Assume that two depositors hold deposits of, say, three million dollars for each, in a bank....

   

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Assume that two depositors hold deposits of, say, three million dollars for each, in a bank. The bank has just invested the six million dollars into some project of two-year maturity. Let us index the years by 0, 1, and 2, where the investment by bank occurs at period 0 and the maturity of the project comes at period 2. At period 1, the depositors, denoted by 1 and 2, decide whether to withdraw the deposit. If at least one of the depositors withdraws money, then the bank needs to liquidate the project and return the money to the depositor. Assume that the liquidation value of the project is three million dollars net of other costs. Therefore, when only one depositor withdraws, the depositor can receive three million dollars while the other receive none. When two depositors withdraw the money at the same time, then they split the liquidation value, which is 1.5 million dollars for each. If none of the depositors withdraws, then the maturity of the project comes and eight million dollars net of costs will be returned to the depositors, each of whom receive four million dollars. The story given above is summarized by the following payoff bimatrix: K W K 4,4 0,3 W 3,0 1.5,1.5 (a) (5 points) Show that (KK) is a Nash equilibrium. (b) (5 ponts) Find out the other Nash equilibrium. (c) (5 points) To see how an uncertainty faced by depositors affect their decision, let us consider the following scenario: As our previous discussion shows, both depositors would like to choose the same action as the other. Since the depositors have no clue about the other depositor's choice, they follow the "rule of insufficient reasons": they suppose that the other depositor would choose each action equally likely. In this case, what is the best choice for the depositors? Assume that two depositors hold deposits of, say, three million dollars for each, in a bank. The bank has just invested the six million dollars into some project of two-year maturity. Let us index the years by 0, 1, and 2, where the investment by bank occurs at period 0 and the maturity of the project comes at period 2. At period 1, the depositors, denoted by 1 and 2, decide whether to withdraw the deposit. If at least one of the depositors withdraws money, then the bank needs to liquidate the project and return the money to the depositor. Assume that the liquidation value of the project is three million dollars net of other costs. Therefore, when only one depositor withdraws, the depositor can receive three million dollars while the other receive none. When two depositors withdraw the money at the same time, then they split the liquidation value, which is 1.5 million dollars for each. If none of the depositors withdraws, then the maturity of the project comes and eight million dollars net of costs will be returned to the depositors, each of whom receive four million dollars. The story given above is summarized by the following payoff bimatrix: K W K 4,4 0,3 W 3,0 1.5,1.5 (a) (5 points) Show that (KK) is a Nash equilibrium. (b) (5 ponts) Find out the other Nash equilibrium. (c) (5 points) To see how an uncertainty faced by depositors affect their decision, let us consider the following scenario: As our previous discussion shows, both depositors would like to choose the same action as the other. Since the depositors have no clue about the other depositor's choice, they follow the "rule of insufficient reasons": they suppose that the other depositor would choose each action equally likely. In this case, what is the best choice for the depositors?

Answer rating: 100% (QA)

a 5 points Show that KK is a Nash equilibrium A Nash equilibrium occurs when both players in a game have no incentive to deviate from their current st... View the full answer