Question

     8. Russian roulette. Two Russian marines on a desert island find 6 thousand euros, a revolver with a cylinder for six bullets, and only one bullet in perfect conditions. They split the money equally. But since they are not happy with this distribution and as they do not appreciate life much, they decide to play the following game: the older one can either put 2.000$ into the pot and give the gun to the young one, or put only 1.000$ into the pot, rotate the cylinder, aim at his own head and shoot. If he is lucky and he survives he has to give the gun to the young one. When the young guy receives the gun, he has the same options the older one had: he can either put 2.000$ into the pot and not use the gun, or put only 1.000$ into the pot, rotate the cylinder, aim at his own head and shoot. The game ends here. If they both survive, they distribute the money from the pot equally. If one guy dies, then the other guy takes all the money from the pot and the money from the first (dead) guy.

1. Represent the game in extensive form, indicating clearly the decision nodes for each player, the terminal nodes, and the chance nodes.
2. Find the SPNE of this game.
3. Is it efficient?

Answer 1

Do like and comment if you have any queries.

Answer for (a):

Answer for (c):

Yes, it is efficient.