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# Numerical example of payoffs using the principles of Game Theory

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.

#### Solution Preview

Let the probability of Bookstore B offering a discount be represented by P

Bookstore-B
P 1 - P
Discount No Discount
Bookstore-A Discount 30% (100,30) (40,70)
No ...

#### Solution Summary

The example demonstrates the use of principles of payoffs as per Game Theory to calculate the values of probability and payoffs using linear equations

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