HW XXXXXXXXXXGame theory
XXXXXXXXXXFor the following game, answer the following.
Left Center Right
Up (0,0) (5,3) (3,6)
Down (4,6) (1,2) (4,3)
a. (+4) Identify all pure-strategy Nash equili
ia, or state that no such
equili
ium exists.
. (+2) Is this game zero-sum? Why or why not?
XXXXXXXXXXA dictator possesses nuclear weapons, and has threatened to use them
unless the UN satisfies its demands. In that case, other countries may retaliate
or not. If the UN satisfies the dictator’s demands, the payoffs (?????? ,????) are
(−20,20). If the UN does not satisfy the dictator’s demands, the dictator could
decide not to use its nuclear weapons, in which case payoffs are (0,0). If the
dictator uses nuclear weapons and the UN does not retaliate, payoffs are
(−100,−1). If they do retaliate, payoffs are (−120,−500).
a. (+6) Identify all pure-strategy Nash equili
ia of this game, or state
that no such equili
ium exists. (Remember, an equili
ium is a list of
contingent strategies for each player. That is, the dictator must decide
whether to nuke or not in the event that the UN does not satisfy. Also, if
the UN does not satisfy then it must decide whether to retaliate or not in
the event that the dictator nukes.)
. (+4) Tell which of the above equili
ia (if any) are sub-game perfect.
c. (+2) On the basis of this analysis, what should the UN do? Why?
XXXXXXXXXXShepsle and Bonchek (1997, p. 148) write,
Some political observers have taken the infrequency with which presidents have
used the veto as an indicator of cooperation between the legislative and
executive
anches. In this view, infrequent use of the veto co
esponds to a
high degree of harmony between the
anches. In his 1994 State of the Union
speech, President Bill Clinton proudly announced the end of gridlock and the
eginning of a new period of inte
anch harmony by pointing to the fact that
not once had he vetoed a piece of congressional legislation during 1993.
Those authors then argue in favor of an alternative view, which is that Congress
amends its laws to the point that they know it will not be vetoed. Write down a
game such that, in equili
ium, Congress amends a bill and vetoes do not occur.
To be fully specified, such a game should include strategies for both Congress
and the President and outcome utilities for every combination of strategies. (If
the game is sequential, a strategy must specify a player’s behavior plan for the
entire game, possibly including multiple decision nodes). Identify equili
ium
strategies and demonstrate that neither Congress nor the President has an
incentive to deviate to a different strategy.
XXXXXXXXXXIn a particular industry, each worker can work 40 hours or 80 hours. If
others work 40, an individual can profit by working 80 hours. If others work 80,
an individual loses substantially by only working 40 hours. In equili
ium, all
workers therefore work 80 hours. If all worked 40 instead, however, then all
would be happier. What game is this situation most similar to: matching
pennies, prisoner’s dilemma, traveler’s paradox, battle of sexes, stag hunt, or
chicken?
HW XXXXXXXXXXGame theory