As explored by others, the three-way duel as depicted in The Good, the Bad, and the Ugly is ripe with exploration with game theory.
Actions: wait, fire at one of the other two players, fire up into the air.
What are the players' utilities for the various possible outcomes?
Is it a single round or multiple round game?
What are the players' probabilities of hitting their target?
Add a mechanism so that "everyone waits" is not Nash equilibrium.
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