Game Theory 101 (#53): Risk Averse, Risk Neutral, and Risk Acceptant Preferences

gametheory101.com/courses/game-theory-101/
Not all individuals have the same preferences for risk. Risk neutral actors simply want to maximize their expected value when faced with a gamble. Risk averse actors willingly take small payments to avoid a gamble, while risk averse actors require large payoffs. Fortunately, all such preferences work within the expected utility framework.

[@stevepurkis5433]

Thanks for publishing this series, @William - very well spoken & visualised!

[@PunmasterSTP]

Accept risk? More like “Good video? Yes!” Thanks again for this entire playlist.

[@rohanpaleja]

How do you determine the mapping from risk to the change in utility (for example squaring or square rooting)?

[@astaragmohapatra9]

That question is like choosing between a job to do and gradually get promoted, to spending all the money on lotteries

[@James-ep2bx]

One thing to point that some like myself would likely become more risk adverse if we had to invest something

[@fkn1088]

Is diminishing marginal utility of money the only cause of risk aversion? Can risk aversion be found in lotteries with equal expected utilities?

[@dominiclebron6073]

william spaniel makes a bold statement 9:20 - he claims to not view the outcomes in monetary gains -> rather value our outcomes at how 'happy' we will become. genius how professor spaniel can simply his language to less complicate how complicated game theory is for newbs like myself. thank u professor spaniel!!!!!!

[@ismailtaskran9740]

It can also be the case that they have a false view or “feeling” of good/bad luck that is not alligned with the probability theory.

[@putione3079]

Wouldn't it be most realistic to use a utility function that is risk acceptant for lower values, risk neutral for medium values and risk averse for high values (something like a scaled sigmoid function). I mean, if you are offered a choice between 1 cent and $1 with 1% probability, you might as well go for the $1, since there is almost nothing you can do with 1 cent. On the other hand, if you are being offered one quadrillion dollars with certainty or one hundred quadrillion dollars with 1% probability, you'll probably go for the one quadrillion, since that is already enough to buy basically everything you could wish for. And somewhere in between, you'd probably be indifferent between $x and 100*$x with 1% probability.

[@philzan3627]

Depending on the buying power of the prize, I would go towards (chance of getting 1 million)*(1 million)

[@jvgama]

If I couldn't find a smarter way to "insure", I would accept $100 000. The funny thing is: if I had the opportunity to pay $1 to get 50% chance of getting 10$ I would love the opportunity. For big amounts however, things change.

[@Szellah7]

It's hard to actually visualise indiffrency. As I came to understand it I were going to choose between to lotteries, where as it was more like a showman was dropping prize from second lottery and i could jump at the first one at any time to hopefuly save some of that $$$.

[@KozzmoKnight]

I listened on before answering, to be honest, my instinct was half a million. I would probably go down to 300,000 and take the sure money. I would certainly take more. If I had a 50/50 chance at a million, my thinking is that half a million is fair for not taking the chance. That's what I would write down. This is what changes everything, do I decide, or am I being offered x amount? Because if you said, I'll give you 300k, or you can roll the dice with a 50/50 chance at a million, I'd be happy with the 300k. I think most people would agree.

[@michawhite7613]

For health insurance, you actually benefit in expectation, because hospitals charge extra if you don't have insurance

[@toomanycharacter]

x = 250000 I predict my happiness function is f(x) = sqrt(x/100000). Then the expected utility of the first lottery is (1/2)*sqrt(0/100000) + (1/2)*sqrt(10) = sqrt(2,5) and of the second lottery is sqrt(250000/100000) = sqrt(2,5). The expected utilities are equal, so I am indifferent between the two lotteries.

[@Shokukumi]

x = 500'000 Because: 0.5 * 0 + 0.5 * 1'000'000 = 1.0 * 500'000 And yes, I knew this from before, but it didn't change my reasoning. I know that I'm "risk-neutral".

[@DK-ym8jr]

I'm going to go with $500,000. The total amount when including the 0.5 coefficients multiplied by 0 and 1,000,000 respectively sums to that value. Depending on how many times I won that lottery I may give thought to different values but I believe it would be about the same.

[@DK-ym8jr]

Well would you look at that I'm risk neutral.

[@BS33875]

Can the preferences adjustment be linear not by roots or square?

[@robinwang6399]

.5*0 + .5*1e6 = 5e5, which should be x. But depending on how many times the lottery is played and the cost, as the repetition lowers and or cost grows, I might lower x so cost and benefit works out.

[@Tygafttf]

i think there is a mistake at 6:43 u said= the smaller x is the more risk averse u are, whereas when a is getting closer and closer to 1 u are getting closer and closer to risk neutral. i think u ment=the smaller a is ....

[@raphgurzo3638]

500k, because on average lottery 1 and lottery 2 will therefore lead to the same payoff

[@eunicemicahelasalazar3731]

how did you arrive with the 400,000 and 300,000?

[@davide816]

sensation

[@user-pj7ou2cf5e]

300k. 300k is worth for escaping risk.

[@Lukas-ee6it]

1 million - lottery ticket costs

[@autumnmnmn]

half a million dollars seems like the 'correct' answer for x

[@WhiteDevStudios]

500,000. The expected average of lottery 1 is 500,000, becuse .5 * 0 + .5 * 1,00,000 = 500,000

[@NaliTikva]

i guess at something like x = 150k like 150k is at the edge of a "life changing" amount of money, if it's like 250k and i would pick the lotery and lose i'd be sour for years to come. But if It's like 50k, then i'd be like "maybe i could have had a million" for years to come

[@wangyuanhang5007]

half million?

[@bobjoe258]

300K because I would say the utility of 1000K is about twice that of 300K, given the massive impact on my life anything over 300K would have.

[@eunicemicahelasalazar3731]

how did you arrive at 300,000?

[@bobjoe258]

@@eunicemicahelasalazar3731 oh man, this was from a year ago so I’m really not sure. Probably just about enough to pay off mortgages, that sorta thing. And money past paying for necessities obviously drops in utility value (for me personally, since necessities are by definition the most important, or high utility). Haha oh man I remember binge watching this series a year back, thanks for bringing back some of the memories :).

[@coloradoing9172]

@@bobjoe258 Do you still remember this series?

[@lastmanstanding5423]

x = $20.000 I'm a poor and need money. edit: after watching the whole video I must say I don't think I'm "super risk averse" I'm actually quite happy to make very risky decisions in my life. It's just that I NEED the money.

[@michawhite7613]

The rational answer would be to give the money you win away, which makes it easier for me to say $500,000

[@kaioxys]

20,000$ Very risk averse.

[@audrey2116]

250 000

[@TheLukeskywalker2]

half a million

[@juliechoudury6912]

200,000

[@ac-uh5lo]

1000

[@sayaks12]

500,000

[@mahmoodalmasri8750]

x = 5000

[@pal3479]

250K

[@sukanyajanardhanan7212]

500'000

[@ksheerajvootori1122]

300,000

[@James-ep2bx]

500,000+$

[@James-ep2bx]

500,000$=1,000,000$*.5

[@davide816]

50k

[@marcschaeffer1584]

$20,000.00

[@KYHONKOMA]

300k

[@chitraretnas4068]

999,999

[@pulkiitsharma2665]

x=1. im happy to get anything for free.

[@EugeneKrevenets]

500,000