Reference no: EM133306530

Question: Consider the sequential-move game.

There are 2 investors. Each has deposited $10 in the same bank. The bank invested both deposits in a single long-term project. Investors can withdraw money from their bank accounts at only two stages: in the first stage and in the second stage.

In the first stage, each investor decides whether to Withdraw (denoted as W in the strategies below) or Not (denoted as N in the strategies below) without knowing the decision of the other investor. If either investor chooses to withdraw, the bank ends the project before its completion and a total of $12 can be recovered (out of the $20 invested). In case both investors choose to withdraw, they share this total value and each gets $6. If only one investor chooses to withdraw in the first stage, the one who chooses to withdraw gets back their $10 investment and the one who chooses not to withdraw receives the remaining $2 value. If both investors choose not to withdraw in the first stage, then they proceed to the second stage.

In the second stage, as in the first stage, each investor decides whether to Withdraw (W) or Not (N) without knowing the decision of the other investor. In case both choose to withdraw at the end of the second stage, they each get $15 (an equal share of the total $30 value of the project in the 2nd stage). If only one investor chooses to withdraw, the one who chooses to withdraw gets $20 and the one who chooses not to withdraw receives the remaining $10 value. In case both choose not to withdraw at the end of the second stage, then the bank keeps the investment for an additional period, and pays out $19 to each investor at the end. (The investors themselves do not make any decisions beyond the second stage. If both choose not to withdraw at the end of the second stage, they automatically receive the $19 payout at a later date. In the game tree, consider the $19 payout as the payoffs to the outcome where both choose not to withdraw in the second stage.)

For simplicity, assume that there is no discounting, i.e. the players value $1 received at the end of first stage equally as $1 received at the end of any future stage.

Answer the following questions considering this game.

- Each player has (1/2/3/4) information set(s) in the whole game.

- The second stage subgame is a (Prisoners' Dilemma/Assurance Game/Game of Coordination and Conflict). In the NE of the second stage subgame (both choose not to withdraw / both choose to withdraw / only one player withdraws.)

- What are the subgame perfect Nash equilibria (SPE) of the whole game? For each strategy profile below, choose True if you think it is an SPE, otherwise choose False. Hints: There might be more than one SPE. The outcomes listed below are written in terms of the players' strategies as discussed in the lectures. The verbal description of the corresponding strategies are also provided for your convenience.

a) (N/W, N/W) Both players choose not to withdraw in the first stage and to withdraw in the second stage.

b) (N/W, W/W) Player 1 chooses not to withdraw in the first stage and to withdraw in the second stage. Player 2 chooses to withdraw in both stages.

c) (W/W, N/W) Player 1 chooses to withdraw in both stages. Player 2 chooses not to withdraw in the first stage and to withdraw in the second stage.

d) (W/W, W/W) Both players choose to withdraw in both stages.