Two computer manufacturers A and B are attempting to sell computer systems to two banks 1 and 2. Company A has 4 salesmen, company B only has 3 salesmen available. The computer companies must decide upon how many salesmen to assign to sell computer to each bank. Thus company A can assign 4 salesmen 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 the total salesmen calling. Thus, if company A assigns three salesmen to bank 1 and company B assigns two salesmen, the odds would be three out of five that bank 1 would purchase company A’s computer system. (If none calls from either company the odds are one-half for buying either computer.) Let the payoff be the expected number of computer systems that company A sells. (2 minus this payoff 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?
