Economics 467 Spring 2010 Karl Dunz Problem Set 1 Answers 1. [6 points] Consider the following three lotteries: 1 = [480, 0.5; 480, 0.5], 2 = [850, 0.5; 200, 0.5], and 3 = [1000, 0.5; 0, 0.5]. Each lottery represents the consumption an agent would receive
Economics 467 Spring 2010 Karl Dunz Problem Set 1 due Monday February 15 You are encouraged to work in groups on these problems; however, you must turn in your own work, not a copy of what the group has done. Also, I will not accept any late assignments s
Economics 467
Professor: John Nachbar
Spring 2011
Homework 4
Answers
1. Gibbons 1.8. There is an asymmetric equilibrium in which two candidates are
at 2/3 and one is at 1/3, and the latter wins. There is no deviation by either
of the rst two that will mak
Economics 504
Professor: John Nachbar
Spring 2011
Homework 3
Answers
1. (a) Each shareholder can be in one of two possible circumstances, given the
actions of the other shareholders. First, suppose 49 or fewer shares are
tendered by the other shareholders
Economics 467
Professor: John Nachbar
Spring 2011
Homework 2
Answers
1. The unique Nash equilibrium of this game is in mixed strategies. In this Nash
equilibrium, your friend (row) randomizes ( 5 , 3 ) and you (column) randomize
88
( 3 , 5 ). In this Nash
Economics 467
Professor: John Nachbar
Spring 2011
Homework 5
Answers
1. Suppose only pirates 1 and 2 are left. Then 2 will propose 100 coins for himself,
and he will win. Write this assignment of coins (0,0,0,0,0,0,0,0,100,0). Next
suppose 1, 2, and 3 are
Econ 467
Professor: John Nachbar
Spring 2011
Homework 7
Answers
1. The unique equilibrium in the proper subgame is for both players to randomize 50:50, with expected payos (1.5,0.5). Therefore, the unique SPE is
(R, (1/2, 1/2), (1/2, 1/2) and the SE is al
Econ 467
Professor: John Nachbar
Spring 2011
Homework 10
Answers
1. (a) If the seller reports c then his expected payo (net of c), assuming v = v ,
is
11
1
111
+ Ev [v 2 ] c2 = c Probv [v c] + + c2
42
2
462
5
1
= c(1 c) +
c2 .
12 2
c Probv [Trade|c] +
Th
Econ 467
Professor: John Nachbar
Spring 2011
Homework 8
Answers
1. (a) qH = 3. To see this, note rst that in any separating NE, the entrant
enters if it sees qH . This is a consequence of the fact that the entrant is
best responding to the incumbents actu
Econ 467
Professor: John Nachbar
Spring 2011
Homework 1
Answers
1. There are innitely many equilibria. For any d [0, 1], (d, 1 d) is an equilibrium. In addition, (1, 1) is an equilibrium.
It should be clear that (d, 1 d) is an equilibrium for any d [0, 1)
Economics 467 Spring 2010 Karl Dunz Problem Set 4 due Monday April 12 You are encouraged to work in groups on these problems; however, you must turn in your own work, not a copy of what the group has done. Also, I will not accept any late assignments sinc
Economics 467 Spring 2010 Karl Dunz Problem Set 4 Answers 1. (a) A perfect Bayesian equilibrium for this game consists of giving values for the following: The probability a low cost monopoly chooses high capacity. Call this . The probability a high cost m
Economics 467 Spring 2010 Karl Dunz Problem Set 3 due Wednesday March 31 You are encouraged to work in groups on these problems; however, you must turn in your own work, not a copy of what the group has done. Also, I will not accept any late assignments s
Economics 467 Spring 2010 Karl Dunz Problem Set 3 Answers 1. Consider a market with an incumbent monopoly and one potential entrant. Suppose that the market demand curve is given by = 100 - and the marginal cost of production is zero for both firms. The m
Economics 467 Spring 2010 Karl Dunz Problem Set 2 due Wednesday February 24 You are encouraged to work in groups on these problems; however, you must turn in your own work, not a copy of what the group has done. Also, I will not accept any late assignment
Econ 467
Professor: John Nachbar
Spring 2011
Homework 6
Answers
Remark. PBE (as dened in Gibbons) and WPBE coincide in these particular
games. So I will simply refer to WPBE.
1. Gibbons 4.1.
(a)
R
L
M
L
R
2, 2 2, 2
4, 1 0, 0
3, 0 0, 1
Pure strategy NE are