Game Strategy (pick the lowest unrepeated number)

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In the game with N players choosing numbers from 0 to 100, the objective is to select the lowest unrepeated number. A common strategy is to avoid choosing 0, as players may anticipate that others will also select it, leading to repetition. One player suggests choosing an extremely small number, like 0.0000000000000000000000000000000000000000000001, to avoid duplication. The discussion highlights that there is no pure Nash equilibrium in this non-cooperative scenario, and a mixed strategy involving random selection from available numbers may be optimal. Overall, the game emphasizes the psychological aspects of decision-making among players.
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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?
 
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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.
 
I'm thinking that more than one will have the strategy of post #2. So I'd choose 0.0000000000000000000000000000000000000000000001
 
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.
 
the guy who answers this1 needs to be a psychologist not a mathwiz
 

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