GAME THEORY

1
GAME THEORY

• PRINCIPLES OF MICROECONOMICS

Dr. Fidel Gonzalez Department of Economics and
Intl. Business Sam Houston State University
2
OPPORTUNITY COST
MARGINAL ANALYSIS
Elasticity
Elasticity
SUPPLY
DEMAND
MARKET EQUILIBRIUM
CONSUMER SURPLUS, PRODUCER SURPLUS AND TOTAL
SURPLUS
MARKET EFFICIENCY
MARKET FAILURE
Pigouvian Taxes Quotas Coase Theorem Command and
control
TAXES
EXTERNALITIES
QUOTAS
PUBLIC GOODS
COMMON GOODS
ARTIFICIALLY SCARCE GOODS
GAME THEORY
3
Consider the following problem of two
fraternities ß? and p? They are throwing a big
party to celebrate the end of the semester. They
will invite a lot of people and are not charging
to enter the party. Each fraternity should buy
one half of the beers consumed in the party. They
calculate that they need about 10 beer kegs for
the whole party. Thus, ß? should buy 5 kegs and
p? should buy 5 kegs. Each kegs costs 8
dollars. The key is that each fraternity arrives
to the party around 8 pm with the beer and at
that time all the liquor stores are closed and
there is no way to buy beer. Each fraternity has
to buy the kegs way before the party and they
have not way to know what the other fraternity
did until they arrive to the party.
4
Q What kind of good is the beer ONCE the beer is
already at the party? A When the beer is at the
party, beer is a common good. It is
non-excludable and rival. It is non-excludable
because once the beer is at the party everyone
inside the party is allowed to drink beer.
Fraternities can not exclude people from drinking
beer. It is rival because every beer drank by one
guest can not be consumed by another guest. As
we studied before common goods suffer from over
consumption. The cost for each party attendant of
an extra beer is zero. In other words, the
marginal cost of a beer is zero. Each party
attendant will consumer beer until the marginal
benefit of an extra beer is equal to the marginal
cost. In this particular case, MB of beer MC
of beer MB of beer 0
5
This is the problem for each fraternity 1) If
ß? buys beers but p? does not (only 5 kegs of
beer bought) ß? pays 5x8 40 ß? gets a
benefit from drinking beer of 30, net benefit
for ß? is30-40 -10 p? gets a benefit from
drinking beer of 30, net benefit for p? is 30
-0 30 (remember the beer is non-excludable and
rival so everyone at the party gets to enjoy the
beer) Note that in this case p? free rides on ß?
. 2) If ß? and p? buy beer (10 kegs of beer
bought) ß? pays 5x8 40 and p? pays
5x840 Each fraternity gets a benefit from
drinking beer of 60 (double than before
because there is the double amount of beer). Net
benefit for each fraternity is 60 40 20 3)
If p? buys beers but ß? does not (only 5 kegs of
beer bought) p? pays 5x8 40 p? gets a
benefit from drinking beer of 30, net benefit
for p? is30-40 -10 ß? gets a benefit from
drinking beer of 30, net benefit for ß? is 30
-0 30 (in this case, ß? free rides on p?) 4)
Nobody buys beer ß? and p? pay zero ß? and p?
get a benefit of zero (without beer the party is
boring and nobody has a good time).
6
This is the pay off matrix for each fraternity
Fraternity p?
Fraternity ß?
7
Fraternity p?
Fraternity ß?
Fraternity ß?s dominant strategy is to not buy
beer, why? If fraternity p? buys beer, then
fraternity ß? can buy beer and get a net benefit
of 20 or dont buy beer and get a net benefit of
30. ß? will choose not to buy beer. If
fraternity p? does not buy beer, then fraternity
ß? can buy beer and get a net benefit of -10 or
dont buy beer and get a net benefit of 0. ß?
will choose not to buy beer. Regardless of
whatever fraternity p? chooses to do, fraternity
ß? is always better off by not buying beer.
8
Fraternity p?
Fraternity ß?
Fraternity p?s dominant strategy is to not buy
beer, why? If fraternity ß? buys beer, then
fraternity p? can buy beer and get a net benefit
of 20 or dont buy beer and get a net benefit of
30. p? will choose not to buy beer. If
fraternity ß? does not buy beer, then fraternity
p? can buy beer and get a net benefit of -10 or
dont buy beer and get a net benefit of 0. p?
will choose not to buy beer. Regardless of
whatever fraternity ß? chooses to do, fraternity
p? is always better off by not buying beer.
9
Fraternity p?
Fraternity ß?
The Nash Equilibrium (or non-cooperative
equilibrium) is for both fraternities not to buy
beer. This is the worst outcome for both
fraternities. Both of them will be better off if
both of them buy beer for the party (this is the
Prisoners Dilemma), each fraternity gets 20
instead of zero. Each fraternity doing what is
best for them does not provide the best solution
for them. In this case, self interest is not
enough to provide an efficient outcome. Remember
that we are at an inefficient point if we can
make someone better off without making someone
else worse off. In this case, we can make both of
them better off, so not buying beer is an
inefficient allocation of resources.