Kaushik Basu Spring 2008 Econ 367: Game-Theoretic Methods Problem Set 5 1. Neither John nor George wishes to show up at a public meeting wearing the same colored hat. Hats can be R (red), W or B. Represent the decision problem of John and George as a
Kaushik Basu Spring 2008 Econ 367: Game-Theoretic Methods Problem Set 4 1. (a) Describe the mixed strategy Nash equilibrium (that is, one that actually involves mixing two strategies) in the game shown below. L U D 4, 4 0, 0 R 0, 0 2, 2
Answer: Supp
Kaushik Basu Spring 2008 Econ 367: Game-Theoretic Methods Problem Set 4 [This is a take-home examination.Total 10 points. Your answer must be turned in (hard copies, please) by 21st February, 5 pm. You may hand it over to Vidya or Sarah after class o
1 Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 2 1. Consider the normal-form game described below. [Here and elsewhere, player 1 chooses rows, and 2 chooses columns.] L 2,2 0,0 R 0,0 1,1
U D (a) (b) (c) (d) 2.
Describe the s
Kaushik Basu Spring 2008 Econ 367. Game-Theoretic Method Prelim Exam 2 - Solutions [1 hour. Total 15 points] 1. Two players are going to play the Prisoners Dilemma described below an infinitely many times. Each player has a discount factor of , such
Kaushik Basu Spring 2008 Econ 367: Game-Theoretic Methods Problem Set 5 1. Neither John nor George wishes to show up at a public meeting wearing the same colored hat. Hats can be R (red), W or B. Represent the decision problem of John and George as a
1 Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 2 Solutions 1. Consider the normal-form game described below. [Here and elsewhere, player 1 chooses rows, and 2 chooses columns.] L 2,2 0,0 R 0,0 1,1
U D (a) (b)
Describe the set of pl
Kaushik Basu Spring 2008 Econ 367. Game-Theoretic Methods Problem Set 1 1. In the game of Hex we proved that Black does not have a winning strategy. The proof took the form of showing that if Black has a winning strategy then White can always win (wh
Kaushik Basu Spring 2008 Econ 367. Game-Theoretic Methods Prelim Exam 1 Solutions [1 hour. Total 15 points] 1. Consider the two-player game described below, in which each player chooses between A and B A B (a) (b) A 5, 5 6, 0 B 0, 6 0, 0
Locate all
Kaushik Basu Spring 2008 Econ 367 Game Theoretic Methods Problem Set 8 1. Two firms, producing the same good, face the following inverse demand function:
p 10 ( x1
x2 )
where xi is the output produced by firm i and p is price in dollars. Firm 2 ca
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 7 1. Consider the extensive-form game described below.
2 2 A 2 x
1 1 B
1 1 C 2 y
4 1 D
L 1 w (a) (b)
R
Describe this game as a normal-form (or strategic-form) game. Locate al
PS 6 Solutions Econ 367 Kaushik Basu 1. Let us consider Firm 1. Since they are symmetric firms, the analysis will be the same for firm 2. P=100-Q Q= q1 + q2 Profit firm 1 = P*q1 Firm 1 maximizes (100-( q1 + q2) q1 =100q1-q12-q1q2 Differentiate w/ res
1. An example of an appropriate payoff matrix is John R 0, 0 1, 1 1, 1 W 1, 1 0, 0 1, 1 B 1, 1 1, 1 0, 0
George
R W B
Payoffs need to follow the rule i ( X , X ) i (Y , Z ) for Y Z and i = George, John. In the above matrix, all off-diagonal ce
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 3 1. Consider a two-player game in which each of two players (A and B) has to choose a positive integer, and they receive payoffs as follows. If both choose 1, they get 1 dollar eac
Kaushik Basu Spring 2008 Econ 367 : Game-Theoretic Methods Problem Set 1 1. In the game of Hex we proved that Black does not have a winning strategy. The proof took the form of showing that if Black has a winning strategy then White can always win (w
Kaushik Basu
Fall 2009
Econ 367
Game-Theoretic Methods
Problem Set 3
Solutions
1.
Consider a two-player game in which each of two players (A and B) has to choose
a positive integer, and they receive payoffs as follows. If both choose 1, they get 1
dollar
Kaushik Basu
Fall 2009
Econ 367 : Game-Theoretic Methods
Problem Set 1
1.
In the game of Hex we proved that Black does not have a winning strategy. The
proof took the form of showing that if Black has a winning strategy then White
can always win (which is
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 2 Solutions 1. Consider the normal-form game described below. [Here and elsewhere, player 1 chooses rows, and 2 chooses columns.] L 2,2 0,0 R 0,0 1,1
U D (a) (b) (c)
(d) 2.
Descr
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 3 Solutions 1. Consider a two-player game in which each of two players (A and B) has to choose a positive integer, and they receive payoffs as follows. If both choose 1, they get 1
Kaushik Basu Spring 2008 Econ 367 Game Theoretic Methods Problem Set 8 1. Two firms, producing the same good, face the following inverse demand function: p = 10 ( x1 + x 2 ) where xi is the output produced by firm i and p is price in dollars. Firm 2
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 7 1. Consider the extensive-form game described below. 2 2 A 2 x L 1 (a) (b) w R 1 1 B 1 1 C 2 y 4 1 D
Describe this game as a normal-form (or strategic-form) game. Locate all the
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 6 1. There are two Cournot duopolists, 1 and 2, selling oil from their private wells, who face the demand function. Q = 100 P. They can produce the good (oil in this case) costless
Kaushik Basu Spring 2008 Econ 367 Game Theoretic Methods Problem Set 9 1. Suppose two individuals play the game, G, described below ten times. Is there a subgame perfect equilibrium (SPE) such that in some periods the players play (C, C ) ? Explain y
Kaushik Basu Spring 2007 Econ 367: Game-Theoretic Methods Problem Set 11 Consider the symmetric normal-form game described below. H 1, 1 0, 3 D 3, 0 4, 4
1.
H D (a) (b)
Locate all the Nash equilibria (pure and mixed-strategy) in this game. Focusin
Kaushik Basu
Spring 2008, Cornell University 11.40-12.55, Tuesdays and Thursdays, Ives Hall 305 18 January, 2008
Econ 367: Game-Theoretic Methods for the Social Sciences
Preliminary Information
There are two teaching assistant for this course-Vidya
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 7 1. Consider the extensive-form game described below.
2 2 A 2 x
1 1 B
1 1 C 2 y
4 1 D
L 1 w (a) (b)
R
Describe this game as a normal-form (or strategic-form) game. Locate al