# Rationing problems in bipartite networks

Rationing problems in bipartite networks Rationing Problems in Bipartite Networks HERVE J. MOULIN Rice University and JAY SETHURAMAN Columbia University The standard theory of rationing problems is extended to the bipartite context. The focus is on consistency, a compelling rationality property of fair division methods in the standard setting. Categories and Subject Descriptors: G.2.3 [Mathematics of Computing]: Discrete Mathematics ”Applications General Terms: Algorithms; Economics; Theory Additional Key Words and Phrases: Games, Networks/Graphs, Fair Division, Consistency We start with a brief description of standard rationing problems, followed by an overview of the main results of our paper [Moulin and Sethuraman 2011]. The nal sections report on more general results (work in progress) and some directions for further research. 1. STANDARD RATIONING PROBLEMS Standard rationing problems are the simplest type of fair division problems, where an amount r of some divisible resource (e.g., money) must be divided between the agents i of a given set N , who each have a claim (or demand ) xi on the resources, and the total claim exceeds the available resources: N xi > r. Bankruptcy and the distribution of emergency supplies are typical examples. A rationing method h selects for every N , every vector x of claims, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

# Rationing problems in bipartite networks

, Volume 11 (1) – Jun 1, 2012
9 pages

/lp/association-for-computing-machinery/rationing-problems-in-bipartite-networks-5Eicr7mW07
Publisher
Association for Computing Machinery
ISSN
1551-9031
DOI
10.1145/2325713.2325715
Publisher site
See Article on Publisher Site

### Abstract

Rationing Problems in Bipartite Networks HERVE J. MOULIN Rice University and JAY SETHURAMAN Columbia University The standard theory of rationing problems is extended to the bipartite context. The focus is on consistency, a compelling rationality property of fair division methods in the standard setting. Categories and Subject Descriptors: G.2.3 [Mathematics of Computing]: Discrete Mathematics ”Applications General Terms: Algorithms; Economics; Theory Additional Key Words and Phrases: Games, Networks/Graphs, Fair Division, Consistency We start with a brief description of standard rationing problems, followed by an overview of the main results of our paper [Moulin and Sethuraman 2011]. The nal sections report on more general results (work in progress) and some directions for further research. 1. STANDARD RATIONING PROBLEMS Standard rationing problems are the simplest type of fair division problems, where an amount r of some divisible resource (e.g., money) must be divided between the agents i of a given set N , who each have a claim (or demand ) xi on the resources, and the total claim exceeds the available resources: N xi > r. Bankruptcy and the distribution of emergency supplies are typical examples. A rationing method h selects for every N , every vector x of claims,

### Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Jun 1, 2012