The Game That Never Ends

published on July 12, 2020

Vsauce Kevin here with a slot car racetrack to visualize how fast I can safelydrive without getting pulled overwhat's my maximum speed without wreakinghavoc on the justice system and how canwe use game theory to find the answerhere we go all right that didn't really

Work out very well honestly I don't evenhave enough room to properly set up thistrack on this table so I'm gonna needsome helpluckily I partnered with curiositystream and I know just the guy hey Sean

As hosts of the awesome new curiositystream show speed I was hoping that youcould help me visualize speeding whatlooks like you already haveyeah well that track here Kevin to dojust that I have magically manifested

Exactly the same track that you hadright here on my favorite convene yeahboom okay so let's race I will be thecop car and you will be the civiliandriver I wouldn't have it any other wayokay do I get a head start yes I'm gonna

Pull you over let's go let's go okay soI'm racing ahead yeah there's a turbobutton if she can use coming in thestraightaway that's helping to gain onyou actually yeahbut turbo in the corner it's too much

Speed and you're fly right off why didthat happen though okay that happensbecause in this case you over seeded thecoefficient of friction between thetires and the slot and the top of thetrack now these cars they can go around

The corner a lot faster than a normalcar can because they have this littlepeg that's riding in that slot yeah sowhen they go around the corner they'reresisting centripetal force which wantsto swing it off but what the car wants

To keep going in a straight line rightbut this slot helps drag it around thecorner now in our cars we don't have aslot so if we go around a corner toofast we slide off when we exceed thecoefficient of friction of our tires and

Our tires oh they look kind of big theyreally don't have that much space on theroad I'm going to show you that Ibrought one of the tires off one of mymotorbikes here I'm just gonna sharpiethe top here this looks like a pretty

Big around tire all rightrides down the road only when it'sriding down the road on the streetit's really only got about one inch Wowall right if we take a look at thatthere there's really only about one inch

Wide and maybe three inches long that'sthe contact between me and themotorcycle on the ground the same istrue on the tires on your car right thetire is all the way around but the onlypart actually touching the ground if

That little bit on the bottom and if youhave your tires overinflated you'regetting a much smaller contact patchthat makes sensetires not deforming yeah yeah so thatlittle bit the contact patch is

Important to understand you've got fourof these little contact patches theremaybe four inches by five inches wide onyour four tires and the weight of thatcar pushing down on that contact patchis the only thing that keeps you from

Sliding off the road when you go arounda corner the weight of the car Laettnersaid the car wants it to go keep goingstraight when you turn the car the frontwheels move off in one direction and thefriction makes those tires track around

The corner the reason that's importantis because you're also using that samefriction not only to go around a cornerbut you're using it to accelerate intobrake if you accelerate too fast youovercome the coefficient of friction

Between your tires and the ground withthat little contact patch and you do aburnout mhx lot of fun in a controlledenvironment but the more important thingfor all of us driving around that'sreally really pertinent to our safety is

That the faster you go you're askingmore and more of that little tinycontact patch to help slow you down whenyou hit the brakes so if you're goingway faster you have to be easier on thebrakes if you lock up the brakes you'll

Slide the whole car forward that'swhat's happening here is you just haveit carrying too much speed into the turntires and the slot can't take it you'resliding right off the track okay I'lltry it again yeah yeah where's the cop

Car let's restore them right okayso that's a technical reason why youdon't want to speak but there's lots ofother reasons why you don't want tospeak – right yeah I mean that's whyit's dangerous to speed but also in

Society you know you have to have ohthere we go in society we can't havethat happen no we can't have thathappening you know we want everyone tobe safe and we have rules andregulations and law enforcement in place

To make sure that everyone is actingsafely the thing we don't really thinkabout is that driving in a systemgoverned by law enforcement is actuallya two-player game and both the driverand the police officer are playing this

Game let's say that the speed limit is65 miles per hour what's the fastestthat you've ever driven because I have afeeling it's a lot more than that I'vedriven about 130 miles now okay yeah butmy question is what is a sensible speed

To drive on the highway the answer thatquestion is somewhat complicated cuz itreally depends on the highway and theconditions and if it's raining and thestate of your car right but in generalfor for roads that are we collectively

Deemed we need to go slower in becauseeither it's near neighborhood or becausethe road itself is twistier we have thelower speed limits yeah and then we havebig straight super highways where we canall do 75 or whatever the limit is in

Your in your area but the point is thatcops can't pull over every single driverjust for going one mile per hour overwhatever that limit is because not onlyis that logistically impossible but thatlevel of law enforcement would probably

Make everyone pretty angry so when wedrive and the police monitor us wereplaying a game of recursion to get thebest result both of the police and thedrivers are sort of playing this gamefrom different sides exactly exactly

We've got a couple of basic rules inthis game we have a legal speed limit oflet's say 65 miles per hour and we havecommon sense rules that tell us that wecan only go so fast before it getsdangerous and we're flying off the edge

Of the road and the police officer has athreshold at which he or she will ticketthe driver so each player is decidingwhat to dobased on what they think the otherplayer will do yeah there's a gray area

