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Maximizing an interval order on compact subsets of its domain

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  • Kukushkin, Nikolai S.

Abstract

Maximal elements of a binary relation on compact subsets of a metric space define a choice function. An infinite extension of transitivity is necessary and sufficient for such a choice function to be nonempty-valued and path independent (or satisfy the outcast axiom). An infinite extension of acyclicity is necessary and sufficient for the choice function to have nonempty values provided the underlying relation is an interval order.

Suggested Citation

  • Kukushkin, Nikolai S., 2008. "Maximizing an interval order on compact subsets of its domain," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 195-206, September.
    • Handle: RePEc:eee:matsoc:v:56:y:2008:i:2:p:195-206
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    References listed on IDEAS

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    1. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
    2. Alcantud, Jose C.R., 2006. "Maximality with or without binariness: Transfer-type characterizations," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 182-191, March.
    3. Kukushkin, Nikolai S., 2006. "On the choice of most-preferred alternatives," MPRA Paper 803, University Library of Munich, Germany.
    4. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, September.
    5. Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
    6. Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, vol. 45(4), pages 889-894, May.
    7. Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-194, February.
    8. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
    9. Nikolai S Kukushkin, 2005. "On the existence of maximal elements: An impossibility theorem," Game Theory and Information 0509004, University Library of Munich, Germany.
    10. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    11. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
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    Cited by:

    1. Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
    2. Kukushkin, Nikolai S., 2010. "On the existence of most-preferred alternatives in complete lattices," MPRA Paper 27504, University Library of Munich, Germany.
    3. Kukushkin, Nikolai S., 2017. "Strong Nash equilibrium in games with common and complementary local utilities," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 1-12.
    4. Kukushkin, Nikolai S., 2023. "Maximizing a preference relation on complete chains and lattices," MPRA Paper 119148, University Library of Munich, Germany.
    5. Kukushkin, Nikolai S., 2014. "Strong equilibrium in games with common and complementary local utilities," MPRA Paper 55499, University Library of Munich, Germany.
    6. Gianni Bosi & Magalì E. Zuanon, 2017. "Maximal elements of quasi upper semicontinuous preorders on compact spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 109-117, April.
    7. Nikolai S. Kukushkin, 2016. "Cournot Tatonnement in Aggregative Games with Monotone Best Responses," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 31-45, Springer.
    8. Nikolai S. Kukushkin, 2012. "On the Existence of Optima in Complete Chains and Lattices," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 759-767, September.
    9. Nikolai Kukushkin, 2015. "The single crossing conditions for incomplete preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 225-251, February.
    10. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    11. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.

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