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Respond to the question: Im looking for a solution to this game?

 03/21/2010 02:56 PM by name withheld; 2042

 08/21/2003 12:52 PM by name withheld;
Quick thought - Why not redefine your numerical game so that the numbers were not necessarily pyramidal - Why not look at them as a series of points on a plane as equal and integral to one another. [View full text and thread]

 08/16/2003 12:49 AM by Ken; I'm looking for a solution to this game – THREAT
THREAT:

- Assign 10 contestants a number from 1 to 10. Every player is aware of every otheer's number.
- Vote off one player each round.
- If there is a tie between two contestants, the highest numbered player wins.
- When there are two players left, both contestants roll a die. Add the dice rolls to the contestant’s numbers. The higher sum wins. A tie goes to the contestant with the lower number.

Contestants may ally and collude any way they wish. There is no punishment for breaking an agreement or alliance, however, beyond what the players might choose to dole out and they can always renege on that as well.

The Reward schedule is exponential (or whatever it takes for players to try to advance as far as possible).
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What is this game about? There are several TV shows with voting. (Survivor, Big Brother, The Weakest Link) On all these shows, there is a strong impetus to "boot the biggest Threat."

"Threat" in these games I mentioned is multi-dimensional. It involves Intelligence, Physical Strength (when physical challenges confer immunity from the vote), and, when a final vote decides the winner, a perceived keen sense of Strategic Ability counts along with overall LIKABILITY. My game reduces all these things into one dimension that is obvious and quantifiable. The point of my game was to eliminate all these factors so that only rationality and Game Theory should come into play. Ideally, the game should be played by 10 Game Theory professors, anonymously, on line. (So there is no animosity/preference for any other player.)

My game shows the Reductio ad Absurdum of "Vote out the biggest Threat.". If you do nothing but vote out the biggest threat, 2 should win and 1 has a 15 in 36 chance of winning! So for a majority of the players, it's really a stupid strategy. Unless you are no threat at all, it makes no sense.
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My solution is that the Median Threat (5 or 6) should win, with everyone playing their best game. With low numbers trying to boot the highest always and the High numbers trying to avoid the Reductio above, by allying with each other to vote out low numbers (starting with 2), Middle numbers should play both sides. [Manage messages]