Expert-Level Hide and Seek: A Game Theory Puzzle

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You can hide behind a hedge or a house. I don't see where you went and have to decide which to search. Fortunately for me, if you hide behind the house, there is a security system attached to it. 75% of the time, it will turn on, and I will know exactly where you are. Where should you hide? And where should I search?

Опубликовано:

18 июл 2021

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Комментарии : 29

@arnauadell4824 3 года назад

So, intuitively, I thought "aight, since the house spots us 75% of the time, let's make it so when it doesn't spot us, it's 50-50, so 80% of times behind the house." That means whenever you don't see light, you don't know. However, that leads to us being spotted very often, i.e. 60% of the time. Intuitively, there ought to be a payoff for slightly favoring the hedge, say that whenever you don't see a light, there's a 52% chance I'm behind the hedge. Yes, that makes it more likely you will search the hedge and spot me, but it will also reduce the amt of times I'll be spotted by the light. It's a bit mind-bending when the math shows that this intuitive payoff doesn't exist, and you should aim for complete 50-50 in non-light situations and not favour the hedge even a very slight bit.

@Gametheory101 3 года назад

That first bit is a really good intuition for what's going on with your strategy. I wish I had said something like it in the video!

@bluedonkey180 Год назад

Ah yes, and because it spots you 1/4 times, you must choose it 4 times more often to make it a 50/50 for the seeker making him indifferent and reaching a nash equilibrium

@sinecurve9999 3 года назад

"The closer we are to danger, the farther we are from harm." -Pippin

@jayschwartz3203 2 года назад

What jf I run behind the house to make the light go on, then hide behind the bush?

@PunmasterSTP 2 года назад

Hide and seek? More like “makes us think!” Thanks for another intriguing and stimulating game theory puzzle.

@zennovak3116 2 года назад

Now that I know your strategy, I will hide 100% of the time behind the hedge. At least until you find there is something fishy...

@michaelmanto6537 6 месяцев назад

If i do this calculation and i assume my enemy is too, they know that 75% of the time, I am hiding behind the house, why would they not just check behind the house 75% of the time? Appreciate the content!

@vaishanthjv2519 5 месяцев назад

You are hiding behind the house 80% of the time. 75% of the time the light turns on. So 25% * 80% of the time you hid behind the house and the light does not turn on. Thats 20%. There is also a 20% chance that you hid in the bush. So given that the light did not turn on, using Bayes theorem you find that there is a 50% chance that you hid in the house. Hence the seeker does not have a bias in searching when the light has not turned on. Hope that explanation helped.

@kennypyrate7554 Год назад

I'd set off the light hide behind the hedge

@bluedonkey180 Год назад

Be quiet id just search hedge more frequently then

@dan0_0nad76 Год назад

amazing content, but how would you derive the equations for the graphs?

@ranimahassen6296 2 года назад

At 5.49 isn't the (1)(1-p) (the top right number) meant to be (0.25)(1)(1-p) as you're considering the probability the house is not searched over the whole amount and therefore excluding the 75% chance.

@Gametheory101 2 года назад

If you look carefully, there are brackets where the .25 gets distributed like (I think) you thought.

@imkharn 3 года назад

Is this the same configuration as soccer penalty kick? I suspect that opposite of intuition will consistently be the best way to teach the value of game theory as well as break the patterns of thinking that lead to bad intuition.

@AnirollAi 3 года назад

It can be. Both the kicker and goalie will adjust their strategies to reach a nash equilibrium where both players will be indifferent of their choices. Ie, you notice the goalie jumping to the left 70% and right 30% so you start shooting right more often. Goalie notices you shooting right more often and adjusts. Till theres a 50-50 equilibrium and neither players can do better by adjusting.

@Ninjashifter 3 года назад

Just discovered your channel, amazing content

@Gametheory101 3 года назад

Thanks! How did you find it? I made a pivot to puzzle-y content a few weeks ago and am wondering if it’s having an effect.

@Ninjashifter 3 года назад

@@Gametheory101 Someone mentioned the term "schelling point" and I was unfamiliar with what that referred to, so I went to youtube to search for "schelling point game theory" and came across your video on focal points in the search results.

@Gametheory101 3 года назад

Cool! Thanks.

@ahgflyguy 3 года назад

@@Gametheory101 I’ve been a subscriber for a long time, but your videos hardly ever were surfaced. I reset my view history recently, and your videos were then being suggested in the side bar if I watched one of Presh Talwacker’s vids.

@Gametheory101 3 года назад

@@ahgflyguy That's awesome. I have known Presh for more than a decade. It has been great to see his channel take off.

@parikshitde3147 2 года назад

Is it ok to call this a simultaneous move game?....especially when the signal works perfectly then it is not so.

@Gametheory101 2 года назад

It isn't simultaneous. An easy way to check on that is whether you can flip flop the temporal ordering of the moves without breaking the game. Here, that clearly won't work because the seeker has to receive a signal (or not) based on the hider's move.

@manaphylv100 3 года назад

If the light works 100% of the time, you should also be indifferent, because you'll always lose anyway.

@AnirollAi 3 года назад

Ya, this wouldn't be a puzzle then

@bluedonkey180 Год назад

Wow mana are you some sort of genius??????

@manaphylv100 Год назад

@@bluedonkey180 Sure, it won't be a puzzle if the light always works, but I suppose the "moral" is that there's no point in mulling over a catch-22, and so it's better to cut your losses and move on.

@stanley5367 2 года назад

you owe me a dollar, i ran and intentionally turn on the light, then ran and hid behind the hedge🤣🤣 now you are gonna go straight to the house, however, if the light doesn’t come on, i’ll hide behind the house, and still have a chance you might go to the hedge🤣🤣