$4.$

In a small town, there are only two stores, Lidl and Albert, that handle sundry goods. The total number of customers is equally divided between the two because the price and the quality of goods sold are equal. Both stores have a good reputation in the community, and they render equally good customer service. Assume that a gain of customers by Lidl is a loss to Albert and vice versa. Both stores plan to run annual pre$-$Christmas sales during the first week of November. Sales are advertised through a local newspaper, radio, and television. With the aid of an advertising firm store, Lidl constructed the game matrix given below. $($Figures in the matrix represent a gain or loss of customers$)$ Strategy of Lidl Strategy of Albert Newspaper Radio Television NEWSPAPER

$30$

$40$

$-80$ RADIO $015-20$ TELEVISION

$90$

$20$

$50$

Required:

a$)$Determine the optimal strategies and the worth of such strategies for both Lidl and Albert.

b$)$What is the payoff value for player Lidl if Albert selected its first strategy?

c$)$What is the payoff value for player Albert, if Lidl selected its second strategy?