2. Consider a bank with two depositors, Jamie and Alison, each of whom has deposits of $100. The bank uses these deposits to issue loans, keeping only 5% as reserves to facilitate withdrawals. These loans have no risk of default. Alison knows this but Jamie thinks that the probability of the bank failing is I >0. 1 Each depositor has the option to withdraw their deposits or do nothing. The bank operates under a sequential service constraint, but Alison is faster so if both agents try to withdraw their funds she will arrive at the bank first. (a) Calculate the expected payoffs for Jamie and Alison for each potential outcome. (b) Using your answer from part (a), write down the payoff matrix. What is the smallest value of x for which both agents doing nothing is a Nash equilibrium? (c) Now suppose the government introduces deposit insurance that guarantees 90% of each depositor's losses. Calculate expected payoffs for each potential outcome. (d) Using your answer from part (c), write down the payoff matrix. What is the smallest value of x for which both agents doing nothing is a Nash equilibrium? Does deposit insurance help prevent bank runs? 2. Consider a bank with two depositors, Jamie and Alison, each of whom has deposits of $100. The bank uses these deposits to issue loans, keeping only 5% as reserves to facilitate withdrawals. These loans have no risk of default. Alison knows this but Jamie thinks that the probability of the bank failing is I >0. 1 Each depositor has the option to withdraw their deposits or do nothing. The bank operates under a sequential service constraint, but Alison is faster so if both agents try to withdraw their funds she will arrive at the bank first. (a) Calculate the expected payoffs for Jamie and Alison for each potential outcome. (b) Using your answer from part (a), write down the payoff matrix. What is the smallest value of x for which both agents doing nothing is a Nash equilibrium? (c) Now suppose the government introduces deposit insurance that guarantees 90% of each depositor's losses. Calculate expected payoffs for each potential outcome. (d) Using your answer from part (c), write down the payoff matrix. What is the smallest value of x for which both agents doing nothing is a Nash equilibrium? Does deposit insurance help prevent bank runs