I am the world's biggest nerd.
So, I've been listening to some Teaching Company lectures on Game Theory, and I had the nerdiest moment of all time. Below is my explanation of this great geekery to my poor victim, Penny. Behold, if you dare, my very brief and non-in-depth proof:
"Vigilantism as a necessity as proved by multi-player Game Theory"
Me
1:49
okay, so the basic concepts of game theory rely on the idea that interactions (games) are dictated by decisions (moves) made by people (players) for some sort of outcome (payoffs)
1:49
Payoffs are not necessarily good things, there can be negative payoffs
Penny
1:49
*nods*
Me
1:50
And there's this concept called the Nash equilibrium
1:50
If you saw A Beautiful Mind, he's the guy that came up with it
Penny
1:50
I haven't seen it, but I know of him
Me
2:00
okay
2:00
so a Nash equilibrium says that it is the combination of moves that arrive at an outcome from which no player wants to unilaterally change their decision
2:01
sometimes this is an outcome from which everyone gets the maximum possible payoffs
2:02
but more often it's not, it's just the only way a person ends up being satisfied that they can't improve their payoffs based on the decisions of the other players
Penny
2:02
*nods*
Me
2:03
And there's this type of game called "The Prisoner's Dillemma" or, in multi-player version "The Tradegy of the Commons"
where if people all cooperate, the overall payoffs are higher, but if just one player defects and does the lazy/harmful/selfish thing, he individually gets a bigger benefit
which means that the Nash equilibrium has to be that everyone will "defect" to the lazy/harmful option
2:07
okay, think of commercial fishing
2:07
obviously, the fish population in a given area is only so large and can only repopulate so fast
2:08
so the long term overall best thing to do is for everyone to limit his own fishing
2:08
right?
Penny
2:08
*nods* That makes sense
Me
2:09
but individually, it benefits a fisherman more to catch as much fish as he possibly can
2:09
after all, he has a family to feed
2:09
and bills to pay
2:09
so he catches all the fish he can
2:10
and so does every other fisherman
2:10
and the fish population collapses and everyone is out of work
2:11
if everyone had simply limited their own fishing in the first place, they would have done better
2:11
but because the individual payoffs were better by being selfish, they did that
2:12
all that make sense?
Penny
2:12
yup!
Me
2:13
there are a few ways around this
2:14
but one of the best ones is to install some sort of third party who will punish those who do the "defecting", making it less profitable to do this defecting
2:15
this person is called an arbiter, and they can come in several flavors
2:17
An important thing to consider here is that punishment almost always incurs a cost to the punishers. Prisons cost money, for instance
Penny
2:17
*nods*
Me
2:18
but as far as arbiters go, the only one that is really effective for....really long reasons I'm going to skip is the "righteous arbiter" who is willing to inflict the punishment on defectors even though they pay a cost (this is different from a sadistic arbiter who just enjoys punishment)
2:19
This means that the payoffs of defecting are much lower because the threat of the righteous arbiter is in place, making following the good of society in general a more profitable option
2:19
and suddenly the Nash equilibrium for this game isn't a tragedy any more
2:20
in the fishing example, this arbiter would be something like the government giving out fines
2:20
but if the game isn't about over fishing, but about obeying the law....
2:20
well, the government can do some arbitration
Penny
2:20
then you get the Goddamn Batman :-P
Me
2:21
:D
2:21
A righteous arbiter is only effective if he or she provides a credible threat
2:22
and a lot of times, the government's threats aren't credible, or they don't change the payoffs enough
2:22
you need one scary, seriously damaging and righteous arbiter
2:22
so...Batman
2:22
Q.E.D.
I either win or fail. You decide.
"Vigilantism as a necessity as proved by multi-player Game Theory"
Me
1:49
okay, so the basic concepts of game theory rely on the idea that interactions (games) are dictated by decisions (moves) made by people (players) for some sort of outcome (payoffs)
1:49
Payoffs are not necessarily good things, there can be negative payoffs
Penny
1:49
*nods*
Me
1:50
And there's this concept called the Nash equilibrium
1:50
If you saw A Beautiful Mind, he's the guy that came up with it
Penny
1:50
I haven't seen it, but I know of him
Me
2:00
okay
2:00
so a Nash equilibrium says that it is the combination of moves that arrive at an outcome from which no player wants to unilaterally change their decision
2:01
sometimes this is an outcome from which everyone gets the maximum possible payoffs
2:02
but more often it's not, it's just the only way a person ends up being satisfied that they can't improve their payoffs based on the decisions of the other players
Penny
2:02
*nods*
Me
2:03
And there's this type of game called "The Prisoner's Dillemma" or, in multi-player version "The Tradegy of the Commons"
where if people all cooperate, the overall payoffs are higher, but if just one player defects and does the lazy/harmful/selfish thing, he individually gets a bigger benefit
which means that the Nash equilibrium has to be that everyone will "defect" to the lazy/harmful option
2:07
okay, think of commercial fishing
2:07
obviously, the fish population in a given area is only so large and can only repopulate so fast
2:08
so the long term overall best thing to do is for everyone to limit his own fishing
2:08
right?
Penny
2:08
*nods* That makes sense
Me
2:09
but individually, it benefits a fisherman more to catch as much fish as he possibly can
2:09
after all, he has a family to feed
2:09
and bills to pay
2:09
so he catches all the fish he can
2:10
and so does every other fisherman
2:10
and the fish population collapses and everyone is out of work
2:11
if everyone had simply limited their own fishing in the first place, they would have done better
2:11
but because the individual payoffs were better by being selfish, they did that
2:12
all that make sense?
Penny
2:12
yup!
Me
2:13
there are a few ways around this
2:14
but one of the best ones is to install some sort of third party who will punish those who do the "defecting", making it less profitable to do this defecting
2:15
this person is called an arbiter, and they can come in several flavors
2:17
An important thing to consider here is that punishment almost always incurs a cost to the punishers. Prisons cost money, for instance
Penny
2:17
*nods*
Me
2:18
but as far as arbiters go, the only one that is really effective for....really long reasons I'm going to skip is the "righteous arbiter" who is willing to inflict the punishment on defectors even though they pay a cost (this is different from a sadistic arbiter who just enjoys punishment)
2:19
This means that the payoffs of defecting are much lower because the threat of the righteous arbiter is in place, making following the good of society in general a more profitable option
2:19
and suddenly the Nash equilibrium for this game isn't a tragedy any more
2:20
in the fishing example, this arbiter would be something like the government giving out fines
2:20
but if the game isn't about over fishing, but about obeying the law....
2:20
well, the government can do some arbitration
Penny
2:20
then you get the Goddamn Batman :-P
Me
2:21
:D
2:21
A righteous arbiter is only effective if he or she provides a credible threat
2:22
and a lot of times, the government's threats aren't credible, or they don't change the payoffs enough
2:22
you need one scary, seriously damaging and righteous arbiter
2:22
so...Batman
2:22
Q.E.D.
I either win or fail. You decide.