07 Jun Question Spring 2015 Assignment 1
Question
Spring 2015
Assignment 1
Econ 314
You must print out this sheet, ll in the personal information requested below, and
then staple it to your assignment as a cover sheet.
Surname or Family Name:
Given Name:
Student ID Number:
Your answers should be clear, neat, and concise.
You must circle or otherwise clearly indicate your nal answers, and show your work.
4 Marks total. Marks are not given for individual portions, but for complete
performance on the entire assignment.
Headers are not correct.
I am told that Joseph Stalin once said I have power because people think I do. We examine
the degree to which this statement is valid in the models that we have examined to date. Stalin
has three guards: Andy, Becky, and Charlie. Andy, Becky, and Charlie are the only players in
this game. They each have a choice to Obey or Disobey Stalin. Stalin orders Andy to arrest the
political dissident Vladimir Petkov. If he Obeys, then the game ends with Vladimir in jail. If he
Dis-obeys, then Stalin order Becky to arrest Vladimir and Andy. If she Obeys, then the game ends
with Vladimir and Andy in jail. If she disobeys, then Stalin orders Charlie to arrest Vladimir,
Andy, and Becky. If he obeys, then the game ends with Vladimir, Andy, and Becky in jail. If he
disobeys, then Stalin pulls his hair in disbelief, faints from shock, and awakens having forgotten
the entire event; nobody goes to jail. The guards dont want to obey Stalin. A guard who obeys
Stalin gets a payo of 2. Jail is worse than obedience; a guard who gets put in jail gets 0. In all
other cases, a guard gets 4. (Notice: the guards dont actually care if Vladimir gets jailed, they
simply dont want to be directly responsible.)
(a) Draw the extensive form of this game.
(b) Find all subgame perfect (backwards induction) equilibria.
(c) Convert the game into the normal form. Be sure to make clear which player chooses row, column
and matrix. Be sure to make clear which payo goes to each player. (If you are using the diagonal
method of listing payos that I use, then I recommend that player A chooses rows, player B to
chooses matrices, and player C to chooses columns.)
(d) Use the circling method to nd all pure strategy Nash equilibria. Clearly write down these
Nash equilibria as well as showing the circles on the matrix.
(e) Select a Nash equilibrium which is not subgame perfect. Select a player who is not demonstrating sequential rationality (in this equilibrium.) Explain the violation of sequential rationality.
(f) Verify that every strategy is rationalizable in the normal form game.
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