Maximality with or without binariness: Transfer-type characterizations

Alcantud, José Carlos R.

doi:10.1016/j.mathsocsci.2004.08.007

Cited by 5 publications

(3 citation statements)

References 16 publications

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“…21 A more detailed discussion of the related literature can be found in Alcantud (2006 Motivated by similar observations, recently Heller (2012) proposed an alternative notion of rationalizable choice behavior. According to Heller's approach, it is "rational" to select a lottery p from a choice set K if and only if p ∈ K ∩ M (≻, co (K)).…”

Section: Incomplete Preferences and Non-binary Choice Behaviormentioning

confidence: 93%

Scalarization methods and expected multi-utility representations

Evren

2014

Journal of Economic Theory

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I characterize the class of (possibly incomplete) preference relations over lotteries which can be represented by a compact set of (continuous) expected utility functions that preserve both indifferences and strict preferences. This finding contrasts with the representation theorem of Dubra, Maccheroni and Ok (2004) which typically delivers some functions which do not respect strict preferences. For a preference relation of the sort that I consider in this paper, my representation theorem reduces the problem of recovering the associated choice correspondence over convex sets of lotteries to a scalar-valued, parametric optimization exercise. By utilizing this scalarization method, I also provide characterizations of some solution concepts. Most notably, I show that in an otherwise standard game with incomplete preferences, the collection of pure strategy equilibria that one can find using this scalarization method corresponds to a refinement of the notion of Nash equilibrium that requires the (deterministic) action of each player be undominated by any mixed strategy that she can follow, given others' actions.

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Section: Incomplete Preferences and Non-binary Choice Behaviormentioning

confidence: 93%

Scalarization methods and expected multi-utility representations

Evren

2014

Journal of Economic Theory

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“…Afterwards, Alcantud (2002b) produced an altogether different model for non-binary optimization. It precedes Alcantud (2006) and Alcantud and Alós-Ferrer (2007). The former supposed the first characterization of existence of maximal elements under lack of binariness.…”

Section: Introductionmentioning

confidence: 99%

“…In a different line of inquiry, Alcantud (2002a) provides necessary and sufficient conditions in the full class of the acyclic binary relations. The first characterization of maximality in a non-binary model has appeared in Alcantud (2006), which benefited from prior insights by Rodríguez-Palmero and García-Lapresta (2002).…”

Section: Introductionmentioning

confidence: 99%

Mixed choice structures, with applications to binary and non-binary optimization

Alcantud

2008

Journal of Mathematical Economics

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Characterization of the existence of maximal elements of acyclic relations

Alcantud¹

2002

Econ Theory

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We obtain a sufficient condition for the existence of maximal elements of irreflexive binary relations that generalizes the theorem of Bergstrom and Walker by relaxing the compactness condition to a weaker one that is naturally related to the relation. We then prove that the sufficient conditions used both in the Bergstrom-Walker Theorem and in our generalization provide a characterization of the existence of maximal elements of acyclic binary relations. Other sufficient conditions for the existence of maximal elements obtained by Mehta, by Peris and Subiza and by Campbell and Walker are shown to be necessary too.

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Maximality with or without binariness: Transfer-type characterizations

Cited by 5 publications

References 16 publications

Scalarization methods and expected multi-utility representations

Scalarization methods and expected multi-utility representations

Mixed choice structures, with applications to binary and non-binary optimization

Characterization of the existence of maximal elements of acyclic relations

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