INTERMEDIATE MICROECONOMIC THEORY II ASSIGNMENT 1

1.   Consider the following game between Player 1 and Player 2. Player 1 moves first and should decide whether to choose A or B. Player 2 moves second and should decide    between C and D. The payoffs (payoffPlayer 1, payoff Player 2) are as follows.

•            If [A, C], then the players’ payoffs are equal to (17, 9).

•            If [A, D], then the players’ payoffs are equal to (5, 5).

•            If [B, C], then the players’ payoffs are equal to (21, 5).

•            If [B, D], then the players’ payoffs are equal to (9, 9).

Assume that before deciding, Player 2 cannot observe the choice of Player 1.

a.   Represent the game in an extensive form.

b.   Represent the game in a normal form. Characterize the set of (pure) strategy Nash equilibria.

Now, assume that Player 2 observes Player’s 1 move.

c.   Represent the game in an extensive form.

d.   Represent the game in a normal form. Characterize the set of (pure) strategy Nash equilibria.

Describe all the steps you use to answer parts a., b., c. and d. and explain/justify your answers.

2.   Consider the following game in which player A chooses a row and player B chooses a column

a.   Characterize the pure- and mixed-strategy N.E. using the Generalized Best- Response Analysis Method.

b.   If your answer in part b. involves more than one pure-strategy N.E., determine the risk-dominant N.E.

3.   Consider the following game with perfect information between Player A and Player B: Player A can choose A1 or A2; after observing the choice made by Player A,      Player B should choose B1 or B2. The payoffs (payoff A, payoff B) are as follows.

•    If Player A chooses A1 and Player B chooses B1, the payoffs = (8, 16)

•    If Player A chooses A1 and Player B chooses B2, the payoffs = (0, 16)

•    If Player A chooses A2 and Player B chooses B1, the payoffs = (16, 8)

•    If Player A chooses A2 and Player B chooses B2, the payoffs = (0, 16)

a.   Represent the game in an extensive form.

b.   Characterize the SPNE for the game.

4.    Consider the simultaneous-move version of the “Matching Pennies” game discussed in class. Characterize the pure- and mixed-strategy N.E. Describe all the steps you use to answer the question, and explain/justify your answers.

5.  An Application: Consider the following situation involving three players, Apple, Sony and Fox Broadcasting Company. Fox is prepared to sell the exclusive promotional      appearance in the show “House” to one of the two companies.1