Isn't there yeah yeah it basically workslike this as the cop I'm thinking howfast does Sean think that he can gowithout getting pulled over right and asthe driver I'm thinking how fast can Iget away with without getting pulled

Over exactly exactly and as the cop I'malso thinking how fast is Sean think Ithink he thinks he can go and he'sthinking how fast do I think he thinkshe can go and that's recursion at theend of this process which can be

Infinite both the driver and the copdecide their best courses of action forthe driver that's like you said how fasthe can go safely without getting aticket and for the cop that's how fasthe'll let the driver go before pulling

Them over and this whole game takesplace in that gray area I mean I know ifI stay under 65 on that we can pulledover that's the easy way to do it rightand I know if I go 130 I'm gonna getpulled over so there's this strip there

And that's the gray area where that thatgame you're talking about is gettingplayed ultimately so what do you thinkwould be an exact value if the limit was65 miles per hour that we could get likeyou could drive without getting pulled

Over and so that you're happy with thespeed that you're going I think it'sgeneral wisdom that you can get awaywith about five miles over the speedlimit especially on the highway whenthere's no chance of coming across the

Stop sign or someone on the road rightso when there's in a safe environmentlike that I think everybody pretty muchfeels like they can go five miles overthe speed limit and not get pulled overor somewhere in that gray area both of

The police and speeder for playing thisgame from their own sides right thespeeder trying to figure out how fastthey can get away with the police tryingto figure out how much they'll allow butthey both have an incentive to make the

Whole system work so when they both playthe game and they find this place wherethey get to speed a little and don't getpulled over there it's in that gray areathey find a balance and that balance iscalled a Nash

Equilibrium what Sean described is thebest reply to another player's bestaction and when neither player has anincentive to deviate from their decisionthey've reached a Nash equilibrium okayI need to talk more about Nash

Equilibrium but I need my whiteboardtable so thank you so much Sean for allof your help make sure that you watchhis show speed on curiosity stream Iknow that you guys will love it but fornow I have to I have to I have to go

Okay now one of the most famous Nashequilibrium scenarios comes in the formof the well-known prisoner's dilemma thescene is simple two people get arrestedfor a crime they're separated and can'tcommunicate with each other the police

Can convict both on a lesser charge butthey need more proof to convict them onthe big one that means one has totestify that the other did the crime sois it in each prisoner's best interestto rat on the other one or to stay quiet

Here's how it plays out if bothprisoners a and B rat on each otherthey'll each get two years in prison ifa blames B but B stays quiet a goes freeand B gets three years in prison andvice versa if both a and B stay quiet

They'll each get one year in prison therational prisoner rats because that'sthe only way he's going to go free andwhen he rats it always gives him abetter result than if he doesn't ratregardless of what the other prisoner

Does that's called a dominant strategyand the Nash equilibrium in theprisoner's dilemma is achieved bybetrayal but if the other prisoner alsobehaves rationally he would rat as welland they'd both get two years the best

Course of action here is cooperationwhere both stay quiet serve a lessersentence and have the least bad outcomein the prisoner's dilemma not betrayingthe other guy goes against the Nashequilibrium but it gives the best

Possible result for both playersmind because if one rats and the otherdoesn't three years are served and ifthey both rat four years are servedthrough cooperation only two years areserved political scientist Robert

Axelrod asked 14 game theory experts tosubmit computer simulations of theprisoner's dilemma the ones thatadvocated more self-interest by betrayalwere noted as not nice players while theones that focused on cooperation they

Were nice after running them all the tophalf of the performers were all nicemodels while the bottom half were allnot nice so it pays to be nice as longas the other player thinks it pays to benice too we play these two-player games

All day long not just with the policewhen we give a gift were playing a gamefor example say you've just met someoneand you kind of like them giving them aspatula is probably not a great giftgiving them a diamond ring on the second

Date is probably a bit muchpump the brakes there Billy in the giftgiving game you want to send the rightmessage based on what you feel and therecursive process that happens with whatyou think they'll feel you want to feel

Good about the gift you gave and theywant to feel good about the gift theyreceived and whether you're driving downthe highway or trying to impress yourcrush you're almost always in some kindof two-player game and sometimes you're

In several at once the best way to playis to be smart to pay attention and keepyour best interest in mindbut you'll usually win the most when youmake sure to be niceI guess grandma was right and as always

Thanks for watchinghey gigantic thanks to Sean Riley foropening up his shop to me go check outhis brand-new show speed it's afour-part DocuSign blasts throughhumanity's Need for Speed on land Wow

On sea through the skies and into spacecuriosity stream and I worked out a dealfor you so that you can sign up and get30 days completely free just click thelink below and go to curiosity streamcomm slash Vsauce 2 and enter the promo

CodeVsauce – all lowercase curiosity streamgives you unlimited access to over 2400brain feeding documentaries starting atjust $299 per month but for you you canwatch Sean's show free by using the

Promo code Vsauce – so you should dothat the show is awesome honestly you'lllike it go watch it go watch it now oknow

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