This article is cited in 1 paper

Introduction to the theory of choice and stable contracts

V. I. Danilov

Central Economics and Mathematics Institute, Russian Academy of Sciences

Abstract: The paper is devoted to the presentation of the basic concepts and results in the theory of stable contract systems. This theory originated in 1962 and has significantly been developed since then. The main results (existence, polarization, lattice structure) have been obtained in the bipartite situation, when the contracting agents are divided into two groups, and contracts are concluded between agents from opposite groups. Another important limitation is that the agents' preferences are described by so-called Plott choice functions. The first part of the paper is devoted to this concept, which generalizes the concept of partial order. The second part sets out the theory of stable contracts itself.
Bibliography: 34 titles.

Keywords: choice functions, consistency, substitutability, Blair's hyperrelation, convex geometries, pre-topology, cardinal monotonicity, stable marriage, stable roommate matching, distributive lattices, Birkhoff's theorem.

UDC: 519.15

MSC: Primary 05A05; Secondary 06A07, 06A11, 06B30, 06F30, 06Dxx, 91B14, 91B40, 91B68

Received: 13.01.2025

DOI: 10.4213/rm10231

 English version: Russian Mathematical Surveys, 2025, 80:4, 549–590

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