Simon Fraser University
Spring 2016
Econ 302 Assignment 5
Due: in Lecture, Tuesday March 1, 2016.
Show all your work.
1. (3 points) Draw the extensive form (game tree) for the following situations:
i Player 1 first chooses L or R. Player 2, after observing the action of player 1, chooses T
or B. Player 3 observes the action of player 2 but not of player 1, and chooses X or Y.
ii Player 1 chooses A or B, and player 2 chooses C or D, simultaneously in the first round.
In the second round, the two players observe the actions chosen in the first round, and
choose their actions simultaneously again.
iii Player 1 chooses A or B first. If player 1 chooses A, player 2 then chooses C or D; if
player 1 chooses B, player 2 does not choose (i.e., has no opportunity to move). Finally,
player 3 chooses E or F, without knowing the actions of player 1 or 2.
2. (3 points) Suppose that Player 1 first plays Top, Middle or Bottom. Player 2 only finds
out whether player 1 has played Bottom. If so, he plays Left or Right; if not, he plays In or
Out. The payoffs are: (1,1) after (Top, In), (0,0) after (Top, Out), (0,0) after (Middle, In),
(1,1) after (Middle, Out), (0.6,0.6) after (Bottom, Left), (0,0) after (Bottom, Right). Draw
the game tree, identify the subgame(s), find the subgame perfect equilibria in pure strategy.
Is there any Nash equilibrium that is not subgame-perfect?
3. (4 points) Suppose that there are 100 symmetric firms each with a constant marginal
cost of 3 and a fixed cost of 4. They first decide (simultaneously) whether to enter or not
enter a market. A firm that does not enter gets payoff 0. A firm i that enters the market
sees the other firms that have entered, plays a Cournot (quantity competition) game with
the others given a demand Q = 45 − P , and earns a payoff of P · qi − 3qi − 4. Find two
subgame perfect equilibria in pure strategy. What are the firms’ profits in these equilibria?
1