Rent-seeking
By Todd Kaplan
Idea of rent seeking.
• Sami Rub is elected mayor of Karkur.
• He has two friends: Todd and Dieter.
• He has to appoint a high-paying deputy mayor.
The duties are pretty easy for anyone with half a
brain. There is no real opportunity cost (can be
done at night).
• The value of such a position is V (net of cost of
performing duties).
• Todd and Dieter bug Sami for this job. Bugging
increases the chance of winning.
Properties.
• This bugging creates no value.
• This bugging is sunk.
• Bugging does increase the likelihood of
getting the job.
• Where else do you see such behaviour?
• Gordon Tullock was the first to model such
waste (called rent-seeking).
FCC+World Cup etc.
• Originally, TV/radio licenses were given off
by beauty contests.
• The nicer the application, the higher the
chance of getting the license.
• Tullock said that a lot of the value is
destroyed in the competition even if the
winner makes a profit.
• How is the world cup allocated?
Formal description
• There are N players and a prize of value
V.
• It costs players c(xi) to expend effort xi.
• The prize is awarded to player i with
xi
probability N
x
j 1
j
• This probability is the Tullock success
function.
Example
• If two players expend effort x1 and x2, there
expected utility is
xi
V
 xi
x1  x2 
V
xi
N
j 1
•
•
•
•
 m c xi
xj
What is the equilibrium here?
Xi=V/4.
Is the SOC satisfied?
What are the players’ profits?
N-player Tullock function
• c(xi)=mc*x
• For N players each player has expected
profits:
x
V
N
x
j 1
•
•
•
•
 m c xi
i
j
What is the equilibrium and profits?
X=(N-1)*V/(mc N2 )
profit=V/N2
totalprofit=V/N
Experimental results
•
•
•
•
•
•
•
•
Treatment 1:
N=4, V=16,000. mc=3000.
X=(N-1)*V/(mc N2)=3*16,000/(3000*16)=1
profit=V/N2=1000
totalprofit=V/N=4000
Treatment 2:
N=4, V=16,000. mc=1000
X=3, profit=1000, totalprofit=4000
Results
• Or Eshed $113,000.00
• Igor Kitainik $111,000.00
• G.F. $-125,000.00
Results
All-pay auction w/ complete
information.
• I have a prize of 10 shekels.
• All write your amount of bugging down xi.
• Each must pay me xi. I will choose a
winner by who paid me the most (ties will
be broken randomly).
All-pay auction with complete info.
• Take the two player case.
• Is there an equilibrium where player 1
chooses x1 and player 2 chooses x2?
– X1=x2>0?
– X1=x2=0?
– X1>x2=0?
– X1>x2>0?
• What can the equilibrium be?
All-pay equilibrium
• Equilibrium must be in mixed strategies.
• Equilibrium is a distribution function F(x) such
that players are indifferent to all strategies in the
support.
• Equilibrium is such that F(x)*V-x=c.
• Can players ever put more than an infinitesimal
amount on a particular x?
• What is F(0)?
• What does this imply about c?
• What is then F(x)?