Bank-matic is planning to enter the ATM business in a particular town. Suppose t

Question

Bank-matic is planning to enter the ATM business in a particular town. Suppose that the town has one main street and Bank-matic must decide how many ATMs to locate along this street. Let’s represent the street by the [0,1] interval. Customers are uniformly distributed along the interval, and they are willing to travel at most 0.25 in order to use an ATM. Suppose that any firm that serves a proportion p of the customers gets a profit of p. In addition, placing an ATM at any location along the [0,1] line costs 0.20. For example, if Bank-matic decides to place two ATMs, one at x = 0 and another at x = 1, then it serves a proportion 0.25 + 0.25 = 0.50 of customers, making a profit of 0.50 but paying an entry cost of 2 × 0.20 = 0.40. Net profits are then 0.10.

(a) Where will Bank-matic decide to place its ATMs? How many ATMs will be placed, and what are the net profits? 1 Things get a little bit more difficult now that a close competitor, ReadyCash, comes to town. ReadyCash has the same cost of 0.20 per each ATM it decides to locate, and customers don’t really care which ATM they use: they always choose to go to the ATM that is nearest to them (and, as before, decide not to use an ATM if there is no ATM within 0.25 of where they live). Bank-matic has been studying the market for a longer time, and is therefore in a position to choose the location(s) of its ATMs before ReadyCash gets to make this choice.

(b) Suppose that Bank-matic made the decision you suggested in (a). Where would ReadyCash decide to locate, after seeing Bank-matic’s decision? What are the net profits for each firm?

(c) If Bank-matic can anticipate that ReadyCash will come to town after its location decision, it is likely that Bank-matic will want to do something different than (a). Where do you recommend Bank-matic to locate in this case? What will happen when ReadyCash comes to town? What will be the profits of both firms?

Explanation / Answer

Answer for (a)

If a Bank plans to place an ATM on a real line where x belongs to [0,1] the best strategy would be to place an ATM at x = 0.25 & x = 0.75 where e belongs to [0 ,0.25] which would in turn provide an opprtunity for bank to cater all the customers hence profit will be 1 & entry cost for 3 ATMs will be 0.20 * 2 = 0.4 therefore Net Profit is 0.6 (1-0.4) and no profit is higher that is obtained from other strategies hence this strategy is Nash Equillibrium for Bank.

Solution for B

if ReadyCash sets up an ATM that is exactly simulating the positions of Bank to half the profit of Bank that is 0.6 hence 0.3 would be the profit for both the players Bank & ReadyCash respectively which is Nash Equillibrium (NE)

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