Questions
1. Economists often model businesses as strictly maximizing
profits. However, we also observe many firms
giving money to charity or providing some of their
products to disadvantaged consumers for free or at a
reduced price. Are these acts altruistic? What other
motives might firms have? Use real-world examples to
argue your case.
2. Consider Hong, who is endowed with a number of
tokens. The tokens can be allocated between Hong and
another person. Each unit of Hong’s own consumption,
x1, can be purchased for p1 tokens. Each unit of the
other person’s consumption, x2, can be purchased for
p2 tokens. Consider each of the following sets of
choices. Determine if each violates WARP, SARP, or
GARP.
(a) When endowed with 20 tokens, with p1 =1 and
p2 = 1 Hong chooses x1 =17, x2 = 2.05. When
endowed with 30 tokens, with p1 =0.5,
p2 = 10.5, Hong chooses x1 = 18, x2 =2. When
endowed with 100 tokens, with p1 =1.72,
p2 = 2.9, Hong chooses x1 = 20, x2 = 1.9.
(b) When endowed with 20 tokens, with p1 =1 and
p2 =1 Hong chooses x1 =18, x2 = 2. When
endowed with 30 tokens, with p1 =0.5,
p2 =10.5, Hong chooses x1 =17, x2 =2.05.
(c) When endowed with 20 tokens, with p1 = 1 and
p2 = 1 Hong chooses x1 = 17, x2 =3. When
endowed with 30 tokens, with p1 = 1, p2 =2,
Hong chooses x1 =10, x2 =10. When endowed
with 100 tokens, with p1 = 5, p2 =5, Hong
chooses x1 = 18, x2 = 2.
(d) When endowed with 20 tokens, with p1 =1 and
p2 =1Hong chooses x1 =17, x2 =3.When endowed
with 30 tokens, with p1 = 1, p2 = 2, Hong chooses
x1 =20, x2 = 5. When endowed with 100 tokens,
with p1 = 10, p2 =5, Hong chooses x1 = 5, x2 =10.
3. Consider the prisoner’s dilemma game, in which two
prisoners are accused of a crime. Both are isolated in
the prison. Without a confession, there is not enough
evidence to convict either. Any prisoner who confesses
will be looked upon with lenience. If one prisoner
confesses and the other does not, that prisoner not
confessing will be put away for a much longer sentence.
The payoffs can be represented as pictured in
Figure 14.7 (Player 1’s payoffs are in the upper right,
and Player 2’s are in the lower left).
Prisoner 1
Prisoner 2
Confess
Confess
Don’t confess
Don’t confess
–10
–10
60
60
–100
–100 50
50
FIGURE 14.7
The Prisoner’s Dilemma
(a) Determine the Nash equilibrium strategy for each
player. What would be the result of the game if
both players chose this strategy?
(b) In most experiments involving the prisoner’s
dilemma, we observe that players tend to choose
not to defect a reasonable proportion of the time.
How might this be motivated by altruism?
(c) If a selfish player is playing the prisoner’s dilemma
against an opponent she believes to be altruistic,
what would her strategy be? Is this similar to the
observation in the TIOLI game? Why or why not?
(d) Now suppose that the prisoner’s dilemma is played
three times in sequence by the same two players.
How might a belief that the other player is altruistic
affect the play of a selfish player? Is this
different from your answer to c? What has
changed?