Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking...
Transcript of Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking...
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Information and Over-dissipationin Rent-Seeking Contests
Francesco Fallucchi, Elke Renner and Martin Sefton
Department of Economics, University of Nottingham & Cedex
July 12th 2012
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Tullock’s Rent-Seeking Contest
Tullock‘s model of rent-seeking extensively used to model a variety of contests:
lobbying, patent races, litigation lawsuits, grant-seeking, etc. (Konrad, Strategy
and Dynamics in Contests, 2009)
I n agents compete for a rent of size R
I agent i receives an endowment w and spends xi on rent-seeking
I X =∑xi denotes aggregate expenditures
I agent i receives the rent with probability xi
X
I agent i earns =
{w − xi +R with probabilityxi
Xw − xi otherwise
I risk neutral equilibrium xi = n−1n2 R
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Tullock’s Rent-Seeking Contest
Tullock‘s model of rent-seeking extensively used to model a variety of contests:
lobbying, patent races, litigation lawsuits, grant-seeking, etc. (Konrad, Strategy
and Dynamics in Contests, 2009)
I n agents compete for a rent of size R
I agent i receives an endowment w and spends xi on rent-seeking
I X =∑xi denotes aggregate expenditures
I agent i receives the rent with probability xi
X
I agent i earns =
{w − xi +R with probabilityxi
Xw − xi otherwise
I risk neutral equilibrium xi = n−1n2 R
![Page 4: Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking extensively used to model a variety of contests: lobbying, patent races, litigation](https://reader033.fdocuments.in/reader033/viewer/2022042806/5f700f093613103b7a0355b8/html5/thumbnails/4.jpg)
Tullock’s Rent-Seeking Contest
Tullock‘s model of rent-seeking extensively used to model a variety of contests:
lobbying, patent races, litigation lawsuits, grant-seeking, etc. (Konrad, Strategy
and Dynamics in Contests, 2009)
I n agents compete for a rent of size R
I agent i receives an endowment w and spends xi on rent-seeking
I X =∑xi denotes aggregate expenditures
I agent i receives the rent with probability xi
X
I agent i earns =
{w − xi +R with probabilityxi
Xw − xi otherwise
I risk neutral equilibrium xi = n−1n2 R
![Page 5: Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking extensively used to model a variety of contests: lobbying, patent races, litigation](https://reader033.fdocuments.in/reader033/viewer/2022042806/5f700f093613103b7a0355b8/html5/thumbnails/5.jpg)
Tullock’s Rent-Seeking Contest
Tullock‘s model of rent-seeking extensively used to model a variety of contests:
lobbying, patent races, litigation lawsuits, grant-seeking, etc. (Konrad, Strategy
and Dynamics in Contests, 2009)
I n agents compete for a rent of size R
I agent i receives an endowment w and spends xi on rent-seeking
I X =∑xi denotes aggregate expenditures
I agent i receives the rent with probability xi
X
I agent i earns =
{w − xi +R with probabilityxi
Xw − xi otherwise
I risk neutral equilibrium xi = n−1n2 R
![Page 6: Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking extensively used to model a variety of contests: lobbying, patent races, litigation](https://reader033.fdocuments.in/reader033/viewer/2022042806/5f700f093613103b7a0355b8/html5/thumbnails/6.jpg)
Tullock’s Rent-Seeking Contest
Tullock‘s model of rent-seeking extensively used to model a variety of contests:
lobbying, patent races, litigation lawsuits, grant-seeking, etc. (Konrad, Strategy
and Dynamics in Contests, 2009)
I n agents compete for a rent of size R
I agent i receives an endowment w and spends xi on rent-seeking
I X =∑xi denotes aggregate expenditures
I agent i receives the rent with probability xi
X
I agent i earns =
{w − xi +R with probabilityxi
Xw − xi otherwise
I risk neutral equilibrium xi = n−1n2 R
![Page 7: Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking extensively used to model a variety of contests: lobbying, patent races, litigation](https://reader033.fdocuments.in/reader033/viewer/2022042806/5f700f093613103b7a0355b8/html5/thumbnails/7.jpg)
Tullock’s Rent-Seeking Contest
Tullock‘s model of rent-seeking extensively used to model a variety of contests:
lobbying, patent races, litigation lawsuits, grant-seeking, etc. (Konrad, Strategy
and Dynamics in Contests, 2009)
I n agents compete for a rent of size R
I agent i receives an endowment w and spends xi on rent-seeking
I X =∑xi denotes aggregate expenditures
I agent i receives the rent with probability xi
X
I agent i earns =
{w − xi +R with probabilityxi
Xw − xi otherwise
I risk neutral equilibrium xi = n−1n2 R
![Page 8: Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking extensively used to model a variety of contests: lobbying, patent races, litigation](https://reader033.fdocuments.in/reader033/viewer/2022042806/5f700f093613103b7a0355b8/html5/thumbnails/8.jpg)
Tullock’s Rent-Seeking Contest
Tullock‘s model of rent-seeking extensively used to model a variety of contests:
lobbying, patent races, litigation lawsuits, grant-seeking, etc. (Konrad, Strategy
and Dynamics in Contests, 2009)
I n agents compete for a rent of size R
I agent i receives an endowment w and spends xi on rent-seeking
I X =∑xi denotes aggregate expenditures
I agent i receives the rent with probability xi
X
I agent i earns =
{w − xi +R with probabilityxi
Xw − xi otherwise
I risk neutral equilibrium xi = n−1n2 R
![Page 9: Information and Over-dissipation in Rent-Seeking Contests · Tullock‘s model of rent-seeking extensively used to model a variety of contests: lobbying, patent races, litigation](https://reader033.fdocuments.in/reader033/viewer/2022042806/5f700f093613103b7a0355b8/html5/thumbnails/9.jpg)
Recent studies...
