There are 2 new burger restaurants. Their owners Sam and Dean are deciding what price to set on the menu. Before the opening night of both restaurants the two owners meet up to discuss their pricing and they both agree that a price of $15 is going to let them have the greatest benefit. Both know that there are 100 potential clients on any given night and that if they lower their price to $14 then everyone would buy from their restaurant. It costs $10 to make a burger.

a) Draw the payoff matrix of the game for the 1st day of opening

b) What type of game does this represent? What are the key features (for example: Nash Equilibrium, Dominant Strategies)?

It takes a considerable amount of time when changing the menu prices the night before opening therefore they need to hire an additional worker which costs $170 to help.

c) Reconstruct the payoff matrix of the game using the new information stated above

d) Does any of the key features change?

Reconsider the original case, now allow for a certain proportion of clients to be loyal to one of the burger restaurants (both have the same number of loyal clients). A loyal client will always buy from their favourite burger restaurant, even if the price is higher.

e) What proportion of people need to be loyal in order for the socially optimal outcome to be the only Nash Equilibrium in this game?

f) Is it possible to have a coordination game with any proportion of loyal clients? What proportion of clients need to be loyal in order for this to be a co-ordination game? Is it possible in the case where the cost of hiring the additional worker to change prices is $100 instead of $170? If so for both, how do these two levels compare?