Dynamic stable set as a tournament solution

Hannu Vartiainen ()

Social Choice and Welfare, 2015, vol. 45, issue 2, 309-327

Abstract: We define a notion of dynamic (vNM) stable set for a tournament relation. Dynamic stable set satisfies (i) an external direct stability property, and (ii) an internal indirect stability property. Importantly, stability criteria are conditioned on the histories of past play, i.e. the dominance system has memory. Due to the asymmetry of the defining stability criteria, a dynamic stable set is stable both in the direct and in the indirect sense. We characterize a dynamic stable set directly in terms of the underlying tournament relation. A connection to the covering set of Dutta (J Econ Theory 44:63–80, 1988 ) is established. Using this observation, a dynamic stable set exists. We also show that a maximal implementable outcome set is a version of the ultimate uncovered set. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: C71; C72 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00355-015-0897-0

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