ECO303 – Find all pure strategy Nash equilibrium

Question
ECO303 Intermediate Microeconomics

Assignment # 5

Due August 17

1. Find all pure strategy Nash equilibrium (equilibria) of the following game.

2. Find all mixed strategy Nash equilibrium (equilibria) of the following game.

3. Look at the following extensive form game. “0” represents chance move who chooses each action with specified probability (numbers
on edges following each move of player 0). I and II are the two players. The first number in the payoff vector is the payoff for Player
I.

(a) List all pure strategies of Player I.
(b) Find all sub-game perfect Nash equilibria and determine the expected equilibrium payoff for each player.

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4. Suppose two firms 1 and 2 with constant marginal production cost c1 , c2 respectively are producing a homogeneous good and compete
with each other in the Cournot fashion. Let the output choices of the two firms be respectively q1 , q2 . Assume 0 < c1 < c2 , namely
firm 1 is more efficient in producing. The market price is determined by p(Q) = ? ? Q, where ? is a positive constant and Q is the
aggregate output of the market.
(a) What’s the strategy space for Firm 1 and Firm 2 respectively? Define clearly the Nash equlibrium of this game. (You may
introduce your own notation if you think necessary. But please explain clearly the meaning of each additional notation that you
introduce.)
(b) Solve for the Nash equilibrium (equilibria)
(c) Compare the equilibrium output levels of the two firms. Which firm has higher output? Explain clearly.

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