The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.


The Least Unique Game

The rules to the Least Unique Game are simple:

Three players each pay $1 to play. They then choose, in secret, a positive integer. The numbers are revealed and the player with the lowest unique integer wins the $3. If they all choose the same number, the round is a draw and their dollars are returned.

Imagine that you find yourself playing this game online. Assume the following conditions apply:

1. The game is repeated indefinitely.
2. The players may not quit.
3. Your opponents are anonymous and there is no mechanism to communicate with one another (i.e., you may rule out secret offline collusions).

Finally, assume that your opponents are at least as rational and capable as you. They understand the rules of the game, game theory, and will act to maximize their return. Like you, they will assume that they are playing against two intelligent opponents unless proven otherwise.

What is your best strategy?

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