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On the nonemptiness of the α-core of discontinuous games: Transferable and nontransferable utilities

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  • Uyanık, Metin

Abstract

The nonemptiness of the α-core of games with continuous payoff functions was proved by Scarf (1971) for nontransferable utilities and by Zhao (1999) for transferable utilities. In this paper we present generalizations of their results to games with possibly discontinuous payoff functions. Our handling of discontinuity is based on Reny's (1999) better-reply-security concept. We present examples to show that our generalizations are nonvacuous.

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  • Uyanık, Metin, 2015. "On the nonemptiness of the α-core of discontinuous games: Transferable and nontransferable utilities," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 213-231.
    • Handle: RePEc:eee:jetheo:v:158:y:2015:i:pa:p:213-231
    DOI: 10.1016/j.jet.2015.04.005
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    5. Philip J. Reny, 2016. "Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 553-569, March.
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    Cited by:

    1. Giorgos Stamatopoulos, 2020. "On the $$\gamma $$γ-core of asymmetric aggregative games," Theory and Decision, Springer, vol. 88(4), pages 493-504, May.
    2. Youcef Askoura, 2019. "On the core of normal form games with a continuum of players : a correction," Papers 1903.09819, arXiv.org.
    3. Zhe Yang & Haiqun Zhang, 2019. "NTU core, TU core and strong equilibria of coalitional population games with infinitely many pure strategies," Theory and Decision, Springer, vol. 87(2), pages 155-170, September.
    4. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    5. Zhao, Jingang, 2018. "Three little-known and yet still significant contributions of Lloyd Shapley," Games and Economic Behavior, Elsevier, vol. 108(C), pages 592-599.
    6. Yang, Zhe & Yuan, George Xianzhi, 2019. "Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 94-100.
    7. Stamatopoulos, Giorgos, 2018. "On the gamma-core of asymmetric aggregative games," MPRA Paper 88722, University Library of Munich, Germany.
    8. Lan Di & George X. Yuan & Tu Zeng, 2021. "The consensus equilibria of mining gap games related to the stability of Blockchain Ecosystems," The European Journal of Finance, Taylor & Francis Journals, vol. 27(4-5), pages 419-440, March.
    9. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.

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    More about this item

    Keywords

    NTU α-core; TU α-core; Discontinuous games;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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