
Game Theory Is Counterintuitive - wspaniel
http://wjspaniel.wordpress.com/2014/05/25/game-theory-is-really-counterintuitive/
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hcarvalhoalves
> Closing roads can improve everyone’s commute time.

SimCity is a great way of showing this effect interactively.

In the simulation, citizens always take the shortest path (individuals try to
maximize individual gain), but if you connect your entire city like a grid
they avoid high-speed roads, deadlocking the traffic (worst game outcome). If
you adopt a city plan full of cul-de-sacs and connect it with high-speed roads
like a tree the traffic flows better (best game outcome), even though there
are less roads and the individual's commutes are longer.

SimCity is an interesting game to explore the concept of game theory since you
don't participate as an actor but rather as the rule maker. It shows how you
have to adopt counter-intuitive solutions from an actor viewpoint to enforce
the desired outcome (backtracking). Once the conditions are met the simulation
converges to what you desire.

~~~
YokoZar
Doesn't some of this behavior come from the rather preposterous way simcity
models its drivers? A model where there is no persistent data and the
heuristic is instead "go to nearest house and declare that home, if someone
beat me there go to the next nearest house" naturally lends itself to a tree
model, as no one actually wants to go anywhere but the next link in the chain!

A more reasonable model (and why gridded streets work in the real world) would
have people who desire to go to different places in the grid.

~~~
hcarvalhoalves
SimCity 4 "Rush Hour" introduces a refined traffic simulation where you can
inspect the commute of each citizen and it's exactly what you would expect in
real life - they go to anywhere in the city, not only nearby.

Grid layouts don't optimize for heavy traffic [1] because drivers choose
shorter paths, making it worse for all [2]. In real life you don't have grid
layouts without large roads, one-way streets, overpasses and other ways to
improve flow.

A tree layout avoids this by directing through traffic to higher-capacity
roads without intersections [3]. The downside is that _individual_ commutes
get longer. It's just one possible solution, but an interesting one because it
improves traffic (removes the Prisioner's dillema) by closing roads (denying
options to the game actors).

[1]
[http://en.wikipedia.org/wiki/Grid_plan#Late_19th_century_to_...](http://en.wikipedia.org/wiki/Grid_plan#Late_19th_century_to_the_present)

[2]
[http://en.wikipedia.org/wiki/Prisoner's_dilemma](http://en.wikipedia.org/wiki/Prisoner's_dilemma)

[3]
[http://en.wikipedia.org/wiki/Street_hierarchy](http://en.wikipedia.org/wiki/Street_hierarchy)

~~~
YokoZar
Thanks, this is all very interesting. I do think there's a bit more to
consider though, such as how it's much harder to design walkably compact
neighborhoods with arterial roadways than with gridded ones, meaning you might
just get fewer cars in the gridded setup.

~~~
hcarvalhoalves
Yes, it's about trade-offs. The point I was making though is how the
simulation models the counter-intuitive concept of "closing roads improve
traffic" because the simulation embodies a property of game theory that also
applies in real life.

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trevyn
One more for your list:

• Shameless self-promotion and "Source" attribution links that all lead to
your own YouTube videos will annoy people, but probably get you more traffic.

~~~
foxhill
well, in his defence -

> Every voting system is manipulable

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YokoZar
This is actually the least defensible claim there. I posted this in the
comments:

"Every Voting System is Manipulable" is an exaggeration of the implications of
strategic voting. Yes, the Gibbard–Satterthwaite theorem proves that a
dishonest vote could profitably exist in any system, however there are already
systems where intentionally doing so requires the voter to: 1) Have perfect
(or near-perfect) information about exactly how everyone else is voting, and
2) Solve an NP-hard math problem.

When breaking the vote requires more knowledge than any politician has, and
more computing power than breaking the cryptography of all the world's banks,
I'd say it's not particularly manipulable.

~~~
gte910h
Could you go over the good solutions then? I have always heard there are about
4-5 "good but complicated" systems, none of which are easily shown to be best
due to strategic voting and haven't seen clear "we should do this one because
it beats all those for sure" type recommendations.

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mathattack
I became a big fan of game theory when I realized that it's the simple effects
that matter, not the complex ones. At a prior employer, I started thinking
about, "Why are so many consulting firms willing to screw the vendor they're
working with for short term gain?" Then I realized it was because, "They don't
think they'll ever work with us again, so it's a single game of Prisoner's
Dilemma"

After that revelation, I started pushing towards longer term incentives to
incent better behaviors. "We're only working with a smaller subset of vendors,
who can count on repeat business, as long as they don't get kicked out of the
club. But they need to make investments in advance to show they're serious."

In general getting clients and partners to repeat games of Prisoner's Dilemma
rather than 1-offs is the key to trust, and long term profitability.

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CGamesPlay
Changing the phrasing from "Source" to "Learn more" would increase the
credibility of your work substantially. Not citing a source is better than
fabricating one and citing yourself.

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rogweiof
The first bullet-point ("People often take aggressive postures that lead to
mutually bad outcomes even though mutual cooperation is mutually preferable.")
is not backed up by the source, is incorrect, and if it was correct it would
be a finding from psychology not game theory.

