Game Theory Simulation

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Enigma90825
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Game Theory Simulation

Postby Enigma90825 » Thu Nov 29, 2007 11:23 pm UTC

Right now in my AP Micro Economics class, we're working on Game Theory. My teacher gave us this simulation and I thought it was pretty cool.

http://www.gametheory.net/Mike/applets/PDilemma/

So far, my best is 99.2 (me) to 60.8 (computer). For the class, we need to try to beat the computer by the highest possible margin (so my margin is 38.4 so far). Post your best here! (and let me know how you got it :lol: )

*Edited to change top scores

*Can anybody get higher than 1.2 profit margin for Firm 1 or Firm 3?
Last edited by Enigma90825 on Thu Nov 29, 2007 11:52 pm UTC, edited 2 times in total.
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arkady
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Re: Game Theory Simulation

Postby arkady » Thu Nov 29, 2007 11:34 pm UTC

They've had competitions with this sort of thing where people entered computer programs to play.

Some where several megabytes.

The winner of every single tournament* was called TIT-FOR-TAT.

Tit-for-Tat works as follows:

Round 1: Co-operate.
Round X: If your opponent cooperated in round X-1, cooperate. If your opponent defected in round X-1, defect.


*Tit-for-tat even wins in the more recent tournaments where everyone entering knows exactly how tit-for-tat works and tries to exploit it!
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Re: Game Theory Simulation

Postby Enigma90825 » Thu Nov 29, 2007 11:36 pm UTC

arkady wrote:They've had competitions with this sort of thing where people entered computer programs to play.

Some where several megabytes.

The winner of every single tournament* was called TIT-FOR-TAT.

Tit-for-Tat works as follows:

Round 1: Co-operate.
Round X: If your opponent cooperated in round X-1, cooperate. If your opponent defected in round X-1, defect.


*Tit-for-tat even wins in the more recent tournaments where everyone entering knows exactly how tit-for-tat works and tries to exploit it!


Yeah, I've heard of that and I think one of the personalities uses that in the simulation I gave. However, doesn't that work to just maximize the profit realized by both parties? In my case, I don't want to do that, I want to beat the other by as much as I can.
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Re: Game Theory Simulation

Postby Pero » Fri Nov 30, 2007 1:14 am UTC

My best was $123.60 - $57.60, for a margin of $66.00. My best without exploiting the broken applet was $96.40 - $62.80 ($33.6).

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Re: Game Theory Simulation

Postby synaesthetist » Fri Nov 30, 2007 1:39 am UTC

$93.80 vs. $49.60 ($44.20) was my best.

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Re: Game Theory Simulation

Postby Enigma90825 » Fri Nov 30, 2007 1:42 am UTC

synaesthetist wrote:$93.80 vs. $49.60 ($44.20) was my best.


HOW!?
I was really bored so I made a program to go through it and do it for me instead haha.
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Re: Game Theory Simulation

Postby william » Fri Nov 30, 2007 2:13 am UTC

arkady wrote:They've had competitions with this sort of thing where people entered computer programs to play.

Some where several megabytes.

The winner of every single tournament* was called TIT-FOR-TAT.

Tit-for-Tat works as follows:

Round 1: Co-operate.
Round X: If your opponent cooperated in round X-1, cooperate. If your opponent defected in round X-1, defect.


*Tit-for-tat even wins in the more recent tournaments where everyone entering knows exactly how tit-for-tat works and tries to exploit it!

Actually I heard that Tit-for-tat was recently beaten in one of the tournaments but only because a bunch of programs were working together.
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Re: Game Theory Simulation

Postby synaesthetist » Fri Nov 30, 2007 3:06 am UTC

Enigma90825 wrote:
HOW!?
I was really bored so I made a program to go through it and do it for me instead haha.


honestly, i just played around with Firm 2 and Firm 4. Firm 1 and Firm 3 seem identical and Firm 5 always cheats. Also, you'll get ahead with 1 and 3 if you cheat on the last one after colluding the whole time. My latest best is $94.00 vs. $49.60. I can't manage to do any better.

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Re: Game Theory Simulation

Postby Enigma90825 » Fri Nov 30, 2007 3:10 am UTC

synaesthetist wrote:
Enigma90825 wrote:
HOW!?
I was really bored so I made a program to go through it and do it for me instead haha.


honestly, i just played around with Firm 2 and Firm 4. Firm 1 and Firm 3 seem identical and Firm 5 always cheats. Also, you'll get ahead with 1 and 3 if you cheat on the last one after colluding the whole time. My latest best is $94.00 vs. $49.60. I can't manage to do any better.


Yeah, the only difference between 1 and 3 is that 1 will go back to colluding after you cheat with it, 3 will continue to cheat. That's the only way to get ahead with them, to cheat at the very end. As for 2, I've been pressing cheat and then collude alternating down and I get a score of 25.6 (me) and 9.6 (computer). 4 is the one that varies and the best I've gotten is 24.4 vs. 2.8........ How?! :lol:
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Re: Game Theory Simulation

Postby OmenPigeon » Fri Nov 30, 2007 3:19 am UTC

william wrote:Actually I heard that Tit-for-tat was recently beaten in one of the tournaments but only because a bunch of programs were working together.


