Two-sided matching. A study in game-theoretic modeling and analysis.

*(English)*Zbl 0726.90003
Econometric Society Monographs, 18. Cambridge etc.: Cambridge University Press. xiii, 263 p. £35.00; $ 54.50 (1990).

This innovative monograph, partly based on earlier work of the authors, deals with the problem of matching considered from the game-theoretic point of view. Thus a matching can be in equilibrium, it may be stable, some problems lead to an (assignment) game which is then studied in detail etc. The book is devoted into four parts which deal, respectively, with the problems of one-to-one matching (marriage problem), one-to-many matching (firms-employees problem), one-to-one matching with money as a continuous variable, open problems, and proposes research directions. Particular questions considered in the monograph include incomplete information, complex preferences as well as concrete algorithms.

Reviewer: A.Wieczorek (Warszawa)

##### MSC:

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91B68 | Matching models |

91A40 | Other game-theoretic models |

05C20 | Directed graphs (digraphs), tournaments |

05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |

90C27 | Combinatorial optimization |

05A05 | Permutations, words, matrices |

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\textit{A. E. Roth} and \textit{M. A. Oliveira Sotomayor}, Two-sided matching. A study in game-theoretic modeling and analysis. Cambridge etc.: Cambridge University Press (1990; Zbl 0726.90003)

##### References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.