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Solving the n-player Tullock contest

Author

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  • Christian Ewerhart

Abstract

The n-player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can that model be solved more generally? In this paper, we show that key characteristics of the equilibrium, such as individual efforts, winning probabilities, and payoffs cannot, in general, be expressed in terms of the primitives of the model using basic arithmetic operations plus the extraction of roots alone. In this sense, the Tullock contest is intractable. We argue that our formal concept of tractability captures the intuitive understanding of the notion.

Suggested Citation

  • Christian Ewerhart, 2024. "Solving the n-player Tullock contest," ECON - Working Papers 447, Department of Economics - University of Zurich.
    • Handle: RePEc:zur:econwp:447
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    File URL: https://www.zora.uzh.ch/id/eprint/261058/1/econwp447.pdf
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    More about this item

    Keywords

    Tullock contest; pure-strategy Nash equilibrium; solution by radicals; Galois theory;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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