Mixed refinements of Shapley's saddles and weak tournaments

Michel Le Breton () and John Duggan
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Michel Le Breton: CORE, Voie du Roman Pays, 34, 1348, Louvain La Neuve, Belgium

Social Choice and Welfare, 2001, vol. 18, issue 1, 65-78

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.

Date: 2001-01-10
Note: Received: 14 August 1998/Accepted: 12 November 1999
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Working Paper: Mixed refinements of Shapley’s saddles and weak tournaments (1999)
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