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نوشته شده در 18 مهر 1389
بازدید : 1792
نویسنده : TAKPAR

 

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<<< بخش شعر و ادبیات >>>
نوشته شده در 18 مهر 1389
بازدید : 1769
نویسنده : TAKPAR



<<< بخش کتاب و کتابخانه >>>
نوشته شده در 18 مهر 1389
بازدید : 1641
نویسنده : TAKPAR



<<< بخش آموزش زبان انگلیسی >>>
نوشته شده در 18 مهر 1389
بازدید : 2089
نویسنده : TAKPAR



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نوشته شده در 18 مهر 1389
بازدید : 1739
نویسنده : TAKPAR



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نوشته شده در 18 مهر 1389
بازدید : 1884
نویسنده : TAKPAR



Liar Game
نوشته شده در 18 مهر 1389
بازدید : 2221
نویسنده : TAKPAR

Liar Game: Game Theory on Screen

Posted by chayanin on 2010-09-20

• There are 11 players locked together in a large hall.

• Each player has a letter code A-K, which will be unknown to other players.

• There are 3 kinds of apples: Gold, Silver, and Red.

• There are 13 (or so) rounds. Each round has the time limit of one hour.

• In each round, the players have to go into a room one by one, pick an apple, brand it with their names, and put it in a box.

• The round will finish after every player has cast his/her apple.

• Players who belong to the majority between Gold and Silver will win $1m, and those in the minority will lose $1m. For example, if 6 players choose Gold and 5 players choose Silver. Those who choose Gold will win $1m each, and those who do not will lose $1m.

• However, some players choose Red, those who choose Red will lose $1m, and those who choose Gold or Silver will win $1m.

• If all the players choose Red, all will win $1m.

• If all the players unanimously choose Gold or Silver, all will lose $1m.

• If all but one player choose Red, one who does not will win $2m.

• If only one player chooses Red, he/she will lose $10m.

• After each round, the result will be announced. The players will know the number of each kinds of apples chosen, and will know the changes in prize money for all the players by the codes. (Which, as explained above, are not known to other players.)

 

The game above is from Japanese film called Liar Game: The Final Stage. Basically, the outline of the game is quite similar to a prisoner’s dilemma. The game is actually more complexed than that, as it is not only about the decision-making part we study in game theory. It is far beyond that. Still, this nicely created game looks rather fun to play with some game theory enthusiasts.

I saw this film on the Air Canada flight from Tokyo to Toronto. It was the most entertaining film I saw on the flights. (The other two that I saw were Thai film Dear Galileo, watched on Bangkok-Tokyo flight, and Sex and The City, on Tokyo-Toronto. Both were very boring.) The film looks like a typical Japanese adaptation of comics, since it is an adaptation from a manga series. (I learnt this fact afterwards.)

I wouldn’t say the film is artistically expressed or anything, but for those who love strategic games, this should be fun.

 


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Algorithmic Game Theory
نوشته شده در 18 مهر 1389
بازدید : 2172
نویسنده : TAKPAR

کتاب

Algorithmic Game Theory

 


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بازدید : 2190
نویسنده : TAKPAR

 

By: hctomorrow Tuesday September 14, 2010 11:36 pm

A common refrain in the lefty blogosphere is that you have to support the candidate with a D after their name, even if they repeatedly betray your causes and ideals, because the Republicans are worse. They’ll repeal all the ‘great’ legislation the Democrats have passed over the past two years, and continue all the terrible policies the Democrats have unfortunately continued – policies which are also, conveniently, the Republicans’ fault.

However, game theory teaches us something quite different – that cooperation without the threat of retaliation for betrayal is a sucker’s game.

The Prisoner’s Dilemma

To see why, let’s back up a bit. First, what’s Game Theory? From Wikipedia:

Game theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology (particularly evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. Game theory attempts to mathematically capture behavior in strategic situations, or games, in which an individual’s success in making choices depends on the choices of others.

In essence, it’s roleplaying as science. To try and understand what the best strategies are when dealing with other actors, you set up a mock version, either on a computer or for kicks in real life, and play out the various strategems, measuring which is more successful and what the pitfalls are. The results can often be surprising.

One of the most famous experiments in game theory is the ‘Prisoner’s Dilemma’. Again, from Wikipedia:

The prisoner’s dilemma is a fundamental problem in game theory that demonstrates why two people might not cooperate even if it is in both their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner’s dilemma" name (Poundstone, 1992).

