Economic Problems: formulate this situation as an extensive form game.

Economic Problems

Suppose some passengers are at the airport waiting at the gate to board their flight on Ryanair airline. Ryanair has open seating (first come, first served). Passengers are thinking whether to get in the queue or remain comfort- ably seated. For simplicity, assume there are only two passengers (Passenger 1 and
Passenger 2) who sequentially decide whether to stay seated or get in line. Also,assume as soon as one passenger gets in line, the other follows. (They anticipate yet more passengers whom we are not modeling, getting in line.) The value to being first in line is 30 and being second is 20. The cost associated with staying in line is shown in the table below. The sequence of decision making continues for at most
six rounds. At the last round, if they decide to wait, then the person to be first in line is randomly determined with equal probabilities. A passenger’s payoff is the value attached to their place in line, less the cost of waiting in line.

Units of Time
Spent in Line         Cost
         1                             5
         2                            12
         3    21
         4                            32
         5                            45

(a) Formulate this situation as an extensive form game. [10 marks]

(b) Find the subgame perfect equilibria of the game. [10 marks]