Yeah, one group entered 60 programs in the tournament. They recognized each other with handshakes and then one would just dump points to the other. That group took the top three spots and the bottom thirty or so.
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Re: Game Theory Simulation

Postby Blatm » Sat Dec 01, 2007 8:30 am UTC

My results:

Firm 1 uses the well known tit-for-tat method, as previously mentioned. The optimal strategy is to cheat only on the last period.

Firm 2 is a bit odd. From what I can tell, he cheats twice in a row if you cheat twice in a row, but only works with groupings of 2, i.e. if you cheat three times in a row (ch,ch,ch,co,X,X...), he will cheat only twice overall (X,X,ch,ch,co,co...). the optimal strategy here is to alternate cheating and colluding (starting with cheating as there are an odd number of periods.)

Firm 3 is very similar to Firm 1, but will continue to cheat. This is called the Grim Trigger Strategy. The optimal strategy is the same as with firm 1.

Firm 4 chooses randomly. I confirmed this by choosing to collude for all periods, recorded his actions, then reloaded the applet, did the same thing, and got a different set of actions. The optimal strategy is to always cheat.

Firm 5 always cheats. The optimal strategy is to always cheat as well.

The optimal scores are 20.4-19.2, 25.2-9.6, 20.4-19.2, 20-5 (on average) and 10-10, totaling 96-63, a difference of 33 points (at lest that's the best I can do).

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Re: Game Theory Simulation

Postby no-genius » Sat Dec 01, 2007 12:00 pm UTC

72.4 - 64.0 :(

Edit: 80-68 :(
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Re: Game Theory Simulation

Postby Enigma90825 » Sat Dec 01, 2007 3:53 pm UTC

Blatm wrote:My results:

Firm 1 uses the well known tit-for-tat method, as previously mentioned. The optimal strategy is to cheat only on the last period.

Firm 2 is a bit odd. From what I can tell, he cheats twice in a row if you cheat twice in a row, but only works with groupings of 2, i.e. if you cheat three times in a row (ch,ch,ch,co,X,X...), he will cheat only twice overall (X,X,ch,ch,co,co...). the optimal strategy here is to alternate cheating and colluding (starting with cheating as there are an odd number of periods.)

Firm 3 is very similar to Firm 1, but will continue to cheat. This is called the Grim Trigger Strategy. The optimal strategy is the same as with firm 1.

Firm 4 chooses randomly. I confirmed this by choosing to collude for all periods, recorded his actions, then reloaded the applet, did the same thing, and got a different set of actions. The optimal strategy is to always cheat.

Firm 5 always cheats. The optimal strategy is to always cheat as well.

The optimal scores are 20.4-19.2, 25.2-9.6, 20.4-19.2, 20-5 (on average) and 10-10, totaling 96-63, a difference of 33 points (at lest that's the best I can do).


Yeah that's been almost my exact strategy too. I think I said earlier, but I created a program that will run through it, clicking on collude or cheat as I want it to do. Then at the end, I made it compare the score I got on that round against my top score. I've found the best strategy on 4 is to cheat the whole way through.

And apparently I misunderstood the teacher originally, it's not that profit margin that matters, but the profit. So you just want to get the highest possible score for yourself (which does often involve a high profit margin, but the profit margin isn't what is important) So far, my highest is 102.8
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Re: Game Theory Simulation

Postby thisisdavid » Sun Dec 02, 2007 6:06 am UTC

Isn't it the idea of game theory that the maximum score is made when both sides cooperate? Does this game show that? Sorry, the extent of my knowledge of game theory comes from wikipedia and a beautiful mind.
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Re: Game Theory Simulation

Postby Shadow Tyrant » Sun Dec 02, 2007 7:22 am UTC

Wow, I can't stop seeing 'stimulation' when I read the title of this thread.
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Re: Game Theory Simulation

Postby Blatm » Sun Dec 02, 2007 7:30 am UTC

Enigma90825 wrote:And apparently I misunderstood the teacher originally, it's not that profit margin that matters, but the profit. So you just want to get the highest possible score for yourself (which does often involve a high profit margin, but the profit margin isn't what is important) So far, my highest is 102.8


That doesn't seem to change the strategy, though.

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Re: Game Theory Simulation

Postby Enigma90825 » Sun Dec 02, 2007 11:05 pm UTC

thisisdavid wrote:Isn't it the idea of game theory that the maximum score is made when both sides cooperate? Does this game show that? Sorry, the extent of my knowledge of game theory comes from wikipedia and a beautiful mind.


It's true that you can use game theory to maximize the score achieved by the group. However, an even higher score can be obtained by "cheating" that plan. This was hinted to in a Beautiful Mind when one of the guys says "if this is just your way for getting the blond all by yourself..." That would be Nash exploiting using game theory if he did that and didn't "cooperate" but rater "cheated."

Blatm wrote:
Enigma90825 wrote:And apparently I misunderstood the teacher originally, it's not that profit margin that matters, but the profit. So you just want to get the highest possible score for yourself (which does often involve a high profit margin, but the profit margin isn't what is important) So far, my highest is 102.8


That doesn't seem to change the strategy, though.


One of the other people who posted here had a large profit margin of 44 or something close to that, yet their highest score was only 97. While that score meets the profit margin requirements, it doesn't do as well in the total profit.
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