A classic example of the prisoner’s dilemma (PD) is presented as follows:
Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

Obviously, the prisoners would be better off if they cooperated – 1 year’s combined jail time is a lot better than 10, which is the result if either betrays the other, or both do. However, it’s not *rational* to cooperate – no matter which choice your opponent makes, betraying them increases your benefit. If they cooperate, you stab them in the back and walk free. If they stab you, you protect yourself by backstabbing them.

A pretty bleak assessment of human nature, eh? The problem here is accountability, or rather, the lack thereof. Remember the setup: the police make sure neither prisoner can confer with the other until after the decision has been made, and you only get to make it once.

If accountability is added, however, things turn can turn out very differently.

The Iterated Prisoner’s Dilemma, aka Politics

If you set up a game where the players have to run through that same scenario multiple times, with memory of what happened before, things turn out differently, and different strategies succeed. If you defect every time, your opponent is free to, and indeed only rational to follow your example. Likewise, however, if you cooperate every time, your opponent can see an easy mark and take advantage.

Wikipedia again:

Retaliating
However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.

Herein lies the fundamental flaw in always voting Dem just because Republicans are worse, and we have decades of math to back it up. If you always cooperate, your opponent will face enormous temptation, arguably selection pressure, to defect and betray you. It’s only a matter of time, and what’s more, they face absolutely no penalty for doing so – you’ll just cooperate again the next round.

If, on the other hand, you are willing to retaliate, a more successful strategy can be devised.

Tit for Tat
As it turns out, cooperating all the time and defecting all the time are both proven losers, given repeat performances. So what works?

It turns out, a combination of the two. I’ll let Carl Sagan explain this one (from his essay ‘The Rules of the Game’, collected in Billions and Billions):

The most effective strategy in many such tournaments is called "Tit-for-Tat." It’s very simple: You start out cooperating, and in each subsequent round simply do what your opponent did last time. You punish defections, but once your partner cooperates, you’re willing to let bygones be bygones. At first, it seems to garner only mediocre success. But as time goes on the other strategies defeat themselves, from too much kindness or cruelty, and this middle way pulls ahead. Except for always being nice on the first move, Tit-for-Tat is identical to the Brazen Rule. It promptly (in the very next game) rewards cooperation and punishes defection, and has the great virtue that it makes your strategy absolutely clear to your opponent. (Strategic ambiguity can be lethal.)

The problem for Progressives is that we’re being told to, and have in the past often utilized an Always Cooperate strategy.. and our partners in elected office learned that long ago, and are exploiting it.

On gay rights, on immigration, on financial reform, on restoring the rule of law, on putting torturers on trial, on unions and the free choice act, on escalating unwinnable wars, on fighting the legalization of marijuana, on just about any and almost every single Progressive issue you can name the current Democratic party has defected. Why?

Because it’s a winning strategy to defect if you know your opponent will always cooperate; in fact, it’s the absolute best strategy to employ.

The Way Ahead

The only way we can expect to stop the exploitation is to show our would-be-defectors in the Democratic Party that we’ve woken up, once and for all, and are willing to retaliate when defected from. Yes, if we do so, we’ll lose in this round of our iterated game. We might, in fact, lose very badly indeed.

The alternative, however, is clear, from both game theory and common sense: the exploitation will *never* stop. Never. Let’s be very clear; the current dilemma Progressives face with their estranged counterparts does not stem from a lack of understanding; the party understands us all too well. It isn’t the result of Dems failing to learn from past mistakes; on the contrary, they’ve learned exceptionally well from ours.

http://seminal.firedoglake.com/diary/71423

 


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Kuhn Poker Solved: Win Money With Game Theory
نوشته شده در 18 مهر 1389
بازدید : 2336
نویسنده : TAKPAR

Yesterday I posted the rules of the very cool Kuhn poker. Here's optimal play:

Playing first:
Interestingly, you can either check or bet a King or a Jack—this is poker, after all and in this case bluffing/slow-playing is as good as playing your cards straight. But holding a Queen is tricky: If you bet, your opponent folds with a Jack or raises with a King. Half the time, you win your opponent's one-chip ante, and half the time you lose your ante plus your bet.

This is not good. In fact, it's bad. You're losing twice as many chips as you're winning.

So you check.

Now your opponent only checks if holding the Jack and you win the one-chip ante. If your opponent bets he/she either has the King or is bluffing with the Jack. So calling this bet wins half the time (assuming your opponent is an ice-cold bluffer). If you call, you've got two chips versus two chips in a 50/50 pot; if you fold, you lose your ante every time.

So your best strategy when holding the Queen and playing first is to check and then call if necessary. Unfortunately, even this optimal strategy loses 1/18th each hand.

So you'd rather play first (see above).

For serious Game Theory geeks, here's the decision tree, with dominated strategies (the bad ones) already removed:


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