Two French aristocrats, Chevalier Chagrin and Marquis de Renard, fight a duel. Each has a pistol loaded with one bullet. They start 10 steps apart and walk toward each other at the same pace, 1 step at a time. After each step, either my fire his gun. When one shoots, the probability of scoring a hit depends on the distance. After k steps it is k/5, and so it rises from .2 after the first step to 1 (certainty) after 5 steps, at which point they are right up against one another. If one player fires and misses while the other has yet to fire, the walk must continue even though the bulletless one now faces certain death; this rule is dictated by the code of aristocracy. Each gets a payoff of -1 if he himself is killed and 1 if the other is killed. If neither or both are killed, each gets 0.

This is a game with five sequential steps and simultaneous moves (shoot or don’t shoot) at each step. Find the equilibrium of this game using backward induction.

Answer rating: 100% (QA)

This problem turned out to be simpler than I expected because all of the subgames are 0sum and have dominant strategies so we dont have to consider mixed Nash equilibrium The complexity might increase ... View the full answer