Many-to-many matching with max-min preferences

نویسندگان

  • John William Hatfield
  • Fuhito Kojima
  • Yusuke Narita
چکیده

We consider the many-to-many two-sided matching problem under a stringent domain restriction on preferences called the max-min criterion. We show that, even under this restriction, there is no stable mechanism that is weakly Pareto efficient, strategy-proof, or monotonic (i.e. respects improvements) for agents on one side of the market. These results imply in particular that three of the main results of [4] are incorrect.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Blocking Lemma and Group Strategy-Proofness in Many-to-Many Matchings

This paper considers group strategy-proofness in many-to-many two-sided matching problems. We first show that the Blocking Lemma holds for a many-to-many matching model under quota-saturability condition and max-min preference criterion that is stranger than substitutability of preferences. This result extends the Blocking Lemma for one-to-one matching and for many-to-one matching to many-to-ma...

متن کامل

Solving Hard Stable Matching Problems Involving Groups of Similar Agents

Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify simple structural properties of instances of stable matching problems which will allow the design of efficient algorithms. We focus on the setting in which all agents involved in some matching problem can be partitioned into k different types,...

متن کامل

The Blocking Lemma and strategy-proofness in many-to-many matchings

This paper considers the incentive compatibility in many-to-many two-sided matching problems. We first show that the Blocking Lemma holds for many-to-many matchings under the extended max-min preference criterion and quota-saturability condition. This result extends the Blocking Lemma for one-to-one matching and for many-to-one matching to many-to-many matching problem. It is then shown that th...

متن کامل

Max-Min Greedy Matching

A bipartite graph G(U, V ;E) that admits a perfect matching is given. One player imposes a permutation π over V , the other player imposes a permutation σ over U . In the greedy matching algorithm, vertices of U arrive in order σ and each vertex is matched to the lowest (under π) yet unmatched neighbor in V (or left unmatched, if all its neighbors are already matched). The obtained matching is ...

متن کامل

Matching with preferences over colleagues solves classical matching

In this note, we demonstrate that the problem of “many-to-one matching with (strict) preferences over colleagues” is actually more difficult than the classical many-to-one matching problem, “matching without preferences over colleagues.” We give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 179  شماره 

صفحات  -

تاریخ انتشار 2014