mid-semester group coursework. Each student i can put in the effort xi that costs
c(xi), in which xi ∈ [0, 1]. This gives each student the utility of u(x1, x2). Formu-
late this situation as a strategic game. [5 marks]
Now, consider two cases below:
(a) u(x1, x2) = 3
2x1x2, c(xi) = x2i , for i = 1, 2
(b) u(x1, x2) = 2x1x2, c(xi) = xi for i = 1, 2.
In each case,
(i) Find the Nash equilibria of the game. [20 marks]
(ii) Draw the best response curves. [10 marks]
(iii) Investigate whether there is a pair of effort levels that yields both students
higher payoffs than the Nash equilibrium effort levels. [5 marks]
(iv) Interpret your results. [5 marks]
Question 3. 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 comfortably 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 inline 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.
3Units 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]
(c) Interpret your results. [5 marks]
