Economics - pay off table?

Suppose the NAB is considering closing some branches. If other banks do likewise, then NAB profits will increase by $500mil and other banks' profits will increase by $1200mil. If the NAB closes branches and the other banks do not then NAB will lose $100mil and the other banks will gain $1400mil. If the other banks close branches and NAB does not, then NAB improves profits by $800mil and other banks lose $300mil.

How would be the outcomes like in a pay-off table between NAB and other banks? and what outcome is likely if the choices are one shot choice? or if it can be changed and repeated?

Answer:
Assuming that you treat the other banks as a single decision-making entity, the answer is very simple.


If you write out the outcomes in a decision matrix, you see that it is ALWAYS in the other banks' interest to stay open.

If NAB stays open and the other banks stay open, they get 0 payoff, versus losing $300 million.

If NAB closes branches and the other banks stay open, they get $1400 million versus $1200 million.

In both cases, staying open nets a higher payoff for the other banks. Knowing this, NAB makes their decision assuming that the other banks will stay open. NAB basically chooses between 0 payoff and -$1 million. In this case, NAB will always choose to remain open.

Things work out the same way if you start with NAB's strategies. NAB will always prefer to remain open, so the other banks will choose to remain open as well.


If the game only occurs once, both parties will always choose to remain open. If there is some sort of repeated game, with some minimal level of communication/signaling between the parties, either of the parties can employ a punishment strategy. If the punishment strategy is well-designed, it can create a situation where both parties will choose to cooperate and close branches.
This is sometimes called the prisoners dilemma. You can show the possibilities in a two by two pay off table. On one side, show the two options for NAB. On the other side, show the two options for the other banks. This leaves 4 squares to show the outcomes. I think that the most likely outcome is for neither NAB or other banks to close branches and the outcome for both is zero, neither a gain or a loss. The term prisoners dilemma came from the common practice of police interviewing two criminals who jointly committed a crime. The police tell each that if he confesses and implicates the other, his sentence will be reduced. If he does not confess and the other does, he will get the maximum sentence. If neither confesses, the police won't be able to convict either and they both go free.

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