Question

2. Consider the centipede game that is described in the figure below. It has two players, A and B, and four stages: Stage 1: Player A has two piles of cash, one with $4 and the other with $1. Player A has two choices: (i) terminate the game ($4), taking the larger pile ($4) and giving the smaller pile ($1) to player B; (ii) pass both piles to player B ($ps$). If player A terminates, the game is over. If player A passes, the game moves to stage II. Stage II: The money in both piles doubles, and player B has two choices: $t$ and $ps$. If player B choses $t$, the game is over and player B receives 8 and player B receives 2. If player B passes, the game moves to stage III. Stages III-IV: The money in both piles doubles, ... The game ends at stage IV. Determine the sub-game perfect Nash equilibrium (SPNE) to this game. (Note that the bold payoff goes to player A.)

          2. Consider the centipede game that is described in the figure below. It has two players, A and B, and four stages:
Stage 1: Player A has two piles of cash, one with $4 and the other with $1. Player A has two choices: (i) terminate
the game ($4), taking the larger pile ($4) and giving the smaller pile ($1) to player B; (ii) pass both piles to player
B ($ps$). If player A terminates, the game is over. If player A passes, the game moves to stage II.
Stage II: The money in both piles doubles, and player B has two choices: $t$ and $ps$. If player B choses $t$, the game is
over and player B receives 8 and player B receives 2. If player B passes, the game moves to stage III.
Stages III-IV: The money in both piles doubles, ... The game ends at stage IV.
Determine the sub-game perfect Nash equilibrium (SPNE) to this game. (Note that the bold payoff goes to player A.)

2. Consider the centipede game that is described in the figure below. It has two players, A and B, and four stages:
Stage 1: Player A has two piles of cash, one with 4 and the other with1. Player A has two choices: (i) terminate
the game (4), taking the larger pile (4) and giving the smaller pile (1) to player B; (ii) pass both piles to player
B (ps). If player A terminates, the game is over. If player A passes, the game moves to stage II.
Stage II: The money in both piles doubles, and player B has two choices:tandps. If player B chosest, the game is
over and player B receives 8 and player B receives 2. If player B passes, the game moves to stage III.
Stages III-IV: The money in both piles doubles, ... The game ends at stage IV.
Determine the sub-game perfect Nash equilibrium (SPNE) to this game. (Note that the bold payoff goes to player A.)

Added by Dawn C.

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