Problem: Two bookstores are competing for customers. Both bookstores can decide to offer discounts to attract more customers. Bookstore-A has a 30% probability of offering a discount. The probability that Bookstore-B will offer a discount is unknown, and is represented by P. The payoffs for the bookstores depending on whether discounts are offered are listed on the attachment as follows. Bookstore-A finds that the expected payoffs are the same whether the discount is offered or not. Bookstore-B also realizes that its expected payoff is identical whether the discount is offered or not. Find the payoff value X and probability level P.
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Bookstore-B
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Discount
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No Discount
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Bookstore-A
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Discount
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(100,30)
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(40,70)
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No Discount
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(60,50)
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(80,X)
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