# Simon Fraser University Spring 2016 Econ 302 Assignment 4 ```Simon Fraser University
Spring 2016
Econ 302 Assignment 4
Due: in Lecture, Tuesday February 23, 2016.
1. (3 points) The market (inverse) demand function for a homogeneous good is P (Q) =
a − b &middot; Q, where a, b &gt; 0, and Q is the total quantity of the good on the market. There are
two firms: firm 1 has a constant marginal cost of 2c for producing each unit of the good,
and firm 2 has a constant marginal cost of c. Firm 1 is the industry leader, so it sets its
quantity of production first. Firm 2 sets its quantity of production after observing firm 1’s
production. Find the subgame perfect equilibrium in this game. And calculate the market
price in this equilibrium.
2. (3 points) Assume the same market demand as in Problem 1. There are now three
firms, each with a constant marginal cost of c for producing each unit of the good. Firm 1
sets its quantity of production first, then firm 2 sets its quantity (after observing firm 1’s
quantity), and finally firm 3 sets its quantity (after observing firms 1 and 2’s quantities).
Find the subgame perfect equilibrium in this game. And calculate the market price in this
equilibrium.
3.
(4 points) Player X, Y and Z are engaging in a three-way duel. The players shoot
sequentially, and each player gets one shot, either at one of the alive players, or shooting
into the air (and hitting no one). X shoots first, Y shoots second (if he is alive), and Z shoots
last (if he is alive), and assume that this is a sequential game with perfect information. X
is a poor shooter, with a 30 percent success rate. Y is better: he hits 60 percent. Z never
misses. Assume that the preference of each player is the following strict ranking over the
possible scenarios (with his utility of that scenario in the parentheses): himself alive and the
other two players dead (2), himself alive and one other player dead (1) 1 , everyone alive (0),
himself dead (-1000000000). Find a subgame perfect equilibrium of this game.
1
He is indifferent over which one of the other two players dies — he hates them equally.
1
Figure 1: The first two “steps” of the game tree: X shoots first, followed by Y (or Z, if Y is