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On the existence of stable contract systems

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  • V. I. Danilov

Abstract

In 1962, Gale and Shapley \cite{GS} introduced the concept of stable marriages and proved their existence. Since then, the statement of the stability problem has been highly generalized. And a lot of proofs has emerged for the existence in these more general statements. It's time to review them and identify the similarities and differences. First, we will briefly discuss the classical case, because the existence proofs in the general case grew out of it. Or rather, from the idea of "deferred acceptance". When the best of the proposed contracts is temporarily retained until a better offer is received.

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  • V. I. Danilov, 2025. "On the existence of stable contract systems," Papers 2505.12721, arXiv.org.
    • Handle: RePEc:arx:papers:2505.12721
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    References listed on IDEAS

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    1. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    2. Yi-You Yang, 2025. "On the existence of stable matchings with contracts," Theory and Decision, Springer, vol. 98(3), pages 367-372, May.
    3. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    4. Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March.
    5. Danilov, V. & Koshevoy, G., 2005. "Mathematics of Plott choice functions," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 245-272, May.
    6. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    7. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    8. Piotr Dworczak, 2021. "Deferred Acceptance with Compensation Chains," Operations Research, INFORMS, vol. 69(2), pages 456-468, March.
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