My attention has been drawn to an error in Amegashie (1999). To save space, I will only reproduce the relevant equations and ask the reader to refer to the original article.

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I propose a simple contest success function which is a variant of the Tullock probability function under certain conditions. It relaxes two features of the Tullock probability function. I show that this contest success function could be used to obtain interesting results and is more tractable than Tullock's function in certain cases. In particular, researchers who are interested in examining the degree to which luck as opposed to effort affects behavior in different contest settings might find it easier to use this contest success function than the Tullock success function. Unlike the Tullock function, there always exists a pure-strategy equilibrium for all values of the parameter which captures the degree of noise. The proposed function has been used in Kolmar and Wagener (2004) with interesting results. Copyright Springer Science + Business Media, Inc. 2006

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The authors study the incentive effects of rematches in sports with an emphasis on professional boxing. If the difference between the boxers' abilities is sufficiently small, the authors find that a clause that stipulates that the winner of the fight is obliged to give the loser a rematch (i.e., a mandatory rematch clause) results in a higher aggregate effort compared to aggregate effort when the probability of a rematch depends on effort. This result sheds some light on the practice of offering mandatory rematch clauses to elite boxers. The authors also argue that their results apply to rivalries and rematches in other sporting events and contests.