There are two players involved in a two-step centipede game.

There are two players involved in a two-step centipede game.

Each player may be either rational (with probability 19 / 20 ) or an Altruist (with probability 1 20 ). Neither player knows the other players type. If both players are rational, each player may either Take the payoff or Pass. Player I moves first and if he Takes, then the payoff is 0.8 to I and 0.2 to II. If I Passes, then II may either Take or Pass. If II Takes, the payoff is 0.4 to I and 1.60 to II. If II Passes the next round begins. Player I may Take or Pass (payoffs 3.20, 0.80 if I Takes) then II may Take or Pass (payoffs 1.60, 6.40 if II Takes and 12.80, 3.20 if II Passes). The game ends. If player I is rational and player II is altruistic, then player II will Pass at both steps. The payoffs to each player are the same as before if I Takes, or the game is at an end. The game is symmetric if player II is rational and player I is altruistic. If both players are altruistic then they each Pass at each stage and the payoffs are 12.80, 3.20 at the end of the second step. Draw the extensive form of this game and find as many Nash equilibria as you can. Compare the result with the game in which both players are rational
There are two players involved in a two-step centipede game.