Bank Run Game. Consider two people who are the only depositors at a bank. To make this example more realistic, you can imagine two types of people. Each person has deposited $100 in the bank and the bank has made loans totaling $150 with the deposits, keeping $50 in reserves. Each person is worried about a bank run such as those that happened in the Great Depression and Great Recession. If both people attempt to withdraw their money, they will each get $25. If one person withdraws, they will get $50 and the other person will get 0. If neither withdraw, they both get $100 plus interest when they do withdraw.

What is the dominant strategy for person 1?

Question

Bank Run Game. Consider two people who are the only depositors at a bank. To make this example more realistic, you can imagine two types of people. Each person has deposited $100 in the bank and the bank has made loans totaling $150 with the deposits, keeping $50 in reserves. Each person is worried about a bank run such as those that happened in the Great Depression and Great Recession. If both people attempt to withdraw their money, they will each get $25. If one person withdraws, they will get $50 and the other person will get 0. If neither withdraw, they both get $100 plus interest when they do withdraw.

What is the dominant strategy for person 1?

BlackTom AI · Accepted Answer

We begin by restating the question to focus on the strategic decision for person 1 in the Bank Run Game. Each player has two possible actions: Withdraw (W) or Not Withdraw (N). The payoffs are described as follows: if both withdraw, each gets 25; if one withdraws and the other does not, the withdrawing player gets 50 and the other gets 0; if neither withdraws, they both will eventually get 100 plus interest when they withdraw.

Now, analyze person 1's best response to each possible action of person 2.
- If person 2 chooses Withdraw (W): person 1 compares withdrawing now (W) versus not withdrawing (N). If 2 withdraws and 1 withdraws, 1 gets 25. If 2 withdraws and 1 does not withdraw, 1 gets 0. Clearly, 25 > 0, so person 1’s best response when 2 withdraws is to Withdraw (W).
- If person 2 chooses Not Withdraw (N): person 1 compares W versus N. If 2 does not withdraw and 1 withdraws, 1 gets 50 now. If 2 does not withdraw and 1 does not withdraw, 1 will eventually get 100 later. Here, 100 > 50, so person 1’s best response when 2 does not withdraw is Not Withdraw (N).

These two best-response conditions show that the optimal move for person 1 depends on what person 2 does. When player 2 withdraws, player 1 should withdraw; when player 2 does not withdraw, player 1 should not withdraw. Since there is no single action that is the best response to all possible actions of player 2, there is no dominant strategy for person 1.

To summarize the reasoning in the context of the options: evaluating each potential action of person 1 against the possible actions of person 2 reveals that neither W nor N dominates the other across both of person 2’s possible choices. The outcome hinges on the other player’s move, so a dominant strategy does not exist.

QAMO 2010-002 Spring 2025 Unit 6: Game Theory -- Short Problems

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