Answer to Question #264844 in Microeconomics for manuze

Question

In a one-shot and simultaneous game, Perfume Shop (PS) and Fragrance Shop (FS) are engaged in an advertising war aimed at earning a larger profit from the sales of perfumes in the Onaapo Kingdom. If Perfume Shop advertise and FS advertises, both firms will earn a sum of 15 million cedis (¢ 15 M) in profits. If neither firm advertises, FS will make 12 million cedis (¢ 12 M) and PS will make 6 million cedis (¢ 6 M). However, if PS advertises and FS does not, PS will make 30 million (¢ 30M) and Fs will earn a sum of 9 million cedis (¢ 9 M) in profit. Also, if FS decides to advertise and PS fails to do same PS will earn a profit of 3 million cedis with FS making a profit of 9 million cedis.

i. Write the above game in normal form (2 marks)

ii. Does Perfume Shop "PS" has a dominant strategy ? Provide a comprehensive explanation for your answer. (4 marks)

iii. Does the Fragrance Shop "FS" has a dominant strategy ? Explain your answer in detail. (4 marks)

Answer 1

(a) we have two shops N = {PS, FS}. Each shop has the strategy set $s_i$ = {Advertise, refrain}, and the utility

function of the form $u_i$ : $S_i$ × $S_i$ → R. If both advertise, they each earn a sum of ¢ 15 M; and if neither advertises, FS will make 12 million cedis (¢ 12 M) and PS will make 6 million cedis (¢ 6 M). if PS advertises and FS does not, PS will make 30 million (¢ 30M) and Fs will earn a sum of 9 million cedis (¢ 9 M) in profit. if FS decides to advertise and PS fails to do same PS will earn a profit of 3 million cedis with FS making a profit of 9 million cedis.

(b) Perfume shop "PS" does have a dominant strategy. PS is maximizes alot of profit when "FS" shop keeps quiet. "PS" will make 30 million (¢ 30M) when it advertises and "FS" will earn a sum of 9 million cedis (¢ 9 M) in profit of which "PS" will make much profit than "FS" shop.

(c)Yes FS has a dominant strategy. FS makes more profit when when neither of the shops advertises, FS will make 12 million cedis (¢ 12 M) and PS will make 6 million cedis (¢ 6 M)

also FS has a dominant strategy when it advertises and PS keeps quiet. FS will make a profit of

9 million cedis much more than that of PS which is 3 million cedis.