[EV-ish] The effect of meta

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[EV-ish] The effect of meta

Post Post #0 (ISO) » Tue Feb 19, 2019 5:42 pm

Post by BNL »

3 Mafia Goons
6 Activated Innocent Children

Now this seems like a stupid setup, as it seems like a town win as they can all confirm themselves as town, PoEing the scum.

However, supposed a group of 9 players play this setup multiple times in succession. If a player establishes a meta where they always reveal themselves when town, then when they cannot reveal it confirms themselves as scum. Hence players may choose to refuse to activate the IC even when town, to give themselves a better chance when playing scum. In fact, this is still a guaranteed win if only one IC refuses to activate, so there is incentive for players to refuse to activate their IC.

Say the long run objective of the players is to win as many games as possible. What's the optimal strategy?

Say there's a further incentive to win as scum by awarding 3 points to a scum win, but only 1 point to a town win. Is the optimal strategy different here?
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Post Post #1 (ISO) » Tue Feb 19, 2019 6:05 pm

Post by Something_Smart »

In post 0, BNL wrote:Say the long run objective of the players is to win as many games as possible. What's the optimal strategy?
It's gotta be to always reveal for .67 points per game.
Say there's a further incentive to win as scum by awarding 3 points to a scum win, but only 1 point to a town win. Is the optimal strategy different here?
I think the optimal strategy is to throw the game to mafia which will produce 1 point per game per player in the long run. If anyone ever reveals as town then it turns into a prisoner's dilemma-esque situation, but every town win decreases the total points available to all the players combined.

If it were 1 point for a town win and 2 points for a mafia win, then the total number of points in circulation would be the same after a town or scum win. That's when you might get to see some weird shit.
It's always the same. When you fire that first shot, no matter how right you feel, you have no idea who's going to die. You don't know whose children are going to scream and burn. How many hearts will be broken. How many lives shattered. How much blood will spill, until everybody does what they're always going to have to do from the very beginning... SIT DOWN AND TALK!
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Post Post #2 (ISO) » Tue Feb 19, 2019 6:06 pm

Post by RadiantCowbells »

In post 0, BNL wrote:What's the optimal strategy?
be able to win as town without revealing
2019 stats: Town WR 76.7%, overall WR 81.667%, 1 scum defeat involving a major mod error in lylo vs 8 scum wins.
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Post Post #3 (ISO) » Thu Feb 21, 2019 1:39 pm

Post by callforjudgement »

Playing for the long run in this setup would violate at least two site rules, so I'm assuming we're talking about a hypothetical version where the rules are different.

An obvious improvement over "always reveal" is "reveal only at L-1", at least if you assume that there are no deadline effects in play.

One strategy that I think might be worth trying would be refusing to reveal if you ever hit L-1 during Day 1. This gives a strong incentive for town to leave you alive for Day 1, and even if they get annoyed with you for this and lynch you, it's still possible for town to win the resulting 4:3 by all revealing, so the strategy isn't even gamethrowing. (Presumably you have to add some proportion of refusing to reveal even if you aren't run up until D2, because otherwise, running you up D2 would become optimal strategy.)
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Post Post #4 (ISO) » Sat Feb 23, 2019 6:39 pm

Post by mhsmith0 »

An equilibrium strategy is to always reveal, guaranteeing town wins if a strong majority embrace this strategy (minor tweaks like “always reveal in LYLO or at L-1 pre lylo” get you to the same point)

There’s really no counter against said strategy, so it’d be very likely to be embraced, this making the setup broken.
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http://wiki.mafiascum.net/index.php?title=Mhsmith0
Conq: you, sir, are great at being town.
BATMAN: Only jugg was the only one we didn’t scum read at least not me
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Post Post #5 (ISO) » Mon Feb 25, 2019 8:25 am

Post by implosion »

In post 4, mhsmith0 wrote:An equilibrium strategy is to always reveal, guaranteeing town wins if a strong majority embrace this strategy (minor tweaks like “always reveal in LYLO or at L-1 pre lylo” get you to the same point)

There’s really no counter against said strategy, so it’d be very likely to be embraced, this making the setup broken.
This is a Nash equilibrium. But so is both sides defecting in a prisoner's dilemma.

I think Something_Smart is basically correct here; assuming that you get 1 point for a town win, then if you get <2 points for a mafia win, town will always reveal and win every game. If it's >2 points for a mafia win, then the "optimal" long-term strategy is a variant on iterated prisoner's dilemma or tragedy of the commons where some subset of players refusing to throw the game to the mafia is 'defecting'. And if it's exactly 2 points then probably the long-term cooperative strategy would be to just cooperate every game but other things might also happen.

However, optimal in this sense is the optimal purely cooperative strategy. There could also be coalition strategies. Obviously this is not kosher in a MS game of mafia but if 5 of the 9 players decide to form a coalition, they can significantly improve their long-term points to the detriment of the other 4 players by accurately announcing/revealing their allegiances each game, and then acting as a bloc to guarantee that whichever side will give the coalition more total points wins. For instance, if a mafia win is 2 points, then if there are 2 mafia members in the coalition, mafia winning would give 4 points to the coalition (2 points * 2 players) while town winning would give 3 (1 point * 3 players), so the five of them will systematically vote out town members outside of the coalition. If there's only one mafia member then mafia winning would give them 2 points (2 points * 1 player) while town would give them 4 (1 point * 4 players) so the mafia member would announce their partners and the coalition would just eliminate them all.

Likewise, if all 5 are town, or 3 are mafia and 2 are town, then the five of them very simply systematically vote everyone else out.

Normally, in a pure cooperative strategy, individual players expect to earn ~0.67 points per game (6 points total awarded per game / 9 players). But now, in the worst case, the coalition earns 4 points total (they may earn 5 or 6 total if all 5 are town or 3 of them are mafia respectively), so even in the worst case, coalition members can expect a payout of 0.8 points per game. The actual average payout will be a little higher.

Notably, this even benefits the coalition (though much more slightly) in the case where town and mafia wins are worth the same amount, as they'll be able to force a mafia win when 3 of them are mafia.
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