Six friends stop at a burger joint for lunch. There are two items on the menu: (i) a regular burger and (ii) a deluxe burger. Each friend feels that eating a regular burger is worth $5 (i.e. their own valuation of a regular burger is $5) while eating a deluxe burger is worth $6. The friends have agreed to split equally the overall cost of the meal; if the total cost is T, then each friend will pay T/6.

a. [10 points]Suppose that a regular burger that costs $4 and a deluxe burger that costs $8. What is the Nash Equilibrium of the resulting game? What class of games does this game fit into? Consider themain classes of games discussed in class: Prisoner's Dilemma, Chicken Game, Games of PureCooridnation (Assurance Game), Game of Coordination and conflict (Battle of the Sexes), Zero-sum game.

b. [10 points]Now suppose the burger joint decides to raise the price of a deluxe burger to $12. (All else is same as defined above.) What is the NE of the resulting game?

Are the friends better off when deluxe burgers cost $12 or when they cost $8?