There are three gunfighters A, B, C.

Each player has 1 bullet and they will fire in the sequence A then B then C, assuming the gunfighter whose turn comes up is still alive. The game ends after all three players have had a shot. If a player survives, that player gets 2, while if the player is killed, the payoff to that player is −1.
(a) First, assume that all the gunfighters have probability 1 / 2 of actually hitting the person they are shooting at. (Hitting the player results in a kill.) Find the extensive game and as many Nash equilibria as you can using Gambit.
(b) Since the game is perfect information and perfect recall we know there is a subgame perfect equilibrium. Find it.
(c) Now assume that gunfighters have different accuracies. A’s accuracy is 40%, B’s accuracy is 60% and C’s accuracy is 80%. Solve this game.