Mixed refinements of Shapley’s saddles and weak tournaments

John Duggan and Michel Le Breton
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Michel Le Breton: Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), 1348 Louvain la Neuve, Belgium

No 1999021, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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: 1999-08-06
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Related works:
Journal Article: Mixed refinements of Shapley's saddles and weak tournaments (2001)
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