Joanna has a credit card account with Card Bank. (Consider Joanna a typical customer for Card Bank.) Card Bank is considering increasing their interest rate from the current 10% to 20%. That is, the bank is evaluating taking one of two possible actions: raise interest rates to 20% or do nothing (i.e. keep rates at 10%). After Card Bank has made its decision, Joanna can either transfer her Card Bank account balance to another creditor or do nothing (i.e. do nothing means staying with Card Bank). If Card Bank raises Joanna's interest rate and Joanna does not transfer her balance, Card Bank payoff is $1,000 while Joanna's payoff is -$1,000. If Card Bank raises Joanna's interest rate and Joanna transfers her account to another creditor, Card Bank's payoff is -$300 while Joanna's payoff is -$100. If Card Bank does nothing and Joanna does not transfer her balance, each player receives a payoff of $0. If Card Bank does nothing and Joanna transfers her account to another creditor, Card Bank receives a payoff of -$300 while Joanna receives a payoff of -$150.

a) Draw the game tree for this game.

b) List the possible strategies for Card Bank and for Joanna. Find all pure-strategy Nash equilibria of this game.

c) Out of the Nash equilibria of part b, find the ones that are unreasonable. Explain why they are unreasonable.

d) Which equilibrium concept rules out unreasonable equilibria? Explain briefly what this equilibrium concept requires.

e) Use the concept from part d to refine the set of equilibria found in part b, that is, to rule out unreasonable equilibria. Clearly state the reasonable equilibrium/a, and the equilibrium payoffs for each player.