Economics 201B HW #3: Solutions
1. Solution
P
(a) The payoff function for each firm is given by i (qi , qi ) = a b Nj=1 q j c qi .
Taking the first order condition with respect to qi , imposing symmetry in
that qi = q for all i, and solving for q gives us
Economics 201B Midterm Exam
Due: Tuesday February 11, 2014 at beginning of lecture
You may use your own class notes and any material posted on the class
website. You may NOT consult any other material: no books, no material
on the web and no other individ
Midterm solutions
Problem 1.
(a) There is no domination for player 1. For player 2, R is never best response,
so lets check if it is dominated by pL + (1 p)M :
5p + 3(1 p) > 4
2p + 8(1 p) > 6
Thus, 12 < p < 13 , i.e. there is no strategy that strictly dom
Economics 201B: Final Solution
Winter 2015
1. Keynes Guessing Game
If player i plays 100,
ui p100, ai q
#
1
N
0
if aj 100, for all j i
otherwise.
If player i plays the following mixed strategy
1
1
1
1
p0q `
p1q `
p2q ` . . . `
p99q,
100
100
100
100
i
sh
Lecture Notes for Economics 203
Core Economics III
Game Theory, Imperfect Competition, and Other
Applications
B. Douglas Bernheim
Department of Economics
Stanford University
[email protected]
Winter 2010
Contents
1 Strategic Environments
1.1 Co
Lecture 9: Extensive Form Games, II
As we have seen, extensive form games with perfect and complete information are easy to model and the assumption of subgame perfection makes
them easy to analyze. But now we want to allow for imperfect and incomplete in
GAMES OF INCOMPLETE INFORMATION, CONCLUSION
1
Example 4:
Matching pennies with cheating
Actions & Payoffs
H
T
H
(+2,-2)
(-1,+1)
T
(-1,+1)
(+1,-1)
2
COL is unsure if ROW honest or cheater
honest: cannot see ROW move
cheater: can see ROW move
Prob(Cheater
Lecture 7: Extensive Form Games, Part I
Up to this point we have considered only static games; we now turn to dynamic games. One way to view the distinction is to think of the action as
taking place at one moment of time (static games) or as taking place
Economics 201B HW #5
Due Tuesday February 18 in class
In class we showed (for the Cournot game) that thinking about a game in
normal form simultaneous moves and in extensive form sequential moves
can lead to very different conclusions. Problems 1 and 2 a
Professor B. Douglas Bernheim
Economics 203
Winter 2009-2010
Problems
Strategic Environments
1. Consider the following game. There are two players, 1 and 2. They
will play either matching pennies version A (as defined in class, where 1
moves first), match
Suggested Solution for Practice Problem 1
by Ziyan Huang 1
1. Nash equilibria in pure strategies are cfw_(C, C), (D, D).
Then let us look at Nash equilibria in mixed strategies. Assume that row
player plays pC + (1 p)D and column player plays qC + (1 q)D.
Suggested Solution for Practice Problem 3
by Ziyan Huang 1
1. See Handout for Week 6.
2. Consider the following strategy:
Phase I: Follow the strategy profile (CD,DC,CD,. . . ). If deviate, go to
Phase II.
Phase II: Play DD forever.
First, we identify the
Economics 201B HW #4: Solutions
1. Solution The minmax payoffs for ROW and COL are (1,1). The strategy
profiles that produce these minmax payoffs are that ROW plays D with probability 1 and COL plays C with probability 1.
2. Solution We consider the strat
Economics 201B Final Exam Solutions
1. Solution
(a) For row player, B is dominated by pA + (1 p)C where p > 12 . Eliminating B, we obtain the matrix
X
A (2,5)
C (3,0)
Y
(4,4)
(2,2)
Z
(2,3)
(4,1)
Then Z is dominated by Y for column player, which leaves us