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Winning by Losing: Incentive Incompatibility in Multiple Qualifiers

  • Dagaev, Dmitry
  • Sonin, Konstantin

In sport tournaments, the rules are presumably structured in a way that any team cannot be better off (e.g., to advance to the next round of competition) by losing instead of winning a game. Starting with a real-world example, we demonstrate that the existing national rules of awarding places for the UEFA Champions Leagues and the UEFA Europa League, which are based on the results of the national championship, a round-robin tournament, and the national cup, a knock-out tournament, might produce a situation where a team will be strictly better off by losing a game. Competition rules of the European qualification tournament to the World Cup 2014 suffer from the same problem. We show formally that in qualifying systems consisting of several round-robin tournaments, monotonic aggregating rules always leave open such a possibility. Then we consider qualifying systems consisting of a round-robin tournament (championship) and a knock-out tournament (cup). We show that any redistribution rule that allows the cup's runner-up to advance in the case that the cup's winner advances based on its place in a championship, has the same drawback, and discuss possible fixes.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 9373.

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Date of creation: Mar 2013
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Handle: RePEc:cpr:ceprdp:9373
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  1. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06.
  2. Giora Slutzki & Oscar Volij, 2005. "Ranking participants in generalized tournaments," International Journal of Game Theory, Springer, vol. 33(2), pages 255-270, 06.
  3. Denis Bouyssou, 2004. "Monotonicity of ‘ranking by choosing’: A progress report," Social Choice and Welfare, Springer, vol. 23(2), pages 249-273, October.
  4. Giora Slutzki & Oscar Volij, 2006. "Scoring of web pages and tournaments—axiomatizations," Social Choice and Welfare, Springer, vol. 26(1), pages 75-92, January.
  5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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