This preview shows pages 1–3. Sign up to view the full content.
Economics 208 Problems
Winter 2004
Vincent Crawford, Department of Economics, UCSD
12 (counts as two questions). Consider the Battle of the Sexes game. Assume, here and
below, that the structure is common knowledge, that both players are selfinterested, and
that there are no observable differences between the players or their roles in the game. In
each of the variations described below, say whether you would expect the players to be
able to coordinate on one of the efficient purestrategy equilibria, and what strategies you
would expect the players to use, on average. Briefly but clearly explain your answers.
Fights
Ballet
Fights
1
3
0
0
Ballet
0
0
3
1
Battle of the Sexes
(a) The original simultaneousmove game is a complete model of the players' situation.
(b) The game is modified so that Row chooses her/his strategy first and Column gets to
observe her/his choice before choosing her/his own strategy.
(c) Row chooses her/his strategy first and Column does NOT get to observe her/his
choice before choosing her/his own strategy.
(d) Row chooses her/his strategy first, Column observes her/his choice before choosing
her/his own strategy, but Row then gets to observe Column’s choice and costlessly revise
her/his own choice, and this decision ends the game (so that Column cannot revise her/his
choice).
(e) The original simultaneousmove game is a complete model of the players' situation,
except that Row (only) can make a nonbinding suggestion about the strategies players
should use before they choose them.
(f) The original simultaneousmove game is a complete model of the players' situation,
except that both players can make simultaneous, nonbinding suggestions about the
strategies players should use before they choose them.
(g) The original simultaneousmove game is a complete model of the players' situation,
except that players can make sequential, nonbinding suggestions about the strategies
players should use before they choose them, say with Row making the first suggestion.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document3. Consider the following twoperson guessing game. Each player has her/his own target,
lower limit, and upper limit. These are possibly different across players, and they
influence players’ payoffs as follows. Players make simultaneous guesses, which are
required to be within their limits. Each player then earns 1000 points minus the distance
between her/his guess and the product of her/his target times the other's guess.
(ad) Find the Nash equilibrium or equilibria for the following targets and limits:
a)
Lower Limit
Target
Upper Limit
Player 1
200
0.7
600
Player 2
400
1.5
700
b)
Lower Limit
Target
Upper Limit
Player 1
300
0.7
500
Player 2
400
1.3
900
c)
Lower Limit
Target
Upper Limit
Player 1
400
0.5
900
Player 2
300
0.7
900
d)
Lower Limit
Target
Upper Limit
Player 1
300
1.3
500
Player 2
200
1.5
900
(e) State and prove a general result that determines the equilibrium as a function of the
targets and limits for these guessing games.
(f) Would you expect intelligent people randomly paired from students who have not
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Sobel,J
 Economics, Game Theory

Click to edit the document details