Question

Question 1

Two Chinese restaurants, 'Lucky Restaurant' and 'Star Restaurant', are planning to offer discount coupons providing a percentage reduction on their customers' bills. In a one-shot game, if only one restaurant offers such coupons, it will earn $4.5 million in profits, however its rival will only earn $0.5 million. If neither of the stores offers coupons, both stores will earn $2 million. If both stores offer coupons, both stores will earn $1 million profit.

(a) Draw the payoff matrix for this game.

(b) Explain whether there is a dominant strategy for each restaurant.

(c) What is / are the Nash equilibrium(s), if any, for the case quoted? What is the name of this game?

(d) Moral hazard is a common problem happened in the catering industry. Suppose that a restaurant manager is considering whether or not to monitor employees, and the waiters are considering whether to work or shirk in their workplace. Draw the payoff matrix for this game and what is / are the Nash equilibrium(s), if any, for this case?

Answer 1

a) The payoff Matrix can be drawn as follows

	Offer Coupon	Don't Offer Coupon
Offer Coupon	1 , 1	4.5 , 0.5
Don't Offer Coupon	0.5 , 4.5	2 , 2

b) For Restaurant 1, Offering a coupon leads to a better payoff irrespective of the decision taken by Restaurant 2.

Likewise for Restaurant, offering a coupon leads to better payout irrespective of the decision taken by Restaurant 1.

So for both the restaurants, the dominant strategy is to Offer a coupon.

c) The nash Equilibrium will be for both restaurants to offer coupons as that is the dominant strategy. However, this is not the most socially optimal outcome. The socially optimal outcome would be for both the restaurants to not offer coupons.

d) This seems to be an unrelated question and adequate information is not given. The payoffs are not given for either of the case as well. So this part cannot be answered.

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