Game Strategy (pick the lowest unrepeated number)

[kaleidoscope]

This is a game with N players where each player secretly picks a number from 0 to 100. The winner is the player who picks the lowest unrepeated number. Which number would you pick? What would be your strategy?

 

[gb7nash]

It's probably not the smartest number to choose, but I'd choose 0. Only because if I assume that every other player has the mentality that at least two people will choose 0, nobody would choose 0. However, if someone else thinks the same way I do, then I'll probably lose.

 

[torquil]

I'm thinking that more than one will have the strategy of post #2. So I'd choose 0.0000000000000000000000000000000000000000000001

 

[JSuarez]

In the non-cooperative scenario, this game has no pure Nash equilibrium. The mixed one is attained when all players pick one of the N numbers randomly, using a uniform distribution.

 

[Nikitin]

the guy who answers this1 needs to be a psychologist not a mathwiz