Game Theory Is Counterintuitive(wjspaniel.wordpress.com)
wjspaniel.wordpress.com
Game Theory Is Counterintuitive
http://wjspaniel.wordpress.com/2014/05/25/game-theory-is-really-counterintuitive/
8 comments
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.
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.
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_...
[2] http://en.wikipedia.org/wiki/Prisoner's_dilemma
[3] http://en.wikipedia.org/wiki/Street_hierarchy
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_...
[2] http://en.wikipedia.org/wiki/Prisoner's_dilemma
[3] http://en.wikipedia.org/wiki/Street_hierarchy
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.
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.
On the other hand, once you can factor road utilisation in your personal preference function, you can take the slightly longer but much less used road, meaning that for certain actors a sub-optimal road grid is better than a tree.
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.
• Shameless self-promotion and "Source" attribution links that all lead to your own YouTube videos will annoy people, but probably get you more traffic.
well, in his defence -
> Every voting system is manipulable
> Every voting system is manipulable
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.
"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.
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.
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.
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.
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.
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.
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.
>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'.
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'.
"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.
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.
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.
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.
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.
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) 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.
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) 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.
> 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.
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.
No, because most games only have Nash Equilbria. Nash Equilibrium assumes that everyone is acting rationally, not just the person you are advising.
Some games, like second price auctions (under certain assumptions about people's values for the good, and knowledge of their own and other people's values) have so called dominant strategy equalibria. In this case, you can say how a person should act regardless of how others act.
But these scenarios are the exception rather than the rule.
Some games, like second price auctions (under certain assumptions about people's values for the good, and knowledge of their own and other people's values) have so called dominant strategy equalibria. In this case, you can say how a person should act regardless of how others act.
But these scenarios are the exception rather than the rule.
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.
That's when you use Bayesian Nash equilibrium or perfect Bayesian equilibrium. No big deal.
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.
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.
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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.