Simon McGregor on Wed, 28 Jul 2010 08:53:26 -0700 (MST)

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

On Wed, Jul 28, 2010 at 2:46 PM, Joel Uckelman <uckelman@xxxxxxxxx> wrote:
> 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.

Nicely spotted. You're good at this ;-)
I'll have to change the rules of the game by making the non-winning
players lose when someone wins; that'll break up those equilibria.

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