Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players
I characterize the optimal accuracy level <i>r</i> of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner’s expected valuation by choosing a contest with an all-pay auction...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Games |
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| Online Access: | https://www.mdpi.com/2073-4336/13/2/24 |
| _version_ | 1827619748971544576 |
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| author | Marco Sahm |
| author_facet | Marco Sahm |
| author_sort | Marco Sahm |
| collection | DOAJ |
| description | I characterize the optimal accuracy level <i>r</i> of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner’s expected valuation by choosing a contest with an all-pay auction equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>). By contrast, if she aims at maximizing the expected aggregate effort or the winner’s expected effort, she will choose a contest with a pure-strategy equilibrium, and the optimal accuracy level <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula> decreases in the players’ heterogeneity. Finally, a contest designer who faces a tradeoff between selection quality and minimum (maximum) effort will never choose a contest with a semi-mixed equilibrium. |
| first_indexed | 2024-03-09T10:36:40Z |
| format | Article |
| id | doaj.art-c9958e45d09040f6b2611c787a9eedb9 |
| institution | Directory Open Access Journal |
| issn | 2073-4336 |
| language | English |
| last_indexed | 2024-03-09T10:36:40Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Games |
| spelling | doaj.art-c9958e45d09040f6b2611c787a9eedb92023-12-01T20:55:26ZengMDPI AGGames2073-43362022-03-011322410.3390/g13020024Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous PlayersMarco Sahm0Department of Economics, Otto-Friedrich-Universität Bamberg, Feldkirchenstraße 21, 96052 Bamberg, GermanyI characterize the optimal accuracy level <i>r</i> of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner’s expected valuation by choosing a contest with an all-pay auction equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>). By contrast, if she aims at maximizing the expected aggregate effort or the winner’s expected effort, she will choose a contest with a pure-strategy equilibrium, and the optimal accuracy level <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula> decreases in the players’ heterogeneity. Finally, a contest designer who faces a tradeoff between selection quality and minimum (maximum) effort will never choose a contest with a semi-mixed equilibrium.https://www.mdpi.com/2073-4336/13/2/24Tullock contestheterogeneous valuationsaccuracydiscriminationoptimal designall-pay auction |
| spellingShingle | Marco Sahm Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players Games Tullock contest heterogeneous valuations accuracy discrimination optimal design all-pay auction |
| title | Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players |
| title_full | Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players |
| title_fullStr | Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players |
| title_full_unstemmed | Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players |
| title_short | Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players |
| title_sort | optimal accuracy of unbiased tullock contests with two heterogeneous players |
| topic | Tullock contest heterogeneous valuations accuracy discrimination optimal design all-pay auction |
| url | https://www.mdpi.com/2073-4336/13/2/24 |
| work_keys_str_mv | AT marcosahm optimalaccuracyofunbiasedtullockcontestswithtwoheterogeneousplayers |