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Mixed refinements of Shapley's saddles and weak tournaments

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Author Info
Michel Le Breton () (CORE, Voie du Roman Pays, 34, 1348, Louvain La Neuve, Belgium)
John Duggan () (Department of Political Science and Department of Economics, University of Rochester, Rochester, NY 14627, USA)

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Abstract

We investigate refinements of two solutions, the saddle and the weak saddle, defined by Shapley (1964) for two-player zero-sum games. Applied to weak tournaments, the first refinement, the mixed saddle, is unique and gives us a new solution, generally lying between the GETCHA and GOTCHA sets of Schwartz (1972, 1986). In the absence of ties, all three solutions reduce to the usual top cycle set. The second refinement, the weak mixed saddle, is not generally unique, but, in the absence of ties, it is unique and coincides with the minimal covering set.

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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 18 (2001)
Issue (Month): 1 ()
Pages: 65-78
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Handle: RePEc:spr:sochwe:v:18:y:2001:i:1:p:65-78

Note: Received: 14 August 1998/Accepted: 12 November 1999
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  1. John Duggan, 2007. "A systematic approach to the construction of non-empty choice sets," Social Choice and Welfare, Springer, vol. 28(3), pages 491-506, April. [Downloadable!] (restricted)
  2. Jeffrey S. Banks & John Duggan & Michel LeBreton, . "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Wallis Working Papers WP14, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
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  3. Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003. "Social Choice and Electoral Competition in the General Spatial Model," IDEI Working Papers 188, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
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