DUEL: (1 Bullet version, p=0.1)
Two players, Adam and Bob, move sequentially and they alternate. At each
move, the player to move decides whether to "shoot" or to "walk".
The probability of hitting the other increases from 0.1 at the first move,
to 0.2, 0.3, and so on.
Each player has only one bullet. That means that after one has shot,
the game is over. If he hit the other, he has won. If he missed, he has lost
(the other, gentleman he is, will not bother to move closer and shoot).
Winning has a payoff of 1, losing without being hurt of -1, and losing by being hit of -2.
Whoever is supposed to move---Adam or Ben---has two buttons under his name,
"shoot" and "walk". Hit these buttons.
Erich Prisner, 2012