Mixed refinements of Shapley's saddles and weak tournaments |
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Authors: | John Duggan Michel Le Breton |
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Institution: | (1) Department of Political Science and Department of Economics, University of Rochester, Rochester, NY 14627, USA (e-mail: dugg@troi.cc.rochester.edu), US;(2) CORE, Voie du Roman Pays, 34, 1348, Louvain La Neuve, Belgium (e-mail: lebretou@core.ucl.ac.be), BE |
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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.
Received: 14 August 1998/Accepted: 12 November 1999 |
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