[QUOTE=LagAttack;930778]I noticed you tagged this thread with the game theory tag. So I will approach it from a game theory perspective.
[SPOILER=post][SIZE=3][COLOR="#00FFFF"]The Honest Prisoner's Dilemma: [/COLOR][/SIZE]
[SIZE=1](This is nothing like the prisoner's dilemma, the name is a pun, leave me alone)[/SIZE]
[IMG]https://i.imgur.com/5kjrcX2.png[/IMG]
[IMG]https://i.imgur.com/yFurG7R.png[/IMG]
[IMG]https://i.imgur.com/bsQxNCg.png[/IMG]
You can think of alpha as the gain you get from not being auto-executed by a town Jailor for not claiming a role.
You can think of beta as the gain you get from not revealing your role to a regular player that rolled kidnapper and know you're town, so they're executing you no matter what you say.
You can think of gamma as the gain you get from not revealing your role to a new player that rolled kidnapper and doesn't know what you are, so they might spare you because you didn't claim a role - like what a neut evil caught in the headlights might do.
And here's the issue with the Honest Prisoner remaining silent:
The ration between regular players that know what you prefer/blacklist, and new players that don't is PROBABLY somewhere around 1 to 1. Being generous we can even say that there are twice as many regular players that have played enough to know your meta as new players.
We'll be generous again and assume that the expected number of jailors is twice the expected number of kidnappers. This is being VERY generous - it's rare to see a setup like that, the ratio is usually closer to 4:1. But alpha is certainly greater than gamma, which means Ja - Ky > a - even when being very generous in your favor.
Which means in order for the ratio to be greater than 1, you need at the very least for 14 beta/alpha to be greater than 1, and beta represents the utility gain from staying silent rather than giving a regular player that knows you're town your role.
They are executing you anyway if they are a regular player that jailed you because they know you're town. The only utility you could possibly get here is if they ALSO have a Janitor and they perhaps decide they want to sanitize your role as well?
But even that utility gain is extremely marginal when compared to the utility gain you get from alpha (not auto-dying to town jailors)
So as a result it is very, very unlikely that 14 beta/alpha is greater than 1. And this was with all the most generous assumptions in place, in reality it's probably not even close and remaining silent is an inferior strategy.
[COLOR="#00FFFF"][SIZE=3]TL;DR The solution to the Honest Man's prisoner dilemma is to give your role every time. Remaining silent does [COLOR="#FF0000"]NOT [/COLOR]get the [COLOR="#00FF00"]Lag's Game Theory Analysis seal of approval[/COLOR]. [/SIZE][/COLOR][/SPOILER][/QUOTE]
Jebus - you even used LaTeX. I must spread rep around before giving you more.
Originally Posted by LagAttack
I noticed you tagged this thread with the game theory tag. So I will approach it from a game theory perspective.
Spoiler : post :The Honest Prisoner's Dilemma:
(This is nothing like the prisoner's dilemma, the name is a pun, leave me alone)
You can think of alpha as the gain you get from not being auto-executed by a town Jailor for not claiming a role.
You can think of beta as the gain you get from not revealing your role to a regular player that rolled kidnapper and know you're town, so they're executing you no matter what you say.
You can think of gamma as the gain you get from not revealing your role to a new player that rolled kidnapper and doesn't know what you are, so they might spare you because you didn't claim a role - like what a neut evil caught in the headlights might do.
And here's the issue with the Honest Prisoner remaining silent:
The ration between regular players that know what you prefer/blacklist, and new players that don't is PROBABLY somewhere around 1 to 1. Being generous we can even say that there are twice as many regular players that have played enough to know your meta as new players.
We'll be generous again and assume that the expected number of jailors is twice the expected number of kidnappers. This is being VERY generous - it's rare to see a setup like that, the ratio is usually closer to 4:1. But alpha is certainly greater than gamma, which means Ja - Ky > a - even when being very generous in your favor.
Which means in order for the ratio to be greater than 1, you need at the very least for 14 beta/alpha to be greater than 1, and beta represents the utility gain from staying silent rather than giving a regular player that knows you're town your role.
They are executing you anyway if they are a regular player that jailed you because they know you're town. The only utility you could possibly get here is if they ALSO have a Janitor and they perhaps decide they want to sanitize your role as well?
But even that utility gain is extremely marginal when compared to the utility gain you get from alpha (not auto-dying to town jailors)
So as a result it is very, very unlikely that 14 beta/alpha is greater than 1. And this was with all the most generous assumptions in place, in reality it's probably not even close and remaining silent is an inferior strategy.
TL;DR The solution to the Honest Man's prisoner dilemma is to give your role every time. Remaining silent does NOT get the Lag's Game Theory Analysis seal of approval.
Jebus - you even used LaTeX. I must spread rep around before giving you more.
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