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Kaushik Basu
Spring 2007
Econ 367: GameTheoretic Methods
Problem Set 11
1.
Consider the symmetric normalform game described below.
H
D
H
1, 1
3, 0
D
0, 3
4, 4
(a)
Locate all the Nash equilibria (pure and mixedstrategy) in this game.
(b)
Focusing on pure strategies alone, locate all the Evolutionarily Stable
Strategies in this game.
Answer:
(a) Pure Strategy Nash Equilibria: (H, H) and (D, D)
Mixed Strategy Nash equilibria: (H, H), (D, D), and (H with probability ½; D
with probability ½)
(b) H is an ESS
D is an ESS
2.
Consider a twoperiod game between a landlord and a laborer in which the
landlord offers the worker a wage of
w
dollars (for a day’s work) and the worker
can accept (A) or reject (R) the offer.
A day’s work has a leisure cost of $4 for
the worker. If the worker accepts the deal, the landlord gets an output of $10.
If
the worker rejects it, the landlord gets 0.
(a)
In the subgame perfect equilibrium of this twoperiod game what wage
does the landlord offer?
What payoffs do the two players receive in the
equilibrium?
Suppose the players meet in period 3 (after the above twoperiod interaction) to
play the following simultaneousmove game.
T
B
T
4, 4
0, 0
B
0, 0
2, 2
(b)
In this 3period game, what is the lowest wage offer that the laborer will
accept in a subgame perfect equilibrium?
Explain why such a wage is
accepted.
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View Full Document Answer:
(a)
10w
0
w4
0
Landlord offers wage = 4 to make the laborer indifferent between accepting or
rejecting the offer and thus the landlord can maximize his own payoff.
Landlord’s payoff is 10 (output) – 4 (labor cost) = 6; worker’s payoff is 4
(wage) – 4 (leisure cost) = 0.
The landlord wants to maximize his payoff by offering a wage that is just
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This note was uploaded on 05/31/2008 for the course ECON 3670 taught by Professor Basu during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 BASU

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