Suppose two shoe stores operate near campus, G Shoes and Shoe World. Each of the

Question

Suppose two shoe stores operate near campus, G Shoes and Shoe World. Each of these two stores has two options for pricing strategies: a high markup and a low markup. Use the aboe normal-form game to carefully discuss the answers to the following questions.

a. Carefully describe the dominant strategy for each store.

b. What is the Nash Equilibrium for a one-shot game?

c. Suppose management at Shoe World approaches their counterpart at G Shoes with a suggestion to collude. How much would Shoe World e will to pay G Shoes to change their strategy?

G Shoes GShoes G Shoes G Shoes High High Low Low Shoe World High $8,000 $8,000 $12,000 $2,000 Shoe World Low $2,000 $7,000 $6,000 $3,000

Explanation / Answer

a. Dominant Strategy : It is a strategy for a player i.e. best response to all strategy profile of other player. If all players in a game have a dominant strategy then we say that game has dominant strategy equilibrium.

Dominant strategy of Shoe World is to charge high markup because payoff while charging high markup is ($ 8,000; $ 12,000) greater than the low markup ($ 2,000; $ 6,000).

Dominant strategy of G shoes is also to charge high markup because payoff while charging high markup is ($ 8,000; $ 7,000) greater than the low markup ($ 2,000; $ 3,000).

b. Nash Equilibrium : Nash equilibrium is a strategy profile such that for each players given strategy, it is best response. Alternatively, nash equilibrium is a set of strategies such that each player is doing their best given the strategy of the other player. The logic behind Nash equilibrium follows as "I am doing the best I can given what you are doing and you are doing the best you can given what I am doing".

If Shoe World chooses high markup then, best response of G shoe will be charging high markup.

If G shoe chooses to charge high markup then, best response of Shoe World is to charge high markup.

Therefore, (High markup; High markup) is the nash equilibrium.

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