9. Two French aristocrats, Chevalier Chagrin and Marquis de Renard, ght a duel. Each has a pistol loaded with one bullet. They start 10 steps apart and walk toward each other at the same pace, one step at a time. After each step, either may re his gun. When one shoots, the probability of scoring a hit depends on the distance. After k steps it is H5, and so it rises from 0.2 after the rst 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 re, the walk must continue even though the bulletless one now faces certain death. Each gets a payoff of -1 if he himself is killed and I 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 not shoot) at each step. Find the subgameperfect equilibrium of this game. Hint: start with the twoby two table for the last stage, find the Nash equilibrium for this game, and then work your way back. Make sure to give a complete action plan for both players