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Problem Set 2b

# Problem Set 2b - ECON 166A Fall 2010      1...

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Unformatted text preview: ECON 166A Fall 2010      1) Consider the following extensive form game    1          2  2          (2,‐2)  (‐2,2)  (‐2,2)  (2,‐2)      a) What is the strategy space for players 1 and 2?  b) Write the normal form of the game.  c) Can you arrive at a unique strategy profile with backwards induction? If so,  what is it?  d) Using the normal form of the game, apply iterated dominance. Does the  procedure find a unique strategy profile that “solves” the game? If so what is  it?    Now considered the modified game:      1          2  2        (2,‐2)  (‐2,2)  (‐2,2)  (2,‐2)    e) Write the normal form of the game.  f) Using the normal form of the game, apply iterated dominance. Does the  procedure find a unique strategy profile that “solves” the game? If so what is  it?        2) Harrington Chapter 3 question 10      (GO ON TO PAGE 2!)        Problem set 2B  Sinervo and Musacchio  3) In Cournot duopoly, two producers of an identical product (call them firms A and  B) simultaneously choose how much of that product to produce, say qA and qB,  between 3 and 7. For simplicity, assume that production cost is 10 per unit. The  price p is 40 – 2(qA  + qB). This is because price falls as the supply increases.  Payoffs are profit = (price – unitcost)*quantity, e.g., (40 ‐ 2qA ‐ 2qB ‐ 10) qA for  firm A. To simplify the game assume that the only available q’s are 3, 5,  and 7.  a. Write out the extensive form for this game.   b. Now write out the extensive form for the Stackelberg variant of this game, in  which firm A chooses first, and firm B observes qA before making its own  choice.  c. Write out the normal form for the simultaneous move version of the game.  For the Stackelberg version of the game, what is specification of B’s strategy?  How big is the table describing this game’s normal form?  d. For the original simultaneous choice version of the game, can you identify  one or more Nash equilibria? If so, what is it (are they)?    4)  Harrington Chapter 4, question 4    4) Harrington Chapter 4, question 9    5)  Harrington Chapter 4, question 10    ...
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