Now substantial body of experimental evidence shows systematic departuresfrom equilibrium predictions.
Study Group Size (N) Expenditure as% of EquilibriumExpenditure
Fonseca (IJIO, 2009) 2 200.2Abbink et al. (AER, 2010) 2 205.2Sheremeta (GEB, 2010) 4 151.6
Sheremeta (Ec Inq 2011)4 133.32 131.3
Chowdhury et al. (2012) 4 174.7Faravelli and Stanca (GEB, 2012) 2 110.2
Lim et al. (2012)2 130.03 127.4
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Recent studies...
Now substantial body of experimental evidence shows systematic departuresfrom equilibrium predictions.
Study Group Size (N) Expenditure as% of EquilibriumExpenditure
Fonseca (IJIO, 2009) 2 200.2Abbink et al. (AER, 2010) 2 205.2Sheremeta (GEB, 2010) 4 151.6
Sheremeta (Ec Inq 2011)4 133.32 131.3
Chowdhury et al. (2012) 4 174.7Faravelli and Stanca (GEB, 2012) 2 110.2
Lim et al. (2012)2 130.03 127.4
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Research Questions
I How does information feedback affect rent seeking expenditures?
We vary whether players observe other players‘ choices and payoffs
I How does this effect depends on contest structure?
We compare:
STOCHASTIC CONTEST
π(xi) =
{w − xi +R with probability xi∑N
j=1 xj
w − xi otherwise
DETERMINISTIC CONTEST
π(xi) = w − xi +xi∑Nj=1 xj
R
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Why should Feedback matter?Consider DETERMINISTIC
Payoffs can be rewritten as
π(xi) = w − xi +xi
XR = w +
xi(R−X)
X
For R > X player choosing highest rent-seeking expenditure gets highestpayoff.
For R < X player choosing lowest rent-seeking expenditure gets highestpayoff.
Imitating players with the highest payoff leads to X = R.
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Why should contest structure matter?Consider STOCHASTIC
I Player i wins rent with probability xi
X
I For a given set of expenditures with mean x̄t−1 and standard deviationσt−1
E(xit|x1t−1, x2t−1, ..., xnt−1) = x̄t−1 +σ2t−1
x̄t−1
I Random walk with upward drift
I Imitating players with the highest payoff leads to xi = w (fullexpenditure)
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A Simulation
(n = 3 and R = 1000, 10 groups)
DETERMINISTIC contest STOCHASTIC contest
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Experimental Design
Groups of 3 subjects (undergraduates at University of Nottingham) interactover 60 rounds in fixed groups:
I Each subject given 1000 points at beginning of round
I Subjects compete for 1000 points prize
I Subject i chooses xiε{0, 1, ..., 999, 1000}I Earnings = 1000− xi+ contest earnings
I Information feedback
Accumulated points exchanged for £s at the end of session.Session lasted 60 minutes, average earning =£9.40
Own Feedback Full FeedbackDeterministic 10 groups 11 groups
Stochastic 10 groups 10 groups
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Screenshot OWN information
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Screenshot FULL information
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Deterministic treatments: Group rent-seekingexpenditures
Periods 1-30 x̄OWN = 842, x̄FULL = 884, p − value = 0.48
Periods 31-60 x̄OWN = 657, x̄FULL = 794, p − value = 0.02
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Deterministic treatments: Group rent-seekingexpenditures
OWN: expenditure close to Nash Equilibrium
FULL: expenditure higher
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Distributions of individual expenditures:DETERMINISTIC
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Stochastic treatments: Group rent-seekingexpenditures
Periods 1-30 x̄OWN = 1152, x̄FULL = 916, p − value = 0.04
Periods 31-60 x̄OWN = 1110, x̄FULL = 752, p − value = 0.02
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Stochastic treatments: Group rent-seekingexpenditures
FULL: expenditure higher than Nash Equilibrium
OWN: expenditure even higher
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Distributions of individual expenditures:STOCHASTIC
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Conclusion
I In deterministic rent-seeking contest expenditures sensitive toinformation about others
I With own information expenditures converge to the equilibriumI With full information expenditures stabilize at a higher level
I In stochastic contest expenditures even more sensitive to informationstructure and the effect of information is reversed
I With own information expenditures close to full-dissipationI With full information expenditures stabilize at a lower level
I This suggests that contests where contestants only observe owninformation may result in more substantial costs of rent-seeking
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Next step?
I Endogenous information sharing