I believe (not an expert) it is more important to minimize losses that to
maximize wins in game theory (cold war roots). Viewed in that light most game
theory results are, in fact, extremely intuitive.

~~~
vubuntu
>I believe (not an expert) it is more important to minimize losses that to
maximize wins in game theory (cold war roots).

That sounds meaningless. Aren't they the same thing? Isn't minimizing losses
effectively mean maximizing wins? Give me an example where minimizing losses
is not the same as maximizing wins. The only cases where it is not is if you
haven't vetted out (or could not vet ) the complete outcome of all possible
moves that you can make next, for example chess, where the game tree could be
of infinite (or deep enough to process in reasonable time) depth.

But chess programs are coded to try all possible tree paths to a reasonable
depth given the time constraints and pick a move that has the best
weight/score/winning chances. Not a move that has least losses. From that
perspective it is all about maximizing the chances of winning. Although I am
sure they are also coded to recognize draw conditions and play for draw if
that is more effective. So it is not so dry and cut.

So when you are not sure of the certainty of the outcome of the several
possible moves you could make next in a game, the best strategy is to pick the
one with maximum winning chances not minimal losses. Especially if you think
the opposite party is also going to play to win. Next, if your chances of
losing are increasing, then play for draw first and lastly mutual destruction
(to force the opposite player to draw)

Even in the 'cold war roots' that you mention, the goal is not just to
occupy/conquer the opposite country. The goal is also to do so at minimal loss
to ourselves. So "winning" in the game of war "is to conquer enemy country at
minimal losses or maintain status quo if the losses would be
substantial/irrecoverable". So you are always playing to 'win'.

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fredup
"Soccer players should kick toward their weaker side more frequently than
their stronger side."

I thought this was an interesting result, so I took a look at the source. It
turns out it is a toy problem where the goalie always stops the penelty kick
if she guesses right and the kicker always makes the goal if kicking to one
side, and misses with some probability when kicking to the other.

This is clearly a toy problem that you can't draw any sort of real world
soccer advice from.

~~~
wspaniel
You could show the same thing by relaxing those assumptions. It would just
require a lot more algebra. The key insight is that, holding everything else
constant (which is done in the lecture), weakening your accuracy to one side
increases the probability you target that side.

~~~
fredup
I think you need to do the algebra. You can't make a blanket statement like
you want to.

You have taken things to an absurd extreme and gotten one result, I can "relax
the assumptions" to the opposite extreme and get the opposite result:

Suppose the goalie only blocks 10% of shots when guessing correctly, and the
kicker makes 80% to the strong side and 50% to the weak side. In this model it
is obviously better to always kick to the strong side.

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marketforlemmas
These are interesting examples of using game theory to model certain
situations but none of these examples show that game theory "tells us"
something about the world. In broad strokes, game theory claims to have a
descriptive model of human behavior but people very rarely follow the
predictions of game theory (and that is even when you're in situations that
are simple enough to have a stab at applying game theory). This is
particularly true for Nash Equilibrium, which it seems most of your examples
rely on.

And I think in the cases where the NE are predictive of actual play, then
there's something intuitively obvious about the NE, and that you could have
arrived at the same conclusions without using the tools and machinery of game
theory. This is the point that Ariel Rubenstein makes
([http://arielrubinstein.tau.ac.il/papers/74.pdf](http://arielrubinstein.tau.ac.il/papers/74.pdf))
when he says that game theory is useless.

That's not to say that I believe that game theory is never useful (for certain
limited settings, like repeated auctions, it works well), nor do I think that
it can never be useful (recent work in behavioral game theory is promising in
my opinion) but I'm skeptical using these counterintuitive claims as examples
of its use.

~~~
cwp
> In broad strokes, game theory claims to have a descriptive model of human
> behavior

Huh? Game theory is the study of strategy. It's not attempting to describe how
people actually behave, but how they _should_ behave if they want to achieve a
specific outcome when interacting with other people.

~~~
curiouslearn
No, it does _not_ say how people _should_ behave? It analyzes strategic
situations using various equilibrium concepts, such as the Nash equilibrium.
If you are not sure that your opponent will play the Nash equilibrium
strategy, Game theory doesn't tell you what you should do.

~~~
wspaniel
That's when you use Bayesian Nash equilibrium or perfect Bayesian equilibrium.
No big deal.

~~~
marketforlemmas
I take some issue with the idea that we can simply just rely on another
equilibrium refinement and say "no big deal".

It seems a bit silly to observe some behavior in a game and say "See that's a
Nash Equilibrium, so game theory works", and then to turn around and observe
some non-NE behavior and say "well in this game, BNE is clearly the right
model, so game theory still works". And then yet again to observe some more
behavior that conflicts with the theory (or to get rid of silly equilibrium)
and say "ah, now we simply use perfect Bayes" or trembling hand equilibrium,
or actually we were totally using correlated equilibrium this whole time.

In any case, it feels weird that a theory should behave like the "No true
Scotsman" fallacy. We can always get the equilibrium by simply redefining what
we mean by equilibrium.

