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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 N 2 ) profit=V/N 2 totalprofit=V/N

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Experimental results Treatment 1: N=4, V=16,000. mc=3000. X=(N-1)*V/(mc N 2 )=3*16,000/(3000*16)=1 profit=V/N 2 =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, Igor Kitainik $111, 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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