Problem Set 4b Solutions

# Problem Set 4b Solutions - Econ 166a   Fall 2010 ...

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Unformatted text preview: Econ 166a   Fall 2010        Problem Set 4b      Sinervo/Musacchio    1) Harrington 8.7          2) Consider the waiting game we studied in class but consider two different alternatives for the waiting cost:    a) the waiting cost is 9*(wait time) for each player  1  2  1  2  1  2  (30,20)                (‐15,‐25)  (‐16,‐6)  (3,‐7)  (2,12)  (21,11)  (20,30)                                                                                                1  2  1  2  1  2  (‐15,‐25)  (‐16,‐6)  (3,‐7)  1  2  1  (2,12)  2  (21,11)  1  (20,30)  (‐15,‐25)  (‐16,‐6)  (3,‐7)  1  2  1  (2,12)  2  (21,11)  1  2  1  (‐15,‐25)  (‐16,‐6)  (3,‐7)  1  2  (2,12)  1  (‐15,‐25)  (‐16,‐6)  (3,‐7)  (‐15,‐25)  (‐16,‐6)  (‐15,‐25)  By BI, the only SPE is that each player plays “gets in line” in each of their information sets. The  outcome in equilibrium play is that player 1 gets in line in his first turn.  b) the waiting cost is  11*(wait time) for each player  1  2  1  2  1  2  (30,20)  (‐25,‐35)  (‐24,‐14)  (‐3,‐13)  (‐2,8)  1  2  1  2  (19,9)  1  (20,30)  2  (‐25,‐35)  (‐24,‐14)  (‐3,‐13)  (‐2,8)  (19,9)  (20,30)                                                                                    1  2  1  2  1  2  (‐25,‐35)  (‐24,‐14)  (‐3,‐13)  (‐2,8)  1  2  1  2  1  (20,30)  2  (‐25,‐35)  (‐24,‐14)  (‐3,‐13)  1  2  1  2  1  (20,30)  2  (‐25,‐35)  (‐24,‐14)  1  2  1  2  1  (20,30)  2  (‐25,‐35)  1  2  1  2  1  (20,30)  2  (20,30)   By BI, the only SPE is for player 2 to wait until his last turn, and then to get in­line. Player 1 waits in all his  turns.    3) Harrington 8.12        4) Harrington 9.3              5) Harrington 9.11      ...
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