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Rent-seeking

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).

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Rent-seeking

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  1. Rent-seeking By Todd Kaplan

  2. 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.

  3. 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).

  4. 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?

  5. 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.

  6. 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?

  7. 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

  8. 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

  9. Results • Or Eshed $113,000.00 • Igor Kitainik $111,000.00 • G.F. $-125,000.00

  10. Results

  11. 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).

  12. 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?

  13. 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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