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Hearing the recent news about disqualified Badminton players in the ongoing 2012 London Olympics got me wondering about how best to design tournaments to avoid situations where players are incentivized to throw matches. I have no doubt that much has been written about this but I have no idea where to start.

Are there any Arrow-like theorems saying that "ideal tournament design" is impossible, i.e. given some short-ish list of generally agreeable desirable features of a tournament, one proves that they are contradictory?

I'm a novice in this sort of mathematics so feel free to recommend introductory surveys or books as well.

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    There is some discussion of the mathematics of the situation at http://www.quantitativepeace.com/blog/2012/08/when-losing-is-the-winning-strategy-game-theory-badminton-and-the-2012-summer-olympics-.html2012-08-02

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There are no impossibility results "Arrow like" regarding tournament design but lots of open problems especially in the incomplete information case.

Kay Konrad's book on contests is a good general reference.

As tournaments can be modeled as all-pay auctions, the literature on optimal auction design may also be relevant, see Vijay Krishna's book.

I know the above economics literature well but I am not familiar with the computer science one that may be also relevant: see this thesis https://stacks.stanford.edu/file/druid:qk299yx6689/TV-thesis-final-augmented.pdf

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    in an all-pay auction, auction you pay your bid even if you lose. Interpret the bid as cost of effort in the sports game.2013-12-17