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Rent-seeking By Todd Kaplan

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**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.

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**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).

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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?

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**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 probability This probability is the Tullock success function.

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Example If two players expend effort x1 and x2, there expected utility is What is the equilibrium here? Xi=V/4. Is the SOC satisfied? What are the players’ profits?

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**N-player Tullock function**

c(xi)=mc*x For N players each player has expected profits: What is the equilibrium and profits? X=(N-1)*V/(mc N2 ) profit=V/N2 totalprofit=V/N

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**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

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**Results Or Eshed $113,000.00 Igor Kitainik $111,000.00**

G.F. $-125,000.00

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Results

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**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).

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**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?

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**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)?

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