Three oligopolistic banks operate in the loan market with the inverse demand function given by r (Q) = a-Q, where r is the interest rate per unit of loan and Q = q1 +q2 +q3 and qi>=0 is the total amount of loans issued by bank i = 1, 2, 3. Also, a > 0 is a constant. The cost of funds for bank i is given by cqi, where c belongs (0, a) is a constant. A bank's profit from loans is (r -c)qi. (1) Suppose the banks engage in Cournot competition. Find the symmetric Nash equilibrium. How much profit does each bank make? (2) Now suppose banks compete in the following sequential manner: Bank 1 chooses q1. Then banks 2 and 3 observe q1 and then simultaneously choose q2 and q3, respectively. Find the subgame perfect equilibrium. How much profit does each bank make here? Does bank 1 enjoy an advantage being the first mover?
Three oligopolistic banks operate in the loan market with the inverse
given by r (Q) = a-Q, where r is the interest rate per unit of loan and Q = q1 +q2 +q3
and qi>=0 is the total amount of loans issued by bank i = 1, 2, 3. Also, a > 0 is a
constant. The cost of funds for bank i is given by cqi, where c belongs (0, a) is a constant.
A bank's profit from loans is (r -c)qi.
(1) Suppose the banks engage in Cournot competition. Find the symmetric
Nash equilibrium. How much profit does each bank make?
(2) Now suppose banks compete in the following sequential manner: Bank
1 chooses q1. Then banks 2 and 3 observe q1 and then simultaneously choose q2
and q3, respectively. Find the subgame perfect equilibrium. How much profit does
each bank make here? Does bank 1 enjoy an advantage being the first mover?
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