Two computer manufacturers A and B are attempting to sell computer systems to two banks 1 and 2. Company A has 4 salesmen and company B has only 3 salesmen available. The computer companies must decide upon how many salesmen to assign to sell on each bank. Thus company A can assign 4 salesmen to assign to bank 1 and none to bank 2, or three to bank 1 and one to bank 2, etc. Each bank will buy one computer system. The probability that a bank will buy from a particular computer company is directly related to the number of salesmen calling from that company relative to total salesmen calling. Thus, if company A assigned 3 men to bank 1 and company B assigns two men, the odds would be three out of five that bank 1 will purchase company A's computer system (if none calls from either company, the odds are one-half for buying either computer). Let the pay-off be the expected number of computer systems that company A sells (then 2 minus this pay-off is the expected number company B sells). What strategy would company A use in allocating its salesmen? What strategy should company B use? What is the value of the game to company A? What is the meaning of the value of the game in this problem?
Two computer manufacturers A and B are attempting to sell computer systems to two banks 1 and 2. Company A has 4 salesmen and company B has only 3 salesmen available. The computer companies must decide upon how many salesmen to assign to sell on each bank. Thus company A can assign 4 salesmen to assign to bank 1 and none to bank 2, or three to bank 1 and one to bank 2, etc. Each bank will buy one computer system. The probability that a bank will buy from a particular computer company is directly related to the number of salesmen calling from that company relative to total salesmen calling. Thus, if company A assigned 3 men to bank 1 and company B assigns two men, the odds would be three out of five that bank 1 will purchase company A's computer system (if none calls from either company, the odds are one-half for buying either computer). Let the pay-off be the expected number of computer systems that company A sells (then 2 minus this pay-off is the expected number company B sells).
- What strategy would company A use in allocating its salesmen? What strategy should company B use?
- What is the value of the game to company A? What is the meaning of the value of the game in this problem?
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