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A short way to the stability

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  • Vladimir Danilov

Abstract

A longer and more correct title is `a short and direct path to the theory of stable contract systems in a bipartite market'. There is no new meaningful results in the article. It is dedicated to the presentation of a short method for obtaining the main body of stability theory: existence, polarization, and latticing. The brevity and uniformity are achieved through the use of the desirability operator (Section 1) and, most importantly, the successful notion of an ample system of contracts (Section 3). The use of the latter radically simplifies the problem of the existence of fixed points. The general bipartite problem (with many agents using Plott choice functions) is reduced easily by the aggregation to the case of two agents (see [2, 5]). Therefore, further, we restrict ourselves to the case of two agents (the Worker and the Firm) and a large set E of contracts between them.

Suggested Citation

  • Vladimir Danilov, 2025. "A short way to the stability," Papers 2511.16104, arXiv.org.
    • Handle: RePEc:arx:papers:2511.16104
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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. A. Alkan & D. Gale, 2003. "Stable Schedule Matching under Revealed Preference," Springer Books, in: Leon A. Petrosyan & David W. K. Yeung (ed.), ICM Millennium Lectures on Games, pages 3-19, Springer.
    4. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    5. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
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