Joel Uckelman on Wed, 28 Jul 2010 06:46:49 -0700 (MST)

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Re: [game-lang] Another quick tangential comment about integers and reals

Thus spake Simon McGregor:
> Some friends and I occasionally played a game of my design (for 3 or
> more players) which used the integers. The rules are simple: each
> player secretly chooses an integer and all choices are revealed
> simultaneously. If the choices are all different, the player who chose
> the second-highest number wins. If any choices are the same, and one
> player chose a higher number than all the others, that player wins. If
> two players are tied for the highest choice, nobody wins. (I didn't
> try to analyse this game properly!)

I think the actual outcomes will depend heavily on the psychology of
the players.

What I can say is that the pure Nash equilibria for this game are
all the strategy profiles n,n+1,n+2. (The high and low players can
deviate to make someone else or no one win, but not themselves.) In
every other profile, one of the nonwinners has a winning deviation.

As for mixed equilibria, I'm not sure; I'll have to think about that,
and whether there's a finite equivalent of this game.

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