Assume that you are at the Christchurch airport waiting to board a flight to visit your family for Christmas. Let us say 190 passengers (including you) want to board the flight. Assume that flight attendants are absent to guide you properly. So, everyone is rushing for no reason. There are two doors to enter the flight (front and back), and each passenger decides which one to take.

The satisfaction/ utility of entering the front door is 10 units (the way to the front door has a footpath bridge that protects you from the rain). In contrast, the back door is the least preferred and has 0 satisfaction/ utility (because it takes more time to reach the seat, you must go out of the terminal, and it is raining heavily). In deciding which door to take, each passenger cares only about net satisfaction/ utility. Passengers’ payoff is assumed to be their net utility.

Net Utility of a Passenger = Satisfaction of Taking a Door – Time Cost to Reach the Seat

If m passengers are taking the front door, the time cost for a passenger to reach the seat is assumed to be m units. In contrast, if m passengers take the back door, the time cost is 2m units to reach the seat. Passengers make simultaneous decisions as to whether to take the front or back door.

a. Derive each passenger’s payoff function (3 marks)

b. Find a Nash Equilibrium (2 marks).