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 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 payoff value X and probability level P.
Bookstore-B
Discount No Discount
Bookstore-A Discount (100, 30) (40, 70)
No Discount (60, 50) (80, X)
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