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Old 11-23-2007, 03:40 AM
Paxinor Paxinor is offline
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Join Date: Sep 2006
Posts: 87
Default Re: Fictitious play for multi-player games

there is definitly no "spite-call" equilibrium.

it doesn't help to fix the callers strategy. then you just use the maximaly exploiting counterstrategy as a pusher. but then its not even a equilibrium since there is only one strategy...

so bascily the other guy is just moving out of the NE trying to make you adjust to an exploiting strategy and go into a kind of "tit for tat" game.

but its really exciting to see that players have GREAT power over the game and it's outcome if they do not choose to max payout.

however strictly theoretic, there is no "spite-call" equilibrium whatsoever. even if you add constraints...

if someone moves away from NE and the other adjusts somehow, there will be no equilibrium. so you cannot just lay back, play your strategy and wait that the opponent makes a mistake. then your in the "he thinks that i thinks that he thinks" not that the state cannot be profitably played

in pracice i think he makes a good move... i mean you should adjust. you improve your EV by that and he improves his. because your strategy will not be public he cannot exploit you perfectly. therefore it is very likely that you will turn out with a better EV than in the NE but he will too!

so actually we have the kind of paradox situation that because he cannot exploit you perfectly because he doesn't know your exact strategy he can improve his EV!! this is pretty sick if you think about it because this goes so much agaisnt intuition.

well (while im writing it) acutally i think there is some kind of equilibrium:

take all possible strategies of the caller and let them be exploitet perfectly by the pusher. there is an EV for all of those situations. if some of those EVs are for the caller are above his NE EV then he should just choose that strategy and risk to get maximaly exploitet.

of course the pusher then as a 23% pushing range and could be exploitet again by thigten up. but the you get into that tit for tat game where when it starts to ge sophisticated in strategy changing, NE strategy would be best again

so you simply don't adjust! you giving up the edge of counterexploiting him to preserve the edge you gain by getting maximaly exploitet over the NE EV (this sounds pretty sick)

so if the calculations of plexiq are correct, the other guy starts calling all the time and is therefore transfering EV to the folders. if you are a thinking player you adjust.

you just push 23% of your hands. good for you, you improved your EV again. but the loose caller improved his too! (if the calculations are correct). so he should keep his strategy up. and there you have a kind of equilibrium where strategys will not be changed due to lack of strategys that are known and the problem that you might loose in a tit for tat game.

well this is really really interesting!
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