Solving the n $n$‐Player Tullock Contest

Christian Ewerhart

Journal of Public Economic Theory, 2026, vol. 28, issue 2

Abstract: The n $n$‐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 the 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 only basic arithmetic operations and the extraction of roots. In this sense, the Tullock contest is intractable. We argue that our formal concept of tractability captures the intuitive notion of the term.

Date: 2026
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