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?