that either general can unilaterally skip the battle by deciding to lass. Unilaterally means it only takes 1 person to make the decision to skip.

[@jamesdi7261]

This lecture is a pure gold 🥇

[@DrQlimakz]

Extremely helpful series

[@Gametheory101]

Thanks!

[@thomasmatthews80]

So brilliant. I am learning to help with my (GTO) poker. Does he ever mention pokers application in this series?

[@slowsatsuma3214]

I don’t understand, I would have thought (3,3) would be the natural Nash equilibrium. Passing guarantees that you won’t lose but putting 3 guarantees that you won’t lose AND gives you the possibility to win. So why would they not, being as intelligent as they are, not just always put 3?

[@generalpinochetfoundthesol3747]

Because of 2 reasons. 1. Rules . - it is still a draw if you opt out of the battle , even if the enemy sends 3 units . 2. We expect that the enemy is perfectly intelligent . This means that it will never send 1 or 2 units and will ether choose to send 3 or will pass the battle . In both cases it is a draw. If one of the two is changed , you will be right , but when both are active the outcome is the same regardless of what you choose . Also if you dont mind me asking from where is your avatar . It is really popular on KZbin , but i don't know why?

[@gmeaki02]

@@generalpinochetfoundthesol3747 JC Denton from Deus Ex

[@Rockernaxo]

Thanks for the explanation! It was well organized and clear

[@jermaine2712]

Diego Simeone plays the "pass" move for all wars.

[@crescentzhang1624]

you've saved my zoom university life, thx much much 😢

[@WithoutException]

even pre-zoom university, college/high school studying has always been youtube videos to cover shitty professors/teachers

[@chocolatesaredelicio]

does this mean that the two actors i.e the generals are most likely either to pass or send out three units assuming the generals are trying to maximize they're wins while also trying to minimize losses (i.e playing it safe)

[@sadeghghazanfari]

Very simple and helpful, thanks

[@noneofyoureffingbizness5806]

ok.i intuitively understand that the best response in the given case is either 0 or 3.how do i prove it though?the one with most asteriscs wins??

[@opinionsarenotmyown8818]

Why is sending three units equivalent to passing? After deciding the Nash Equilibrium, it's clearly better for both players to just pass; if he sends 3 units and the other one sends e units, so they go to war, they get a draw. If either one passes, they get a draw still. So it's better for both of them to pass to make sure at least one of them is passing. How do we represent this in the outcomes table?

[@TheCisSilent]

+Privacy Required But in the game, the players are against each other. Passing can give both an equal payoff, but sending 3 units has the chance of a bigger advantage - with no greater risk than simply passing.

[@shakerliciouslaw2404]

There is no risk in either passing or sending 3 troops.

[@OrenLikes]

not true "looked at 8"... could look at 10: 4 in the diagonal + 6 (either side of diagonal, or any side but not mirrored).

[@mrbinhesam]

It was great, I do appreciate it.

[@hansolavvelle]

Extremely helpful. Thank you :-)

[@arjunsingha703]

Game theory now really is fun .. ****

[@thaer12345]

Makes sense. Thanks.

[@yaswanths]

Thanks a lot...

[@rv.9658]

If a game is in Nash Equilibrium, there is no game.

[@zacharycat]

Reminds me of Risk.

[@kulbidam]

the matrix is obviously wrong. Both the first row and the first column supposed to be 0,0; 0,1.... and 0,0; 1,0.... respectively.

[@jasondean88888]

Nope. He states that if either general decides to pass then the battle does not happen.

[@sz027566]

Your the man !!

[@Martin23650]

I'm confused, isn't the objective in this game winning? Optimizing your opponents end result isn't a consideration in a battle, so the only acceptable outcome is a 1. Also, wouldn't sending in 3 troops be the ONLY best response because it's the only option with a positive expected value, assuming equal chance of each response (0,1,2, or 3) by the other general? And also, considering that it's logically sound to never deal in absolutes, you can never say the chance of the other general sending in 1 or 2 troops is 0% (though it would be close). That would only further prove that no matter what the case, the only positive expected value is found in either general sending in 3 troops? Any help would be greatly appreciated! Thank you for these great videos!

[@shakerliciouslaw2404]

Yes, it is true that sending in 3 troops is the best possible strategy for either general to win the battle. What Nash equilibrium means is that no party can gain an advantage base on a unilateral change of strategy. For instance, if Blue general passes, Red general cannot gain an advantage even if he refuses to pass and decides to send 3 troops. That's a Nash equilibrium. In short, a Nash equilibrium doesn't necessarily mean the outcome that will maximise winning potential, but an outcome that cannot be improved if either side changes his or her strategy while the other sticks with a strategy.

[@SymphoDeProggy]

something doesn't mesh with me here... why would any player ever choose to pass ? looking at the Pass option, you'd draw in every single scenario. the Three unit option, you draw half the time, and win half the time. so how can anything but "3,3", be a stable solution ? since there's no risk involved, wouldn't both players always prefer Three on the off chance they get lucky and get a win ? choosing 3 can either pay off more than pass, or equal to pass, so why is pass a "best response" ?

[@Iwasonceanonionwithnolayers]

I don’t understand why her sending 1, 2, or 3 units and him sending 0 units is a draw. Why wouldn’t she win?

[@gregoryturk1275]

Enemy just runs away

[@Iwasonceanonionwithnolayers]

@@gregoryturk1275 Winning only counts if you kill the other army?! Surrender doesn't exist? PoW? Nothing?

[@gregoryturk1275]

@@Iwasonceanonionwithnolayers If the opponent doesn’t send his army to fight and just keeps on running away how are you supposed to win when nobody controls land

[@danielchoritz1903]

there arent 16 different outcomes, there are only 3 outcomes, but 16 ways to it.