Al and Bo are playing a game. There is a pot of money in front of...

Al and Bo are playing a game. There is a pot of money in front of them, and they each will take turn to decide if they will take the money or pass. If either player decides to take the money, the game is over, and the other player will have nothing. If he chooses to pass, the game will continue and the pot of money will grow, but it will be the other player’s turn to decide if he wants to “take” or “pass”. Any player’s choice to “take” the money will end the game. The game will be over regardless, after four rounds.

To be specific, Al will play first. The pot has $1 in it. Al will choose between “take” and “pass.” If he takes it, the game is over. Al will get the $1 while Bo will have nothing. If Al chooses to pass, the game enters into the second round. In Round 2, the money will grow to $2 and Bo will decide if he wishes to “take” or “pass.” Similarly, if he takes it, the game is over. Bo will get the $2 while Al will have nothing. If Bo chooses to pass, the money will grow to $3 in Round 3, and it will again be Al’s turn to decide if he wishes to “take” ($3 and end the game) or to “pass” (the potential $4 to Bo). The fourth round will be the last round for the game, meaning that the game will be over regardless of Bo’s choices. If he takes, he will keep the money. If he “passes”, the game will be over and neither player will get anything.

For this game, the payoff is measured by the amount of money each player would receive.

Draw the strategic form (game tree) for this game. Please clearly identify the players, actions, and final payoffs (Al’s first, followed by Bo’s).
Identify the subgame perfect equilibrium.
Identify the equilibrium payoff.
Identify the equilibrium path.

Solutions

Expert Solution

The Solution to the above game is given as below:

Rahul Sunny answered 1 year ago

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