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Author Topic: Zero Sum Games/The Nash Equilibrium used in Mafia..  (Read 4327 times)

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Re: Zero Sum Games/The Nash Equilibrium used in Mafia..
« Reply #25 on: July 31, 2015, 03:53:05 am »

IDK about you guys, but if I was SK I'd be looking to kill Mafia.
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Re: Zero Sum Games/The Nash Equilibrium used in Mafia..
« Reply #26 on: July 31, 2015, 04:06:11 am »

Also No-Lynch is the only thing that makes sense for all three parties. Town will say "I will vote for the first person to vote me" which then no one would vote. So then the question becomes who does SK NK and who does Mafia NK? That would be when the real fun starts I think. The Townie just might win through the Mafia and SK targeting each other for the NK.
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Ghacob

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Re: Zero Sum Games/The Nash Equilibrium used in Mafia..
« Reply #27 on: July 31, 2015, 11:14:31 am »

Well that's the more trivial part
I'm reminded vaguely of prisoner's dilemma here

Let's say you're the SK and you don't know who the Mafia will kill
Well there are two options:
Mafia kills town, in which case it's clearly better that you should kill the Mafia for the win
Mafia kills you, in which case you could argue it's null, you lose either way
If there's even a slight chance Mafia kills town, it's better to kill Mafia every time. Specifically, killing town will only hurt you

Mafia goes through the same options, therefore they always kill each other at night, as lio nicely led on

The No Lynch only makes sense for town, as it's the only way for them to win, and unfortunately for the Mafia and SK, I can't see anyway they can beat town here
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pacovf

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Re: Zero Sum Games/The Nash Equilibrium used in Mafia..
« Reply #28 on: July 31, 2015, 11:24:52 am »

The nightkill is exactly the prisoner dilemma for the SK and Mafia. Killing town is considered "cooperating", killing each other is considered "betraying". The only question is how do the players value a draw, compared to a win or a loss.

It is important to note that town loses if there is a lynch, so he is not ever going to vote, unless he values the different losses differently (ex: SK winning instead of Mafia winning, etc.). Which means that the only possible lynch is town. So SK and Mafia can safely choose if they want to cooperate or not during the day, by voting town. If they don't lynch town, they are sending a very clear message that they don't want to cooperate, which means that both will betray during the night, and then town wins.

So the sensible choice is for the SK and the last Mafia to lynch town. However, if a mutual nightkill is ruled as a loss for both factions, then there is no way for anyone to win the stalemate.

This assumes that all players are perfectly rational... which they most often are not. In this situation, I fully expect that considerations about who "deserves to win" will tip the scales one way or another (probably in favour of the SK, since it's usually the hardest role to play).

EDIT: I am assuming that an endgame with only a SK and a Mafia player is considered as a draw for the SK and Mafia, but as a loss for town.

EDIT2: And of course liopoil has already gone over all this quite nicely.
« Last Edit: July 31, 2015, 11:35:23 am by pacovf »
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Re: Zero Sum Games/The Nash Equilibrium used in Mafia..
« Reply #29 on: July 31, 2015, 11:50:47 am »

This is exactly why I prefer VT over any other role.
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