Game Theory 101 (#52): Pareto Efficiency

gametheory101.com/courses/game-theory-101/
An outcome is Pareto efficient if there is no other outcome that gives at least one player a greater payoff while giving no other player a worse payoff. An outcome is Pareto inefficient if there is at least one other outcome that gives at least one player a greater payoff while giving no other player a worse payoff.
Because expected utility transformations render interpersonal utility comparisons meaningless, Pareto efficiency is the standard measure of efficiency in game theory and economics.

[@PunmasterSTP]

This videos was Paretotally awesome! Thanks again for this entire series.

[@uristrauss6106]

this triple negative in the definition of pareto efficiency makes it processing-inefficient. this formulation is equivalent (i think) and easier for me to use: an outcome is pareto efficient iff in every other outcome, either nobody is better off, or somebody is worse off.

[@Jacobus-k8g]

I think it is fight-fight, because if player 2 doesn't cooperate then, if there is a second game, player 1 won't cooperate and will gave a punishment.

[@absbi0000]

Best explanation of Pareto Efficiency. Thank you!

[@messididit]

Love you for no reason! subscribed!

[@prashantnegi1828]

Thanks for the explanation.

[@SohamChakraborty42069]

From my intuitive understanding of efficieincy, I think for the first case, (Ballet, Ballet) would be a more efficient outcome. This is because in (B, B) the payoffs are almost equally distributed (1,2) than in (Fight, Fight) where the payoff of player 1 is disproportionately higher than that of player 2 (100>>1). Similarly, in the second case (Fight, Fight) is the more efficient outcome since the payoffs are equal, whereas player 1 receives a much lower payoff in (Ballet, Ballet) (0.01

[@bobvance9519]

When I took game theory in college, our professor referred to this as Pareto Optimality.

[@urnbaby]

It depends on whether we assume side payments are allowed and utility is transferable. Trick question because this wasn’t specified. But the Nash Bargaining solution makes the assumption of transferable utility. So it’s not clear without knowing that.

[@AlamgirHossain-qu1kx]

Ballet-ballet and fight-fight

[@jvgama]

Both games relate to the same preferences (in the second there was just a positive afine transformation for the blue player's utilities), and it is difficult to find a criterium to say that one outcome is more efficient than the other. For sure not the Pareto criterium. There could exist a "group utility" created as a function of each individual utility, but in that case the positive affine transformations would no longer be "neutral", as they would distort the group utility result (as it happens here).

[@blacky6552]

Interesting question. The answer for the first one is obviously the fight-fight equilibrium. For the second one, you have to think about what efficiency means. Is it the sum or the product of the utilities. The former makes ballet-ballet and the latter fight-fight the most efficient equilibria. There is the fact that the second game is the first one but scaled down for player one, giving credence to product, but I still think the sum makes more sense Edit: f

[@pulkiitsharma2665]

hows the defect cooperate outcome pareto effecient ? one player is clearly worse off than the other player.

[@sadzidsmajkic6181]

Hi William, I have a question for you. Does every game need to have at least one outcome that is Pareto efficient? Or there might be some games that don't have an outcome that is Pareto efficient. Thanks.

[@michawhite7613]

Fight, fight Ballet, ballet I picked both because they result in the greatest total amount of utility

[@01Versatran]

Fight/fight in the first is more efficient if we are counting total utility.

[@boju9529]

Counting utility is not generally a good way of calculating efficiency though. It is if there is some direct mapping between utility values and real life outcomes How we, generally speaking, we choose rough numbers which most importantly capture preference ordering.

[@rohanvaswani9418]

I think fight fight is more efficient because in the original game because the overall payoff is higher. In the second game I think Ballet Ballet is more efficient because same argument as 1

[@joycewang1586]

why all of your example number is positive

[@RACHNArocker]

thanks, i get it now

[@alebuller8321]

both are efficient

[@MikaelKarlssonForest]

1: Fight/Fight 2: Ballet/Ballet (gives the highest average score)

[@heramb575]

What does it even mean to say a Nash equilibrium is efficient?

[@andy4226uk]

I said Fight fight, then ballet ballet because both these options offer the higher average earning for both players

[@stephanieford8035]

So is war pareto inefficient?

[@heramb575]

Wait couldn't you do an affine transformation on both the hare and make both of them 3 as well? Doesn't this throw a wrench into Pareto efficiency

[@praneshsaisridhar2823]

That is because these affine transformations should be applied only to one person's utility. Imagine you have utilities for outcomes - they are just ranked. You can transform your own outcomes and have the same preference ordering. You cannot do that for the other person playing the game. How his preference ordering occurs is not under your control, and therefore you cannot scale up or down those numbers.

[@bobjoe258]

Say I had two utilities of 1 and 2 for two outcomes A and B respectively. Then i transform them with a=1, b=-1 to get 0,1 then i further transform them with a=50, b=1 to get 1,51. but clearly 1,2 and 1,51 are not the same utilities? What is wrong with this here?

[@uristrauss6106]

I think they are the same, though, in the sense that in any game with a 1x2 matrix where you have two choices, you would always choose the strategy that gives you 2 or 51, never the one that gives you 1.

[@carlcjjohnson7147]

1) Ballet Ballet 2) Ballet Ballet Because this seem to show reflect the outcome of what we put into something

[@poguy]

100,100 AND 0.01,2

[@jamesbeacham621]

ballet ballet!

[@anodaone6525]

who is player 1 in this video? Label please

[@xahiru]

player 1 = blue, player 2 = red

[@marioduranbustamante412]

Fight because the payoff is really big instead of they other equilibrium

[@marcmelwin8762]

fight fight (because 100+1>1+2) ballet ballet (because 2+0.1 >1+1)

[@James-ep2bx]

#1 fight/fight 101>3. #2 ballet/ballet 2.01>2

[@mou7519]

Ballet, ballet

[@dariusdresp8931]

i think both are the same

[@mlng1623]

Fight, Fight

[@Yustiks]

ballet-ballet

[@alen-commentnazi8774]

what is this even about

[@erlekj8018]

fight fight

[@kal9492]

this is so unhelpful

[@heloisea6513]

Unrelated to Pareto efficiency but this original name of the game "battle of the sexes" and the original description are extremely sexist. Why not use the new alternative versions as Bach or Stravinsky, which is already well-known in the game theory community?

[@Gametheory101]

I understand your point, but Bach or Stravinsky is not anywhere close to the "common name" for that type of payoff structure. There are about 500,000 google results for "'battle of the sexes' game theory" but only about 5000 for "'Bach or Stravinsky' game theory". Of those 5000, 4000 contain the word "battle" anyway. There is a good argument to be made that we are inferior equilibrium of a coordination game, which I suppose is a lesson all of its own.

[@heloisea6513]

@@Gametheory101I understand your motivation and thanks for the explanation. I believe that search result is even a very good reason to start changing this. Otherwise we are mostly placing subconscious sexist believes in young brains and it has long terrible consequences.

[@kayrakarabacak8810]

How is it sexist

[@jwbpark]

Ballet bal.et