# New York University POL-UA POL-UA 844 A, B, and C are in a truel, all have one bullet, are perfect shots, and can either fire or not fire at another player (no shooting in the air is

New York University POL-UA POL-UA 844 A, B, and C are in a truel, all have one bullet, are perfect shots, and can either fire or not fire at another player (no shooting in the air is

# A, B, and C are in a truel, all have one bullet, are perfect shots,

and can either fire or not fire at another player (no shooting in the air is possible). A, who hates B, goes first; B, who hates C, goes second; C, who hates A, goes third. (If a player fires, he will shoot only his antagonist—the player he hates.) If the goals of the players are (1) to survive and (2) to eliminate their antagonists, what will A, B, and C do? Answer this question if the game (i) goes exactly one round (each player gets only one turn) and if it (ii) continues indefinitely. Will your results change if there are no antagonists, and each player is equally happy to shoot either other player? Explain your results in each case.

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