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SABANCI UNIVERSITY
ECON 201 – A
GAMES AND STRATEGY
ASSIGNMENT
2 ANSWERS
1
(
25 points
). A pedestrian and a motorist play the following game: Each player has three
strategies: exercise NO CARE, SOME CARE, and DUE CARE. An accident happens
with
probability %2 (0.02)
if
both
players choose “due care.” In all other cases, an
accident happens for sure (with probability 1).
When an accident happens, pedestrian’s
cost
is
100
, whereas motorist has no cost.
For each player, exercising
no care is costless
, to exercise “
some care” costs 1
, and to
exercise
due care costs 3
. The payoffs are (0,0) if no accident occurs (any care cost must
be subtracted). Consider the following legal liability rule:
Liability rule:
•
If the motorist exerts more care than the pedestrian, the motorist has no liability.
•
If the players exert the same level of care, when an accident happens, the motorist
compensates the pedestrian for half of the damage.
•
In all other cases, the motorist is liable for any harm that the pedestrian may incur.
(i)
[10p] Construct the strategic form game under the liability rule given above.
(ii)
[5p] What are each player’s rationalizable strategies?
(iii)
[5p] What is (or are) the Nash equilibrium?
(iv)
[5p] Does the liability rule generate a desirable outcome? In what sense is it or is not
desirable?
Answer
:
Motorist
Pedestrian
No Care
Some Care
Due Care
No Care
50 , 50
100 , 1
100, 3
Some Care
1 , 100
51 , 51
101, 3
Due Care
3, 100
3, 101
4, 4
All three strategies of the pedestrian are rationalizable (one can find a strategy fort he
motorist to which each strategy of the pedestrian becomes a best response).
Fort he motorist, No Care is not rationalizable (in fact, it is strictly dominated by Due
Care), while “some care” and “due care” are rationalizable.
The Nash equilibrium is “due care, due care”.
The liability rule changes the game you had to solve in the first midterm. It generates
a Pareto Efficient Nash equilibrium in the game (it is impossible to improve one
player’s payoff without harming the other) Moreover total payoffs are maximal: we
also have a Pareto Efficient outcome with expost transfers. These are desirable
features in gamelike social interactions.
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View Full Document 2. (
40 points
) Some of you may be familiar with the children’s game “rockscissors
paper”: two players
simultaneously
choose between either “rock” or “scissors” or
“paper” by putting their hands in the shape of one of the three choices. Rules are:
scissors beats paper, paper beats rock, and rock beats scissors. If the players choose
the same object, there is a tie: no one wins, no one looses.
Suppose that each player gets the payoff 10 from winning, 10 from losing and 0
if there is a tie.
(i)
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This note was uploaded on 03/16/2012 for the course FENS 101 taught by Professor Selçukerdem during the Fall '12 term at Sabancı University.
 Fall '12
 SelçukErdem

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