Quinneapolis
Based on the comments to the previous video, here's a mind puzzle for plurk!
Quinneapolis
You're playing a game with five players
Quinneapolis
The rules of the game are as follows
Quinneapolis
In each round, each player picks a number between one and five, and the numbers are revealed simultaneously
Quinneapolis
The winner is the person who picked the lowest number that nobody else picked.
Quinneapolis
So, if the votes are 1,1,5,4, 3, then the winner is the person who picked 3
Quinneapolis
and the winner is awarded $100, multiplied by the number they picked.
Quinneapolis
Your goal is to maximize the total money earned by the group, but it's possible that some of the other players might be greedy and try to win money for themselves.
Quinneapolis
Three rounds, so the total max amount of money that can be won is $1500 - three rounds where the winner was a 5.
Quinneapolis
Now, here's the question:
Quinneapolis
Is there a group strategy you can agree to with the group that will ensure this outcome, even if one person decides to go against the group strategy and vote greedily?
Quinneapolis
If you can come up with one, the group total is $1500, and impressed by your cooperative spirit they will agree to split it five ways, and everone walks home $300 richer.
Quinneapolis
How do you ensure that a bad actor doesn't break it?
Princess Emily
i bring a knife,
Quinneapolis
no physical coercion allowed
BattroidBattery
seems like it works fine if you just assign out numbers so that one person picks 5, two vote 1, and two vote 2 every round. There's no useful number to defect to.
Quinneapolis
bingo!
Quinneapolis
1/1/2/2/5 is the winning strategy
Quinneapolis
if a 1 defects to 3 or 4, the other 1 wins
Quinneapolis
if a 2 defects to 3 or 4, the other 2 wins
Quinneapolis
and there's no reason for the 5 to defect
Quinneapolis
so nobody benefits from breaking from the plan
mózhēngist
i don't understand, so only when you reach $1500 will it be split evenly? Otherwise winners keep their money?
mózhēngist
Then the best way is assign 12345, so any one bad actor can't profit by defecting.
mózhēngist
Hmm actually that won't work, because whoever $500 in previous round would possibly sabotage other rounds to walk away with $500 > $300
Quinneapolis
how can they sabotage?
Quinneapolis
there isn't a rule that the money is split five ways when you get $1500, it's just me making the $1500 win condition more clear
Quinneapolis
idk maybe I've phrased the problem poorly
Quinneapolis
in context, the $500-haver couldn't have just kept the $500 and refused to share because there were subsequent games left to play
Quinneapolis
so with that in mind, if you're playing this game by itself then there's no way to enforce sharing the money
Quinneapolis
so you get $1500 away from the house but no guarantee that it's split equally